PyMetaMath.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "PyMetaMath.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNOg/nDSXfto+m3nQhshZYK",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "widgets": {
      "application/vnd.jupyter.widget-state+json": {
        "eb7d1eea496d4594a0e0399686cb6b70": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "94: $p |- ( sqrt ` 2 ) e/ QQ"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": null,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_fa9c610609f04d39b7fff8635a2ab6c8",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_1126521135f249bf80292e0bab4d8170"
            ]
          }
        },
        "fa9c610609f04d39b7fff8635a2ab6c8": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "1126521135f249bf80292e0bab4d8170": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "93: $p |- -. ( sqrt ` 2 ) e. QQ",
              "1": "nelir"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_76666286b6c94707bd6c59ccc55a8c9a",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_1b7bf44235164790b9709beb4b89ab60",
              "IPY_MODEL_fa09acafc2c444979a6ca3ffe56fd4b8"
            ]
          }
        },
        "76666286b6c94707bd6c59ccc55a8c9a": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "1b7bf44235164790b9709beb4b89ab60": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "89: $p |- -. E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y )",
              "1": "92: $p |- ( ( sqrt ` 2 ) e. QQ <-> E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )",
              "2": "mtbir"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_59b464b47fb0439885d825573a0d2e89",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_fb367081d44c4824b54a42aae3a4dc4b",
              "IPY_MODEL_386e060617e14842b1e917a15b13a5d1",
              "IPY_MODEL_6de100041a3345db823b95732aebe6f0"
            ]
          }
        },
        "fa09acafc2c444979a6ca3ffe56fd4b8": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_b392de99d58140358435710bd8c8af94",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "59b464b47fb0439885d825573a0d2e89": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "fb367081d44c4824b54a42aae3a4dc4b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "88: $p |- ( y e. NN -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )",
              "1": "nrex"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_699eccabcee6408186a5a4a49542cc06",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_5cc4e6fe2ba64887b06e6f3bdeb97129",
              "IPY_MODEL_54637d86f40340dcbbe196486dd8be88"
            ]
          }
        },
        "386e060617e14842b1e917a15b13a5d1": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "90: $p |- ( ( sqrt ` 2 ) e. QQ <-> E. x e. ZZ E. y e. NN ( sqrt ` 2 ) = ( x / y ) )",
              "1": "91: $p |- ( E. x e. ZZ E. y e. NN ( sqrt ` 2 ) = ( x / y ) <-> E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )",
              "2": "bitri"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_7c83b3089faa401a853eb6e51b8122b0",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_b0f4d7ab1bf747bc836fdbd20585dfd2",
              "IPY_MODEL_ccfa3adc4ed84986925a196d8b79b650",
              "IPY_MODEL_daf7d20692044184b99706056ef1e64a"
            ]
          }
        },
        "6de100041a3345db823b95732aebe6f0": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_2aa3cf28ccb145eaa8381fbdb85dc302",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "699eccabcee6408186a5a4a49542cc06": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "5cc4e6fe2ba64887b06e6f3bdeb97129": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "78: $p |- ( y e. NN -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )",
              "1": "79: $p |- ( y e. NN -> y < ( y + 1 ) )",
              "2": "87: $p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( y < ( y + 1 ) -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) ) )",
              "3": "mp2d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_62428fc7b7fa41a593867558c4515601",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_496790ed6a5549d5ae82e89123afed68",
              "IPY_MODEL_f4c22954561243c796492ae89dd4ad0b",
              "IPY_MODEL_1ac087c254a74fadafde9a34ccbcdd31",
              "IPY_MODEL_778742cd39a94ae3a52a58bb78d9ed9d"
            ]
          }
        },
        "54637d86f40340dcbbe196486dd8be88": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_975c98f167004057a06624876b9fdb46",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "7c83b3089faa401a853eb6e51b8122b0": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b0f4d7ab1bf747bc836fdbd20585dfd2": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "elq"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_dcdbe53e251e4d0c88f6c3abcf440e92",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_e9312a74f1cc4557a99260eba723f3ba"
            ]
          }
        },
        "ccfa3adc4ed84986925a196d8b79b650": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "rexcom"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_9f3c6e60f76648ea803327cdaeba6161",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_ab0434e642014b349f13f3f61788a863"
            ]
          }
        },
        "daf7d20692044184b99706056ef1e64a": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_7766ab8032764cc0a282324c70391abe",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "62428fc7b7fa41a593867558c4515601": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "496790ed6a5549d5ae82e89123afed68": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "1: $p |- ( y e. NN -> ( y + 1 ) e. NN )",
              "1": "77: $p |- ( ( y + 1 ) e. NN -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )",
              "2": "syl"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_c3ebd29271e2410f8139ca8007d672de",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_8a86836a6a0b4039977fdce87cffecf1",
              "IPY_MODEL_04ff01b5e2ac44bdbd1794c19f6ef573",
              "IPY_MODEL_214ec5b92d1943c78a28ed8d1f9925d2"
            ]
          }
        },
        "f4c22954561243c796492ae89dd4ad0b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "65: $p |- ( y e. NN -> y e. RR )",
              "1": "ltp1d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_b14ac893bf4f4e99b58c52fa194bdda5",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_458db5a5542043c786b820e56887ba20",
              "IPY_MODEL_71aa2af25ce643adab0ea79be9d668fd"
            ]
          }
        },
        "1ac087c254a74fadafde9a34ccbcdd31": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "86: $p |- ( z = y -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( y < ( y + 1 ) -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) ) )",
              "1": "rspcv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_3f420072e6704381814ac3754936870e",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_9cb1955bbaef46a49bbb7c02141ec730",
              "IPY_MODEL_be246052bd184e759289f25724081123"
            ]
          }
        },
        "778742cd39a94ae3a52a58bb78d9ed9d": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_9ecf86e97b4f4d158c7ecf59064b3f3e",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "dcdbe53e251e4d0c88f6c3abcf440e92": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "e9312a74f1cc4557a99260eba723f3ba": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_d847e2604ec74683a4133294697d080d",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "9f3c6e60f76648ea803327cdaeba6161": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ab0434e642014b349f13f3f61788a863": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_e33aa8a69bf3472c8b098b0b9bf19973",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "c3ebd29271e2410f8139ca8007d672de": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "8a86836a6a0b4039977fdce87cffecf1": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "peano2nn"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_8fa99e47b5ed42879f4dc60a3ce5d5a9",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_893a5cf455744c7787aa927189bb5b8e"
            ]
          }
        },
        "04ff01b5e2ac44bdbd1794c19f6ef573": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "4: $p |- ( n = 1 -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "1": "7: $p |- ( n = y -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "2": "10: $p |- ( n = ( y + 1 ) -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "3": "10: $p |- ( n = ( y + 1 ) -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "4": "13: $p |- A. z e. NN ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) )",
              "5": "76: $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "6": "nnind"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ef8138e4822c41118b5dca22fa861c5d",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_2a35aac81dbd4e9c9f6313f4f32d84c2",
              "IPY_MODEL_23e79fe7f6434853aa20b396d27766de",
              "IPY_MODEL_f8bdcb0f32d44bac9b5519b2738375b3",
              "IPY_MODEL_3707d6625a044178bf912f954d52dfe5",
              "IPY_MODEL_1f42a614d60541e894fdacb165de73d3",
              "IPY_MODEL_2a58534ef617403b83823f220702c856",
              "IPY_MODEL_4d0098b7e217406dbdcd6d43526e546f"
            ]
          }
        },
        "214ec5b92d1943c78a28ed8d1f9925d2": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_6d31d2448a9e44f5b2dbb5235eae9e46",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "b14ac893bf4f4e99b58c52fa194bdda5": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "458db5a5542043c786b820e56887ba20": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "nnre"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_6f6107a05c1749b0b6c15f68a8464e4b",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_0df6de36b0d644c5bf625307e46b5a60"
            ]
          }
        },
        "71aa2af25ce643adab0ea79be9d668fd": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_4f51b13a1c544222bb942e4f410216a0",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3f420072e6704381814ac3754936870e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9cb1955bbaef46a49bbb7c02141ec730": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "80: $p |- ( z = y -> ( z < ( y + 1 ) <-> y < ( y + 1 ) ) )",
              "1": "85: $p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) )",
              "2": "imbi12d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_0bdbb7e07bd94f3b8c02a20f1e89b0fb",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_498f397ae99f41618e0f6c8b5027791c",
              "IPY_MODEL_b9c16c33924c4c32a0f2772040e1c12a",
              "IPY_MODEL_5311c1bda5b24b7fbc3c7d402e67b55f"
            ]
          }
        },
        "be246052bd184e759289f25724081123": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_37478058407640f1bb4af980f1c7e0b6",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "8fa99e47b5ed42879f4dc60a3ce5d5a9": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "893a5cf455744c7787aa927189bb5b8e": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_ed0b691edf0e450caa2aa55fc45bfa0e",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ef8138e4822c41118b5dca22fa861c5d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "2a35aac81dbd4e9c9f6313f4f32d84c2": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "3: $p |- ( n = 1 -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "1": "ralbidv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_60aa3b071b3c4318bb524b6a2d0dc709",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_12148052ad7f48d2b44cfb46a66495eb",
              "IPY_MODEL_c0947a83531242d78e89921c51162f0d"
            ]
          }
        },
        "23e79fe7f6434853aa20b396d27766de": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "6: $p |- ( n = y -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "1": "ralbidv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_3e0d8371e3044ab7a05a81a237966aed",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_cb24e596b5734eb89f9543ea2a12f83b",
              "IPY_MODEL_7bdb703f549046459682aa3c2fbfbb86"
            ]
          }
        },
        "f8bdcb0f32d44bac9b5519b2738375b3": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "9: $p |- ( n = ( y + 1 ) -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "1": "ralbidv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_fddda069a6574829a0cda893bae591ed",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_00d3207e02f54b85b2189622dfa4fd3e",
              "IPY_MODEL_0fa79a33b245499b991c40fdb7192f6c"
            ]
          }
        },
        "3707d6625a044178bf912f954d52dfe5": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "9: $p |- ( n = ( y + 1 ) -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "1": "ralbidv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_3cb1b1db0432441f9dc7d3cc878ad6f4",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_4e14f15cca054bb18aeb8ce9b59dd4b9",
              "IPY_MODEL_cc66c359e7014f71ac2d1ce2bb4ac582"
            ]
          }
        },
        "1f42a614d60541e894fdacb165de73d3": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "12: $p |- ( z e. NN -> ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )",
              "1": "rgen"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_b5305f40e94e4674be69ca6f18612bc9",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_89a0cb6d4eb14048aeba5a56894f8c60",
              "IPY_MODEL_18dceb1223c0468994194b23fa499166"
            ]
          }
        },
        "2a58534ef617403b83823f220702c856": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "62: $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )",
              "1": "75: $p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )",
              "2": "sylibrd"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_3badfed6e4dd4d6f9698b905a77a45b8",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_32aedc1570384c0f859391bffa56614d",
              "IPY_MODEL_940887318126479e90bd7c60eaafa95f",
              "IPY_MODEL_6228d8d603274f6bb9c80f7f94e191bf"
            ]
          }
        },
        "4d0098b7e217406dbdcd6d43526e546f": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_57fe6e4df4044a7b9848cac70b15eaa2",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "6f6107a05c1749b0b6c15f68a8464e4b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "0df6de36b0d644c5bf625307e46b5a60": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_c190fd1b64df44069110a61728862628",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "0bdbb7e07bd94f3b8c02a20f1e89b0fb": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "498f397ae99f41618e0f6c8b5027791c": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "breq1"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ad066f3374794cd4a571b4239182afc3",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_f7822e491531488c972fcee5ad82605a"
            ]
          }
        },
        "b9c16c33924c4c32a0f2772040e1c12a": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "83: $p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ -. ( sqrt ` 2 ) = ( x / y ) ) )",
              "1": "84: $p |- ( A. x e. ZZ -. ( sqrt ` 2 ) = ( x / y ) <-> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )",
              "2": "syl6bb"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_c9a8b151afa54c7ca67388d4a9838ed4",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_ac312c9a5009443e872f306cd2da9855",
              "IPY_MODEL_18c2e27f48874b128ab5162e67ea08af",
              "IPY_MODEL_b4885793b05d4668aa5d6a715f34a6de"
            ]
          }
        },
        "5311c1bda5b24b7fbc3c7d402e67b55f": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_06e98b14eb174d2fb1184f86dad2b0d3",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "60aa3b071b3c4318bb524b6a2d0dc709": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "12148052ad7f48d2b44cfb46a66495eb": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "2: $p |- ( n = 1 -> ( z < n <-> z < 1 ) )",
              "1": "imbi1d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_e2b3eebbbe57486e8e22a7d4b310f318",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_216b46e436c14b34bb79c1db0e596c17",
              "IPY_MODEL_7114627467204ce0927aec5304808e49"
            ]
          }
        },
        "c0947a83531242d78e89921c51162f0d": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_2e48bb1862da47489261fb0bbd5a6ffd",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3e0d8371e3044ab7a05a81a237966aed": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "cb24e596b5734eb89f9543ea2a12f83b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "5: $p |- ( n = y -> ( z < n <-> z < y ) )",
              "1": "imbi1d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_5d9ef2260366448eb524d917ca4d1e9a",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_999e5f1668854e00ba6a75cf40660497",
              "IPY_MODEL_2288082df357495d8fdada7992a98aa6"
            ]
          }
        },
        "7bdb703f549046459682aa3c2fbfbb86": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_cfd85dc1ea2e4d11affd4bc7fae7f69d",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "fddda069a6574829a0cda893bae591ed": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "00d3207e02f54b85b2189622dfa4fd3e": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "8: $p |- ( n = ( y + 1 ) -> ( z < n <-> z < ( y + 1 ) ) )",
              "1": "imbi1d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_e8ceff3b76bc477b917d2c923923fded",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_14f75d27f0564f86b2ebbd3653bb733d",
              "IPY_MODEL_8e088c5bc9da4f73959082b01245234d"
            ]
          }
        },
        "0fa79a33b245499b991c40fdb7192f6c": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_d380d6abfb6e4136b4fd977219ba4199",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3cb1b1db0432441f9dc7d3cc878ad6f4": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "4e14f15cca054bb18aeb8ce9b59dd4b9": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "8: $p |- ( n = ( y + 1 ) -> ( z < n <-> z < ( y + 1 ) ) )",
              "1": "imbi1d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_316a79fb29b7438aa5af0902d8e9b9ff",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_1967dd6621914c6c8d51f6918b531aa4",
              "IPY_MODEL_fd21b4ebd3fc43c591544230d53cfb67"
            ]
          }
        },
        "cc66c359e7014f71ac2d1ce2bb4ac582": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_7d1c752a93084411961b787c7389932a",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "b5305f40e94e4674be69ca6f18612bc9": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "89a0cb6d4eb14048aeba5a56894f8c60": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "11: $p |- ( z e. NN -> -. z < 1 )",
              "1": "pm2.21d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_c3bb812e368a4aca9ffcac08e02671a6",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_4ad26d9f83a94e61b07542473e7c9ccd",
              "IPY_MODEL_9a176de9f8bb4ae6980ec4da1c9b9628"
            ]
          }
        },
        "18dceb1223c0468994194b23fa499166": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_fdbd5dcad1ba4e5b8e5fa762ec6c9107",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3badfed6e4dd4d6f9698b905a77a45b8": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "32aedc1570384c0f859391bffa56614d": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "61: $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "1": "ancld"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_7310ed5c1799406aa1c794bcf165cf93",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_0c3a2b220e5649d4aa29d7223c375a40",
              "IPY_MODEL_1619090a74e641d5afcf5e799c81fa82"
            ]
          }
        },
        "940887318126479e90bd7c60eaafa95f": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "73: $p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )",
              "1": "74: $p |- ( A. z e. NN ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) <-> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "2": "syl6bb"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_33b11c456f5649739c326ad88b19d923",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_cdda06cccfc140e8a1d0c0c05cdd7f52",
              "IPY_MODEL_699688103d074e9d903021d5676f262f",
              "IPY_MODEL_046bc185913340a49fca128705c48445"
            ]
          }
        },
        "6228d8d603274f6bb9c80f7f94e191bf": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_3fe1b6f2278941b1805de7ee4a1d8c44",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ad066f3374794cd4a571b4239182afc3": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "f7822e491531488c972fcee5ad82605a": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_0dff734e4b224018acea5e47b66d6e79",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "c9a8b151afa54c7ca67388d4a9838ed4": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ac312c9a5009443e872f306cd2da9855": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "82: $p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> -. ( sqrt ` 2 ) = ( x / y ) ) )",
              "1": "ralbidv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_698f40278b174e3ba939ccaf030fc88f",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_f5a9d2db9549464eaac3b97e8b163421",
              "IPY_MODEL_dc2818efbafa4ed092abd5b4b561dd6b"
            ]
          }
        },
        "18c2e27f48874b128ab5162e67ea08af": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "ralnex"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_bfe53e5ec5cd47f5a6a0b5cf4e1e9e02",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_f64c27c9f6ac4ef3a00fa996c83b8ddb"
            ]
          }
        },
        "b4885793b05d4668aa5d6a715f34a6de": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_3069db68eff04468ab5661e2170ada40",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "e2b3eebbbe57486e8e22a7d4b310f318": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "216b46e436c14b34bb79c1db0e596c17": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "breq2"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_e8cbf1ea18eb49a39da6e004d8b6c4e5",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_cf29a6e4b6354c46876dfad635408c22"
            ]
          }
        },
        "7114627467204ce0927aec5304808e49": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_0b03c4e324e64f48bfe070de3977dd39",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "5d9ef2260366448eb524d917ca4d1e9a": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "999e5f1668854e00ba6a75cf40660497": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "breq2"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_b7495b0bd59c483eb14acbcd48a98f84",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_4fa4bd517bdc49548ec94a482e86bfe3"
            ]
          }
        },
        "2288082df357495d8fdada7992a98aa6": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_0531b4d51690404988fea9a5f1d9b27c",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "e8ceff3b76bc477b917d2c923923fded": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "14f75d27f0564f86b2ebbd3653bb733d": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "breq2"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_5fe946c796f6479f8d7aee0ced89735f",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_9a83db1f1e834bae81a39d02babbcf7e"
            ]
          }
        },
        "8e088c5bc9da4f73959082b01245234d": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_9bf61733584045e4bffa8d07eed0033c",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "316a79fb29b7438aa5af0902d8e9b9ff": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "1967dd6621914c6c8d51f6918b531aa4": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "breq2"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_58c838132b8a45b78bd44efa1ee7d811",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_805b6810abae4eddb2fa5a87c481e7dd"
            ]
          }
        },
        "fd21b4ebd3fc43c591544230d53cfb67": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_50253b3cefdd47d59430f3255e00d1fa",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "c3bb812e368a4aca9ffcac08e02671a6": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "4ad26d9f83a94e61b07542473e7c9ccd": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "nnnlt1"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_7b9c9056330f46509c4b8019f58b8c5c",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_dbc1c305df92419d865d1f6cef4b4c37"
            ]
          }
        },
        "9a176de9f8bb4ae6980ec4da1c9b9628": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_0e9415e854c6477b9701617652ba3258",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "7310ed5c1799406aa1c794bcf165cf93": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "0c3a2b220e5649d4aa29d7223c375a40": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "56: $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )",
              "1": "60: $p |- ( y e. NN -> ( A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )",
              "2": "sylibrd"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_6593b51845e24a6ca058f069e42aeb24",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_909c86dfb15341b8adfcf507425a97c2",
              "IPY_MODEL_f47204c3cfce45179af31367364431cf",
              "IPY_MODEL_e1ee20ddac734dd0bfb69cb2189ce883"
            ]
          }
        },
        "1619090a74e641d5afcf5e799c81fa82": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_d014ce05f3934497bf616a8c20b2391f",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "33b11c456f5649739c326ad88b19d923": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "cdda06cccfc140e8a1d0c0c05cdd7f52": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "72: $p |- ( ( y e. NN /\\ z e. NN ) -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )",
              "1": "ralbidva"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ad97bfb30bfc481bb61320a0d3048586",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_da6fb3ea7eed4f24ae64b4e9e217ebf0",
              "IPY_MODEL_dd3dc1f96f16430b8fa9ea0418d8bcc3"
            ]
          }
        },
        "699688103d074e9d903021d5676f262f": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "r19.26"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_8df4dd25b78a4b5da2a2b35e3a168fbb",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_a3556fba60fe491a81d73607aebbedbb"
            ]
          }
        },
        "046bc185913340a49fca128705c48445": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_a7fadebfc46b43778df526aaf1b03610",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "698f40278b174e3ba939ccaf030fc88f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "f5a9d2db9549464eaac3b97e8b163421": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "58: $p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / y ) ) )",
              "1": "81: $a |- ( ( sqrt ` 2 ) =/= ( x / y ) <-> -. ( sqrt ` 2 ) = ( x / y ) )",
              "2": "syl6bb"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_623c0af26f40499c8267d5d1cbd15cbe",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_ce60a20e3847481cb6a7c8ab208a0964",
              "IPY_MODEL_0a6452d283264d6e8e44e97a1477daa2",
              "IPY_MODEL_1648370d4ab743ce9bc42dc334f5b7c9"
            ]
          }
        },
        "dc2818efbafa4ed092abd5b4b561dd6b": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_c86cfeaed61f40d49f0970432a3ac6ed",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "bfe53e5ec5cd47f5a6a0b5cf4e1e9e02": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "f64c27c9f6ac4ef3a00fa996c83b8ddb": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_1aea7b4d2d33419bb4669e2b0b523a1c",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "e8cbf1ea18eb49a39da6e004d8b6c4e5": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "cf29a6e4b6354c46876dfad635408c22": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_033e3f8dfc1c4c40a85db561e6f25a3f",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "b7495b0bd59c483eb14acbcd48a98f84": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "4fa4bd517bdc49548ec94a482e86bfe3": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_c2d9e046a56144e682685d78ca94cb31",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "5fe946c796f6479f8d7aee0ced89735f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9a83db1f1e834bae81a39d02babbcf7e": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_424543c9ab844d7f8ce238bca1606dc2",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "58c838132b8a45b78bd44efa1ee7d811": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "805b6810abae4eddb2fa5a87c481e7dd": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_80fa7df8d9704cd492bf9e0fdbe6b556",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "7b9c9056330f46509c4b8019f58b8c5c": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "dbc1c305df92419d865d1f6cef4b4c37": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_fa2eb0ca79bd46d68ea07bb7f71e690f",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "6593b51845e24a6ca058f069e42aeb24": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "909c86dfb15341b8adfcf507425a97c2": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "52: $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) ) )",
              "1": "55: $p |- ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) <-> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) )",
              "2": "syl6ibr"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_2ea4369368b14272a6f331f07655e04e",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_fb6272247d5b44ee8064806dbd73ca86",
              "IPY_MODEL_851046fdf6114a67b113ebde0a2e287b",
              "IPY_MODEL_5e19d23e2cb5431aa46da97749b93ef0"
            ]
          }
        },
        "f47204c3cfce45179af31367364431cf": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "59: $p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )",
              "1": "ceqsralv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_c69a028e6ac541c4940ef26bb2ad5668",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_485e32bbb12f44b793e0c8c6b19a6757",
              "IPY_MODEL_c695e0e4c25644a0bf10a935d8a0e155"
            ]
          }
        },
        "e1ee20ddac734dd0bfb69cb2189ce883": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_92e861209e1f4a468315f972b312dcd2",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ad97bfb30bfc481bb61320a0d3048586": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "da6fb3ea7eed4f24ae64b4e9e217ebf0": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "70: $p |- ( ( y e. NN /\\ z e. NN ) -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y \\/ z = y ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "1": "71: $p |- ( ( ( z < y \\/ z = y ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )",
              "2": "syl6bb"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_3d5be39f5cee48358d0daa79f531fb28",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_cbbb58ba5a384b8f9571a0904e2004c7",
              "IPY_MODEL_289a8eb2e761498ab36c7314078fe6c4",
              "IPY_MODEL_725a7e12e50b4d29b968668d7a29436a"
            ]
          }
        },
        "dd3dc1f96f16430b8fa9ea0418d8bcc3": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_79a73dfe3d9848e4b07eddcf60e7368f",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "8df4dd25b78a4b5da2a2b35e3a168fbb": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "a3556fba60fe491a81d73607aebbedbb": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_b0f1ab7267394171bf88590d897e0673",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "623c0af26f40499c8267d5d1cbd15cbe": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ce60a20e3847481cb6a7c8ab208a0964": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "57: $p |- ( z = y -> ( x / z ) = ( x / y ) )",
              "1": "neeq2d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_5eb769a46111407493a268b2438e8dff",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_ac53775b2a2c42e98c6b16dc30c302f9",
              "IPY_MODEL_6413673951bd45088ae0a4faf931e3e4"
            ]
          }
        },
        "0a6452d283264d6e8e44e97a1477daa2": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "df-ne"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_def35a7829b742a886f19596220273d6",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_9f6c663753264868acdc928d219eab1f"
            ]
          }
        },
        "1648370d4ab743ce9bc42dc334f5b7c9": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_11bbc54884c544bba813bb3663401d23",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "2ea4369368b14272a6f331f07655e04e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "fb6272247d5b44ee8064806dbd73ca86": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "24: $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )",
              "1": "51: $p |- ( y e. NN -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) ) )",
              "2": "syld"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_50675553fc7643da8390f546d1b90f6b",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_af76efc8e675406ea67be8cbe9d7769b",
              "IPY_MODEL_7eb2d2c1a9684f6b9c327141a67b84fd",
              "IPY_MODEL_26e8bb1ddd3e4ad2b88e2baf6ddcf45b"
            ]
          }
        },
        "851046fdf6114a67b113ebde0a2e287b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "54: $p |- ( x = z -> ( ( sqrt ` 2 ) =/= ( x / y ) <-> ( sqrt ` 2 ) =/= ( z / y ) ) )",
              "1": "cbvralv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_9f368524c7044529b09e418901b98246",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_7a8a655344b1461585a77d120850c9aa",
              "IPY_MODEL_7e9d769f80e84e578abbff75f7d88f52"
            ]
          }
        },
        "5e19d23e2cb5431aa46da97749b93ef0": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_23e869b31ea0485ca76a08aa1bcbc527",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "c69a028e6ac541c4940ef26bb2ad5668": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "485e32bbb12f44b793e0c8c6b19a6757": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "58: $p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / y ) ) )",
              "1": "ralbidv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_cf0d823004854d9890c55b64d23b70b1",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_2cb7cd402bf140f3a1608a991dc4fb90",
              "IPY_MODEL_5ec55cbbb0fe46dd8bacdb93b687b929"
            ]
          }
        },
        "c695e0e4c25644a0bf10a935d8a0e155": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_7b87c844691945aeac88c5e61807b51e",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3d5be39f5cee48358d0daa79f531fb28": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "cbbb58ba5a384b8f9571a0904e2004c7": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "69: $p |- ( ( y e. NN /\\ z e. NN ) -> ( z < ( y + 1 ) <-> ( z < y \\/ z = y ) ) )",
              "1": "imbi1d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_04362f6a05374ae9b67c3afec9b29ab9",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_e835096a202945f6992515115fc9fae9",
              "IPY_MODEL_7feb79450299421ba7d77b27a7c5771a"
            ]
          }
        },
        "289a8eb2e761498ab36c7314078fe6c4": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "jaob"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_7993a1d452a44ab7b278c18d4a74b144",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_9c81493b38fa4ec68663b493ed27e87e"
            ]
          }
        },
        "725a7e12e50b4d29b968668d7a29436a": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_2b752e11dd6a41c395a4378e3a2faa2e",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "5eb769a46111407493a268b2438e8dff": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ac53775b2a2c42e98c6b16dc30c302f9": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "oveq2"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_1b5c00a8310446789a84c3492c0d16b1",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_c4df935143af4eacad07cdf7b29003d5"
            ]
          }
        },
        "6413673951bd45088ae0a4faf931e3e4": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_0fae406b95c3410a90187476cd38fa73",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "def35a7829b742a886f19596220273d6": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9f6c663753264868acdc928d219eab1f": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_88866bd04954449b89e8104bce421b2d",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "50675553fc7643da8390f546d1b90f6b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "af76efc8e675406ea67be8cbe9d7769b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "16: $p |- ( y e. NN -> ( y / 2 ) < y )",
              "1": "23: $p |- ( ( y / 2 ) < y -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )",
              "2": "syl"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_bb9c567a3fca4a938e42ecd979f07618",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_12423bc67d7a485c9d6a325758caa686",
              "IPY_MODEL_829dada504484021909ef0fa759adeef",
              "IPY_MODEL_2c8bc4f4491b4ba68ac9bb5f23cbacaa"
            ]
          }
        },
        "7eb2d2c1a9684f6b9c327141a67b84fd": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "50: $p |- ( ( y e. NN /\\ z e. ZZ ) -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> ( sqrt ` 2 ) =/= ( z / y ) ) )",
              "1": "ralrimdva"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_c96721d34a1a4c34b9609c454e83f08d",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_3724812f9d8f4527b7acc222da8109fa",
              "IPY_MODEL_ac41ebd0d0c64fa58d1ded3398b542ce"
            ]
          }
        },
        "26e8bb1ddd3e4ad2b88e2baf6ddcf45b": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_583cb59bae8a4b788b87c27e48b59d29",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "9f368524c7044529b09e418901b98246": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7a8a655344b1461585a77d120850c9aa": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "53: $p |- ( x = z -> ( x / y ) = ( z / y ) )",
              "1": "neeq2d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_3a9ab159702549049194b623ef5c3f0f",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_5ce4861da8b14887af6d554b39f2a0ab",
              "IPY_MODEL_2230bc961cd2415aa767d707927ba40c"
            ]
          }
        },
        "7e9d769f80e84e578abbff75f7d88f52": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_d2a21ef301c24193966885243eace121",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "cf0d823004854d9890c55b64d23b70b1": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "2cb7cd402bf140f3a1608a991dc4fb90": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "57: $p |- ( z = y -> ( x / z ) = ( x / y ) )",
              "1": "neeq2d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_c693c94ae1124d9c91331762c6a5b5c1",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_7d26947b51c74ac8b75444ebe8ee0cd7",
              "IPY_MODEL_48fbbb94c67b418f90752151a6de6730"
            ]
          }
        },
        "5ec55cbbb0fe46dd8bacdb93b687b929": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_78c609f3c1e54ba6bebba6b645cdbd51",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "04362f6a05374ae9b67c3afec9b29ab9": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "e835096a202945f6992515115fc9fae9": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "68: $p |- ( ( z e. NN /\\ y e. NN ) -> ( z < ( y + 1 ) <-> ( z < y \\/ z = y ) ) )",
              "1": "ancoms"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_5f684ff8e51940be939a7c0ace4d70fb",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_37342a7a9ae34e558687b55f9bad76a7",
              "IPY_MODEL_ec21b4a4122a4a3a8ee68b74305b7a5e"
            ]
          }
        },
        "7feb79450299421ba7d77b27a7c5771a": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_15a3ece0cd3c49189f1c246f50fa226b",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "7993a1d452a44ab7b278c18d4a74b144": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9c81493b38fa4ec68663b493ed27e87e": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_b6b16d28c6814dcdaf30d3dbda458405",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "1b5c00a8310446789a84c3492c0d16b1": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "c4df935143af4eacad07cdf7b29003d5": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_ec4fddaaafba41879ef7a6bcb380cd79",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "bb9c567a3fca4a938e42ecd979f07618": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "12423bc67d7a485c9d6a325758caa686": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "14: $p |- ( y e. NN -> y e. RR+ )",
              "1": "15: $p |- ( y e. RR+ -> ( y / 2 ) < y )",
              "2": "syl"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_b13a2471adf542b9925886a79fb6d78b",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_e14b0d2420564c0daba93663d2ce8f33",
              "IPY_MODEL_8788ce32b59c47aca82a921038c5a051",
              "IPY_MODEL_1842b0297e8a4e8d870daccde9f1475b"
            ]
          }
        },
        "829dada504484021909ef0fa759adeef": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "22: $p |- ( ( y / 2 ) e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )",
              "1": "com13"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_5b13dc62998e4a5a829991ff6744d9fc",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_09daf6cb91994570ab2430b26bef0c5a",
              "IPY_MODEL_ab8903570fbd44d097ee94d6b73da377"
            ]
          }
        },
        "2c8bc4f4491b4ba68ac9bb5f23cbacaa": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_ab60a9b840c640088eaa529a5fd4d1e1",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "c96721d34a1a4c34b9609c454e83f08d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "3724812f9d8f4527b7acc222da8109fa": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "49: $p |- ( ( y e. NN /\\ z e. ZZ ) -> ( ( sqrt ` 2 ) = ( z / y ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )",
              "1": "necon2ad"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_f106aef5c116477fbf865cd6c529588f",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_2cc0e1fabd83426cb95b238b93f2bc86",
              "IPY_MODEL_76b0ac20fee642c3a4ec6c585dc4fbc9"
            ]
          }
        },
        "ac41ebd0d0c64fa58d1ded3398b542ce": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_403179bf179c423da000ba720dfb607a",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3a9ab159702549049194b623ef5c3f0f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "5ce4861da8b14887af6d554b39f2a0ab": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "oveq1"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_c2784e1350e543e3b000a02bb03e7b7d",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_35ce6f9665f14b4b8b0f3ee3ff8a45e4"
            ]
          }
        },
        "2230bc961cd2415aa767d707927ba40c": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_d44954be68dc4af98176897a5c089a79",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "c693c94ae1124d9c91331762c6a5b5c1": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7d26947b51c74ac8b75444ebe8ee0cd7": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "oveq2"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_eb22cc46da4a4dd4826437cd6d129f6d",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_eb2a7e2b91a44993a7251de45f50c54a"
            ]
          }
        },
        "48fbbb94c67b418f90752151a6de6730": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_b2ddbf571033407c953e974a4ef3e2ca",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "5f684ff8e51940be939a7c0ace4d70fb": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "37342a7a9ae34e558687b55f9bad76a7": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "63: $p |- ( ( z e. NN /\\ y e. NN ) -> ( z <_ y <-> z < ( y + 1 ) ) )",
              "1": "67: $p |- ( ( z e. NN /\\ y e. NN ) -> ( z <_ y <-> ( z < y \\/ z = y ) ) )",
              "2": "bitr3d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_27e2cbc348d14465bf3702afa92bbd03",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_b9b10ea09d0d4459adecb477a4692b04",
              "IPY_MODEL_c920219b0d8b482c8c2a7082cf612587",
              "IPY_MODEL_83c88731597c4d24b282ac3588bafc4f"
            ]
          }
        },
        "ec21b4a4122a4a3a8ee68b74305b7a5e": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_68954f14f6f7460289d8077ee20b29c0",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "b13a2471adf542b9925886a79fb6d78b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "e14b0d2420564c0daba93663d2ce8f33": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "nnrp"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ac67b954b0134c44829530575d69bf13",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_011c156cc1a34eaeb07b6c1df06ec42f"
            ]
          }
        },
        "8788ce32b59c47aca82a921038c5a051": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "rphalflt"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_1aac9a0e930142f0a6bbf2ccbecb767d",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_c72d70cb56da468087560322d62443a6"
            ]
          }
        },
        "1842b0297e8a4e8d870daccde9f1475b": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_6ebfd58bfd6642a6a10ec9c4ac5ee5eb",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "5b13dc62998e4a5a829991ff6744d9fc": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "09daf6cb91994570ab2430b26bef0c5a": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "21: $p |- ( z = ( y / 2 ) -> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( y / 2 ) < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )",
              "1": "rspcv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_fb21275d5f954de18a6f09040e93715f",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_1fba51aa73934c9b86540ffa22cd005c",
              "IPY_MODEL_334d6db0e70e448da350fab34609b0f0"
            ]
          }
        },
        "ab8903570fbd44d097ee94d6b73da377": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_7947d99d5eb74148bbe8974f2cc9911d",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "f106aef5c116477fbf865cd6c529588f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "2cc0e1fabd83426cb95b238b93f2bc86": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "48: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )",
              "1": "ex"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_2da34768afe94d15991106b095b29eb0",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_9e4b19dfd58b457db13b25d0a4e3f600",
              "IPY_MODEL_6616b185dc4c420a897371ad25456764"
            ]
          }
        },
        "76b0ac20fee642c3a4ec6c585dc4fbc9": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_d5c6b8755a044afc8bcd9f9d95dba8a0",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "c2784e1350e543e3b000a02bb03e7b7d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "35ce6f9665f14b4b8b0f3ee3ff8a45e4": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_be1d4ba9b41e403b82535e4e54c4866d",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "eb22cc46da4a4dd4826437cd6d129f6d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "eb2a7e2b91a44993a7251de45f50c54a": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_999f839e8b9c41bea74067b380fb5737",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "27e2cbc348d14465bf3702afa92bbd03": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b9b10ea09d0d4459adecb477a4692b04": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "nnleltp1"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_c781adb4509441fa94c0d0357f6f80de",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_dbd2633955b249939e615ea51b33f601"
            ]
          }
        },
        "c920219b0d8b482c8c2a7082cf612587": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "64: $p |- ( z e. NN -> z e. RR )",
              "1": "65: $p |- ( y e. NN -> y e. RR )",
              "2": "66: $p |- ( ( z e. RR /\\ y e. RR ) -> ( z <_ y <-> ( z < y \\/ z = y ) ) )",
              "3": "syl2an"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_a82a476444e9489d846e4ae234d30458",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_88dd612dfebb4c67b2ae6a1dc0b44785",
              "IPY_MODEL_64bb76d6195b463ba4b80b5ce05742c1",
              "IPY_MODEL_1b79c9e7549543c39571b19e86d02fd3",
              "IPY_MODEL_1c8590cb32f04615a3f697d9189e4c8d"
            ]
          }
        },
        "83c88731597c4d24b282ac3588bafc4f": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_7664d62652694f76a09038f2bd57679f",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ac67b954b0134c44829530575d69bf13": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "011c156cc1a34eaeb07b6c1df06ec42f": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_c5496e372e1547608f6c2ae92eb9d14a",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "1aac9a0e930142f0a6bbf2ccbecb767d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "c72d70cb56da468087560322d62443a6": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_b5a06d90d6c942639f8e03d4d925960d",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "fb21275d5f954de18a6f09040e93715f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "1fba51aa73934c9b86540ffa22cd005c": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "17: $p |- ( z = ( y / 2 ) -> ( z < y <-> ( y / 2 ) < y ) )",
              "1": "20: $p |- ( z = ( y / 2 ) -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )",
              "2": "imbi12d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_fefc8c3317f340e4ab4f286878f81eec",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_cc4a6e3c40f34e3295ad89c9f086ed7c",
              "IPY_MODEL_97a55f5beda94c3aa0946a233d847d01",
              "IPY_MODEL_39fb64fdf8af4a47a0c2e6067a38889b"
            ]
          }
        },
        "334d6db0e70e448da350fab34609b0f0": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_ee6b540900c3434fb608f2b24479190c",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "2da34768afe94d15991106b095b29eb0": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9e4b19dfd58b457db13b25d0a4e3f600": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "36: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( ( z / 2 ) / ( y / 2 ) ) )",
              "1": "47: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( sqrt ` 2 ) = ( ( z / 2 ) / ( y / 2 ) ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )",
              "2": "mpd"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_a44c389b0eea4da49caf597621f53706",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_31994644c59c46eabe7b22ca3921d9ac",
              "IPY_MODEL_822ef94976e8433796c3656d2e6ff332",
              "IPY_MODEL_ee41d05000ec4cd297de3d180c6c9925"
            ]
          }
        },
        "6616b185dc4c420a897371ad25456764": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_30004fb0232b44588dd2dbaf6a1cf0d4",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "c781adb4509441fa94c0d0357f6f80de": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "dbd2633955b249939e615ea51b33f601": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_9a973f5c2abb481a9aff8ceea7763697",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "a82a476444e9489d846e4ae234d30458": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "88dd612dfebb4c67b2ae6a1dc0b44785": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "nnre"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_9c1d7fe68a7a45b1b2868bcc23eb106d",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_ca1395ca24c04970ae1dc0b8ba81d5be"
            ]
          }
        },
        "64bb76d6195b463ba4b80b5ce05742c1": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "nnre"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ee9e8f97164b444bb14bc5e2a480e879",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_f133043b6de147df8365eafb945b422b"
            ]
          }
        },
        "1b79c9e7549543c39571b19e86d02fd3": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "leloe"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_16e0510bf0ed4078a704d1791bc335fb",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_bd81db6b1736424997856caf5622fad2"
            ]
          }
        },
        "1c8590cb32f04615a3f697d9189e4c8d": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_cd2d3daa97aa4df79ecfb605ad94f0a9",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "fefc8c3317f340e4ab4f286878f81eec": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "cc4a6e3c40f34e3295ad89c9f086ed7c": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "breq1"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_61e7d9381452473fbccb9b6710dfcec5",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_31f03884d784402f9c30bf98539c6556"
            ]
          }
        },
        "97a55f5beda94c3aa0946a233d847d01": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "19: $p |- ( z = ( y / 2 ) -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )",
              "1": "ralbidv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_3b9e993d0c1b40d0938a67da525eb0a6",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_36156f0669f6428ca7452aa9bec86df0",
              "IPY_MODEL_eb6a5674bf0c471597447cd3e5365ec6"
            ]
          }
        },
        "39fb64fdf8af4a47a0c2e6067a38889b": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_ad63940e41d545ef86e64e5745f1a260",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "a44c389b0eea4da49caf597621f53706": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "31994644c59c46eabe7b22ca3921d9ac": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "25: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( z / y ) )",
              "1": "35: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) / ( y / 2 ) ) = ( z / y ) )",
              "2": "eqtr4d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_4180859288044f61b39bc87d757475c7",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_3d447bd161f14fd0b522b18e806b345f",
              "IPY_MODEL_3f2eef516868442680bd942057dbff73",
              "IPY_MODEL_5a14f936aece4e1abd343709c7e6fed6"
            ]
          }
        },
        "822ef94976e8433796c3656d2e6ff332": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "46: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )",
              "1": "necon2bd"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_d268b391d5bb4c5ea78b871970f36d77",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_595cf14c613d48f1aff9cf0b9540140a",
              "IPY_MODEL_3af490d18c7049dd8c8c95cd74ca0c23"
            ]
          }
        },
        "ee41d05000ec4cd297de3d180c6c9925": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_a1f9b6b9bc274d088dd90032cc4ec7e2",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "9c1d7fe68a7a45b1b2868bcc23eb106d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ca1395ca24c04970ae1dc0b8ba81d5be": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_c7d5e80ed0c6410e836626b962084640",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ee9e8f97164b444bb14bc5e2a480e879": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "f133043b6de147df8365eafb945b422b": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_6385fe3f1fca436e88b17fe38b147758",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "16e0510bf0ed4078a704d1791bc335fb": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "bd81db6b1736424997856caf5622fad2": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_78c98f35800c4e188be2b29a137189a0",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "61e7d9381452473fbccb9b6710dfcec5": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "31f03884d784402f9c30bf98539c6556": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_1271f0de0e364049a50ec5d2c2d5fd45",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3b9e993d0c1b40d0938a67da525eb0a6": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "36156f0669f6428ca7452aa9bec86df0": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "18: $p |- ( z = ( y / 2 ) -> ( x / z ) = ( x / ( y / 2 ) ) )",
              "1": "neeq2d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ebc36affc27b47d3b15834bc25ad4aa5",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_38eac5688ec34f9ea35707bcdb2e3d6d",
              "IPY_MODEL_54c66c59aaf4463bb4e969ef4f2613b2"
            ]
          }
        },
        "eb6a5674bf0c471597447cd3e5365ec6": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_31c4af548119456e9cc6c2568139d703",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "4180859288044f61b39bc87d757475c7": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "3d447bd161f14fd0b522b18e806b345f": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "simpr"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_fcde836d90844d47a553e4541ea2846c",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_f825abd68df946cc9e8f1c90e2821e49"
            ]
          }
        },
        "3f2eef516868442680bd942057dbff73": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "27: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> z e. CC )",
              "1": "29: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y e. CC )",
              "2": "30: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> 2 e. CC )",
              "3": "32: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y =/= 0 )",
              "4": "34: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> 2 =/= 0 )",
              "5": "divcan7d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_bd6fc778119d49efb269c35071e5ba08",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_324461a06b2342b982156061eb8b7250",
              "IPY_MODEL_4821f4b955074e8ca1ad80cd6ff2a9fd",
              "IPY_MODEL_10bbe43fe4734bba97ec77240da399ae",
              "IPY_MODEL_8b3fd42ff7b041c29211a30845fcea1d",
              "IPY_MODEL_c3853d17ad564a01811d7cb947e7f76b",
              "IPY_MODEL_6671d84187b64427a5b91e0e81c8085a"
            ]
          }
        },
        "5a14f936aece4e1abd343709c7e6fed6": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_69446a27ea674474ad541270efd38a1f",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "d268b391d5bb4c5ea78b871970f36d77": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "595cf14c613d48f1aff9cf0b9540140a": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "40: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( y / 2 ) e. NN )",
              "1": "45: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )",
              "2": "embantd"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_2a529124a41b4455a5e651f2b4ec110b",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_9afc7939120a4e84a149697edb3275df",
              "IPY_MODEL_75c70d044f824925aa582469f1091533",
              "IPY_MODEL_3bfa8ed979374a948e39108f69464876"
            ]
          }
        },
        "3af490d18c7049dd8c8c95cd74ca0c23": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_ab62cfd6c39e4e5eb6e7335136bdfa67",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ebc36affc27b47d3b15834bc25ad4aa5": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "38eac5688ec34f9ea35707bcdb2e3d6d": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "oveq2"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_22261645d0ee45d28376d4cc04c8b20e",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_c3bc79c6930b4ece9d8fb71084abd1d5"
            ]
          }
        },
        "54c66c59aaf4463bb4e969ef4f2613b2": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_6153c29c6fe440dbb3c1765a19ea405f",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "fcde836d90844d47a553e4541ea2846c": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "f825abd68df946cc9e8f1c90e2821e49": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_319a9eae798441fa8579598318564e00",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "bd6fc778119d49efb269c35071e5ba08": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "324461a06b2342b982156061eb8b7250": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "26: $p |- ( z e. ZZ -> z e. CC )",
              "1": "ad2antlr"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_8023671e49a24e8e87cb755d6e85f4b3",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_64db0fe21ccb4051ae29df1ef2cef9ca",
              "IPY_MODEL_dba115c4cab74729aa4bff54b676de3d"
            ]
          }
        },
        "4821f4b955074e8ca1ad80cd6ff2a9fd": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "28: $p |- ( y e. NN -> y e. CC )",
              "1": "ad2antrr"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ccb5c9e40ec24a748a073ff677e110ce",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_74d80d5af9b1467db89f0f129fb90ccf",
              "IPY_MODEL_81157ce531cb4359abb87427d0c5da1d"
            ]
          }
        },
        "10bbe43fe4734bba97ec77240da399ae": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "2cnd"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_20c77f3d86ff4227bbfcbbed57345b28",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_99c21dbdb08a43d2bacb8c56bfe202c0"
            ]
          }
        },
        "8b3fd42ff7b041c29211a30845fcea1d": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "31: $p |- ( y e. NN -> y =/= 0 )",
              "1": "ad2antrr"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_39ca9f0d50b44039988d0bff3accc57f",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_b07f9c49392c4b3088b0c6a47957ce5a",
              "IPY_MODEL_19fdc16a04174583a5183b55aef13420"
            ]
          }
        },
        "c3853d17ad564a01811d7cb947e7f76b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "33: $p |- 2 =/= 0",
              "1": "a1i"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_067d86a57f3f404883ad543c9178b60b",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_feb44f273c6a44eaa446cd368afba39b",
              "IPY_MODEL_cdf8c72a190f4fd5ad9f23c0a3207876"
            ]
          }
        },
        "6671d84187b64427a5b91e0e81c8085a": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_3e9b9696b58f4920825276fb0b4cbef4",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "2a529124a41b4455a5e651f2b4ec110b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9afc7939120a4e84a149697edb3275df": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "39: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) e. ZZ /\\ ( y / 2 ) e. NN ) )",
              "1": "simprd"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_1f62166dda5842f98cf346df6833f0e9",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_f7ede39ecd9647299fd7df1e4811529b",
              "IPY_MODEL_479678c2b7f04553a20117bdc15c4471"
            ]
          }
        },
        "75c70d044f824925aa582469f1091533": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "41: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( z / 2 ) e. ZZ )",
              "1": "44: $p |- ( ( z / 2 ) e. ZZ -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )",
              "2": "syl"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ab1ab38ce09a4addb5024086be8eefc3",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_569fc2a727af4a018a60754db0e834d3",
              "IPY_MODEL_c4dd92b63f114a59878296257cf78bc1",
              "IPY_MODEL_d07df7e5136940a6bee989e3a62d1319"
            ]
          }
        },
        "3bfa8ed979374a948e39108f69464876": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_435bbeb9e61940a2abbfd37e6cf79812",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "22261645d0ee45d28376d4cc04c8b20e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "c3bc79c6930b4ece9d8fb71084abd1d5": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_6cdcd46595194e2599d23b5caf4c18b5",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "8023671e49a24e8e87cb755d6e85f4b3": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "64db0fe21ccb4051ae29df1ef2cef9ca": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "zcn"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ca4ed642f2a84f099e14bcb4bbd96213",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_769c4521b80245e999ee62d8e9c555aa"
            ]
          }
        },
        "dba115c4cab74729aa4bff54b676de3d": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_0b36a386e7ac40f39060df07e182bed6",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ccb5c9e40ec24a748a073ff677e110ce": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "74d80d5af9b1467db89f0f129fb90ccf": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "nncn"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_44c0cbbfb5f44cd4989fadb982c299ff",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_77c9c489556849d898f2ce36861021e5"
            ]
          }
        },
        "81157ce531cb4359abb87427d0c5da1d": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_02b65cd9df294673a5642a19ccc8e8a1",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "20c77f3d86ff4227bbfcbbed57345b28": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "99c21dbdb08a43d2bacb8c56bfe202c0": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_0a280549c9e84552a3ca518f67688501",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "39ca9f0d50b44039988d0bff3accc57f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b07f9c49392c4b3088b0c6a47957ce5a": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "nnne0"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_f3f5f0ca9dc946de96d3eb95556f9d33",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_2df6125b19bf46229e88bb7a91f93686"
            ]
          }
        },
        "19fdc16a04174583a5183b55aef13420": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_aa4fa170c8bd4002a4098c60cb46346e",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "067d86a57f3f404883ad543c9178b60b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "feb44f273c6a44eaa446cd368afba39b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "2ne0"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_a3ff2b680f4043a4bf473805410d0869",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_7f58f34a3e9d4d698454e6396349c438"
            ]
          }
        },
        "cdf8c72a190f4fd5ad9f23c0a3207876": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_6f2299b54cf447f0aac026ea2efadb3e",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "1f62166dda5842f98cf346df6833f0e9": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "f7ede39ecd9647299fd7df1e4811529b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "37: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> z e. ZZ )",
              "1": "38: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y e. NN )",
              "2": "25: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( z / y ) )",
              "3": "sqr2irrlem"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_81caa3e3626944458ac8ef50683a94bb",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_7bba29319d7a4e9faa21c56f8d6dcbeb",
              "IPY_MODEL_f1438f9292114e31a60f3e8cf535d29b",
              "IPY_MODEL_a14d20b9d344464b852fa11d7b1ac4ee",
              "IPY_MODEL_b99f9f513f8c48e585df3686f577e23a"
            ]
          }
        },
        "479678c2b7f04553a20117bdc15c4471": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_6c8bd8a457fe4039a205767e10675346",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ab1ab38ce09a4addb5024086be8eefc3": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "569fc2a727af4a018a60754db0e834d3": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "39: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) e. ZZ /\\ ( y / 2 ) e. NN ) )",
              "1": "simpld"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_4d01b6ea0bb943f98ad1ef5fa8ec24b2",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_3240f02597734e8b9266b2b2b5fbeff5",
              "IPY_MODEL_52e14363e9df4f9db0a91a7c948304b9"
            ]
          }
        },
        "c4dd92b63f114a59878296257cf78bc1": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "43: $p |- ( x = ( z / 2 ) -> ( ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) <-> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )",
              "1": "rspcv"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_eba9dcfef33143029328d7f7b71b2925",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_1ced4d8de5924ae39a454e8043ee475d",
              "IPY_MODEL_45a1a0aaad3d46629e4df0a233b679b1"
            ]
          }
        },
        "d07df7e5136940a6bee989e3a62d1319": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_eb92714ff27a422d8d3e617ab9cea909",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ca4ed642f2a84f099e14bcb4bbd96213": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "769c4521b80245e999ee62d8e9c555aa": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_f5116f6d71c54959a6e27ef89e83032a",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "44c0cbbfb5f44cd4989fadb982c299ff": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "77c9c489556849d898f2ce36861021e5": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_9a72479801e244a6b4bd8a719603339b",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "f3f5f0ca9dc946de96d3eb95556f9d33": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "2df6125b19bf46229e88bb7a91f93686": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_9a64c056559c4627bd3a7bd302884584",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "a3ff2b680f4043a4bf473805410d0869": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7f58f34a3e9d4d698454e6396349c438": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_a1e0c13446c24eb298657c00928ad2fc",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "81caa3e3626944458ac8ef50683a94bb": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7bba29319d7a4e9faa21c56f8d6dcbeb": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "simplr"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_5286c096febd4779901d64b6d06951c7",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_297f212515e548a48030860d32f15d02"
            ]
          }
        },
        "f1438f9292114e31a60f3e8cf535d29b": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "simpll"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_7c19400e925945d3b2e83ae068bc31ce",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_884ec1a268884de0a523e07eeeeb5b2f"
            ]
          }
        },
        "a14d20b9d344464b852fa11d7b1ac4ee": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "simpr"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_3649cb6f78f34265b7793a0637106229",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_4857cf719f06446aac0d01082ad8f24e"
            ]
          }
        },
        "b99f9f513f8c48e585df3686f577e23a": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_1d6e54b9aca24b71a5e6b9ef005f3e78",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "4d01b6ea0bb943f98ad1ef5fa8ec24b2": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "3240f02597734e8b9266b2b2b5fbeff5": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "37: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> z e. ZZ )",
              "1": "38: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y e. NN )",
              "2": "25: $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( z / y ) )",
              "3": "sqr2irrlem"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_9e8f951afaa945aaaecd04626112806b",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_2a508579261a4dea9ba168343f056144",
              "IPY_MODEL_0ec04acda6144323ac0e036d4c1e0779",
              "IPY_MODEL_e0b950db1d6e458eb241cb2d84e5269f",
              "IPY_MODEL_a5a3aec96cd549cfa2f834cf4bb37ea1"
            ]
          }
        },
        "52e14363e9df4f9db0a91a7c948304b9": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_14727d51f6a4430ebe96329b466fb89b",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "eba9dcfef33143029328d7f7b71b2925": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "1ced4d8de5924ae39a454e8043ee475d": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "42: $p |- ( x = ( z / 2 ) -> ( x / ( y / 2 ) ) = ( ( z / 2 ) / ( y / 2 ) ) )",
              "1": "neeq2d"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_864580e4501b483da2b6ff5ccc116677",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_7ca401ff9a0a4f558d04d7561c299f47",
              "IPY_MODEL_3630197f830e4fe9a9846a5b30c6a03f"
            ]
          }
        },
        "45a1a0aaad3d46629e4df0a233b679b1": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_42a4a2681e264d889e93a8b3c48d3a7b",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "5286c096febd4779901d64b6d06951c7": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "297f212515e548a48030860d32f15d02": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_b15f2d03e4cb4a1ebcbe148a51cc3a3b",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "7c19400e925945d3b2e83ae068bc31ce": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "884ec1a268884de0a523e07eeeeb5b2f": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_8f1aeffc00304c18a369bacbe488844c",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3649cb6f78f34265b7793a0637106229": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "4857cf719f06446aac0d01082ad8f24e": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_2b9f4c1b07844757add5aec16c2dacfa",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "9e8f951afaa945aaaecd04626112806b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "2a508579261a4dea9ba168343f056144": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "simplr"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_989d55d0c1ff455fac40fdd8a26e0ae9",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_343fdcb8416d4903addb5181b77b892c"
            ]
          }
        },
        "0ec04acda6144323ac0e036d4c1e0779": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "simpll"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ab223753ec4047a28f14b8e4b0d52c6a",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_51b7cb872c0a42df98fe31e1a8d5c214"
            ]
          }
        },
        "e0b950db1d6e458eb241cb2d84e5269f": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "simpr"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_854b79919b954677879b1799f1d8cbad",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_b88daff41ff24eb9845abab63f3db736"
            ]
          }
        },
        "a5a3aec96cd549cfa2f834cf4bb37ea1": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_f8bd77ec49674be896a7e3117ea4bedc",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "864580e4501b483da2b6ff5ccc116677": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7ca401ff9a0a4f558d04d7561c299f47": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "oveq1"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_3e5470c8978b401ea93d9f1acd5ce02d",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_4e51086126954f7c961394a6b8cb2d56"
            ]
          }
        },
        "3630197f830e4fe9a9846a5b30c6a03f": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_271d2e1728aa4fb9af38730779bf60f6",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "989d55d0c1ff455fac40fdd8a26e0ae9": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "343fdcb8416d4903addb5181b77b892c": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_b229f7df9e6d430b9affa5905c78f608",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ab223753ec4047a28f14b8e4b0d52c6a": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "51b7cb872c0a42df98fe31e1a8d5c214": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_85f4728ed36a4071a276cf9457b1d151",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "854b79919b954677879b1799f1d8cbad": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b88daff41ff24eb9845abab63f3db736": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_a5279777fa104167806bbb4ebd54f832",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3e5470c8978b401ea93d9f1acd5ce02d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "4e51086126954f7c961394a6b8cb2d56": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_3a6510b5df6a46b79a3e4c833abd545c",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "b392de99d58140358435710bd8c8af94": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "2aa3cf28ccb145eaa8381fbdb85dc302": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "975c98f167004057a06624876b9fdb46": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7766ab8032764cc0a282324c70391abe": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9ecf86e97b4f4d158c7ecf59064b3f3e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "d847e2604ec74683a4133294697d080d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "e33aa8a69bf3472c8b098b0b9bf19973": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "6d31d2448a9e44f5b2dbb5235eae9e46": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "4f51b13a1c544222bb942e4f410216a0": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "37478058407640f1bb4af980f1c7e0b6": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ed0b691edf0e450caa2aa55fc45bfa0e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "57fe6e4df4044a7b9848cac70b15eaa2": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "c190fd1b64df44069110a61728862628": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "06e98b14eb174d2fb1184f86dad2b0d3": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "2e48bb1862da47489261fb0bbd5a6ffd": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "cfd85dc1ea2e4d11affd4bc7fae7f69d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "d380d6abfb6e4136b4fd977219ba4199": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7d1c752a93084411961b787c7389932a": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "fdbd5dcad1ba4e5b8e5fa762ec6c9107": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "3fe1b6f2278941b1805de7ee4a1d8c44": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "0dff734e4b224018acea5e47b66d6e79": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "3069db68eff04468ab5661e2170ada40": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "0b03c4e324e64f48bfe070de3977dd39": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "0531b4d51690404988fea9a5f1d9b27c": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9bf61733584045e4bffa8d07eed0033c": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "50253b3cefdd47d59430f3255e00d1fa": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "0e9415e854c6477b9701617652ba3258": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "d014ce05f3934497bf616a8c20b2391f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "a7fadebfc46b43778df526aaf1b03610": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "c86cfeaed61f40d49f0970432a3ac6ed": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "1aea7b4d2d33419bb4669e2b0b523a1c": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "033e3f8dfc1c4c40a85db561e6f25a3f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "c2d9e046a56144e682685d78ca94cb31": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "424543c9ab844d7f8ce238bca1606dc2": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "80fa7df8d9704cd492bf9e0fdbe6b556": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "fa2eb0ca79bd46d68ea07bb7f71e690f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "92e861209e1f4a468315f972b312dcd2": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "79a73dfe3d9848e4b07eddcf60e7368f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b0f1ab7267394171bf88590d897e0673": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "11bbc54884c544bba813bb3663401d23": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "23e869b31ea0485ca76a08aa1bcbc527": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7b87c844691945aeac88c5e61807b51e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "2b752e11dd6a41c395a4378e3a2faa2e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "0fae406b95c3410a90187476cd38fa73": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "88866bd04954449b89e8104bce421b2d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "583cb59bae8a4b788b87c27e48b59d29": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "d2a21ef301c24193966885243eace121": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "78c609f3c1e54ba6bebba6b645cdbd51": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "15a3ece0cd3c49189f1c246f50fa226b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b6b16d28c6814dcdaf30d3dbda458405": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ec4fddaaafba41879ef7a6bcb380cd79": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ab60a9b840c640088eaa529a5fd4d1e1": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "403179bf179c423da000ba720dfb607a": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "d44954be68dc4af98176897a5c089a79": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b2ddbf571033407c953e974a4ef3e2ca": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "68954f14f6f7460289d8077ee20b29c0": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "6ebfd58bfd6642a6a10ec9c4ac5ee5eb": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7947d99d5eb74148bbe8974f2cc9911d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "d5c6b8755a044afc8bcd9f9d95dba8a0": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "be1d4ba9b41e403b82535e4e54c4866d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "999f839e8b9c41bea74067b380fb5737": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "7664d62652694f76a09038f2bd57679f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "c5496e372e1547608f6c2ae92eb9d14a": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b5a06d90d6c942639f8e03d4d925960d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ee6b540900c3434fb608f2b24479190c": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "30004fb0232b44588dd2dbaf6a1cf0d4": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9a973f5c2abb481a9aff8ceea7763697": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "cd2d3daa97aa4df79ecfb605ad94f0a9": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ad63940e41d545ef86e64e5745f1a260": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "a1f9b6b9bc274d088dd90032cc4ec7e2": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "c7d5e80ed0c6410e836626b962084640": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "6385fe3f1fca436e88b17fe38b147758": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "78c98f35800c4e188be2b29a137189a0": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "1271f0de0e364049a50ec5d2c2d5fd45": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "31c4af548119456e9cc6c2568139d703": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "69446a27ea674474ad541270efd38a1f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "ab62cfd6c39e4e5eb6e7335136bdfa67": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "6153c29c6fe440dbb3c1765a19ea405f": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "319a9eae798441fa8579598318564e00": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "3e9b9696b58f4920825276fb0b4cbef4": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "435bbeb9e61940a2abbfd37e6cf79812": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "6cdcd46595194e2599d23b5caf4c18b5": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "0b36a386e7ac40f39060df07e182bed6": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "02b65cd9df294673a5642a19ccc8e8a1": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "0a280549c9e84552a3ca518f67688501": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "aa4fa170c8bd4002a4098c60cb46346e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "6f2299b54cf447f0aac026ea2efadb3e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "6c8bd8a457fe4039a205767e10675346": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "eb92714ff27a422d8d3e617ab9cea909": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "f5116f6d71c54959a6e27ef89e83032a": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9a72479801e244a6b4bd8a719603339b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "9a64c056559c4627bd3a7bd302884584": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "a1e0c13446c24eb298657c00928ad2fc": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "1d6e54b9aca24b71a5e6b9ef005f3e78": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "14727d51f6a4430ebe96329b466fb89b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "42a4a2681e264d889e93a8b3c48d3a7b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b15f2d03e4cb4a1ebcbe148a51cc3a3b": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "8f1aeffc00304c18a369bacbe488844c": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "2b9f4c1b07844757add5aec16c2dacfa": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "f8bd77ec49674be896a7e3117ea4bedc": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "271d2e1728aa4fb9af38730779bf60f6": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "b229f7df9e6d430b9affa5905c78f608": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "85f4728ed36a4071a276cf9457b1d151": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "a5279777fa104167806bbb4ebd54f832": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "3a6510b5df6a46b79a3e4c833abd545c": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "62bc4d18b7344f838f979a5bcb9fb498": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "3: $p |- ( A F B ) e. _V"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": null,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_e715efb80a804f59970993b770e74334",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_32805d3a100c4f7cb000e7c269cfcc04"
            ]
          }
        },
        "e715efb80a804f59970993b770e74334": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "32805d3a100c4f7cb000e7c269cfcc04": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "1: $a |- ( A F B ) = ( F ` <. A , B >. )",
              "1": "2: $p |- ( F ` <. A , B >. ) e. _V",
              "2": "eqeltri"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_81e9f3825bbd49179d0f55017f8abac9",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_5296ce6a8d66449aa52ac2f4e9dd71de",
              "IPY_MODEL_bd01792309cd4ec19d98c1098aa0c3df",
              "IPY_MODEL_3efcf3d89479413f84d9f26fcac2b980"
            ]
          }
        },
        "81e9f3825bbd49179d0f55017f8abac9": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "5296ce6a8d66449aa52ac2f4e9dd71de": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "df-ov"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_ab44e93e38874a51b177cfc4b80b4968",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_fb95e0c7afc042f1997d51db8b053653"
            ]
          }
        },
        "bd01792309cd4ec19d98c1098aa0c3df": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "AccordionModel",
          "state": {
            "_view_name": "AccordionView",
            "_dom_classes": [],
            "_titles": {
              "0": "fvex"
            },
            "_model_name": "AccordionModel",
            "_view_module": "@jupyter-widgets/controls",
            "selected_index": 0,
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.5.0",
            "box_style": "",
            "layout": "IPY_MODEL_8ae7193d5b43412aa6cce3cc1075d6ea",
            "_model_module": "@jupyter-widgets/controls",
            "children": [
              "IPY_MODEL_a61040a5ee9b4e5d892275fb4d08dc67"
            ]
          }
        },
        "3efcf3d89479413f84d9f26fcac2b980": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_3dcce0dda0154d6abbb228484d3c0c67",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "ab44e93e38874a51b177cfc4b80b4968": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "fb95e0c7afc042f1997d51db8b053653": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_385a893106494fad9fecdb9f12fc90dc",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "8ae7193d5b43412aa6cce3cc1075d6ea": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "a61040a5ee9b4e5d892275fb4d08dc67": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_908f6b8e4664460cb0c87968b13ca737",
            "_model_module": "@jupyter-widgets/output"
          }
        },
        "3dcce0dda0154d6abbb228484d3c0c67": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "385a893106494fad9fecdb9f12fc90dc": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        },
        "908f6b8e4664460cb0c87968b13ca737": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/YoraiLevi/PyMetaMath/blob/master/PyMetaMath.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E-8RnDTbKUXn"
      },
      "source": [
        "#PyMetaMath\n",
        "**This notebook aims to provide a bridge between the metamath program to python by providing an interface between the metamath interactive shell to python objects.**\n",
        "See The [Metamath: Chapter 5 - The Metamath Program](http://us.metamath.org/downloads/metamath.pdf#page=175)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wFgfN8PmNQTo"
      },
      "source": [
        "Requirements:  \n",
        "* the metamath program in your path: \n",
        "* set.mm\n",
        "* python3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3T3ZaWASMppS"
      },
      "source": [
        "%cd /tmp/\n",
        "!wget http://us.metamath.org/downloads/metamath.tar.bz2\n",
        "!tar -xvf metamath.tar.bz2\n",
        "%cd metamath\n",
        "!gcc *.c -o metamath\n",
        "!cp metamath /content\n",
        "!cp set.mm /content\n",
        "%cd /content\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dvl4PtiKK7HJ"
      },
      "source": [
        "import pexpect.replwrap\n",
        "\n",
        "class RegexREPLWrapper(pexpect.replwrap.REPLWrapper):\n",
        "  \"\"\"Generic wrapper for read-eval-print-loops, a.k.a. interactive shells\n",
        "  Rather than REPLWrapper which evaluates 'prompt' and 'continuation_prompt' based on string search, this class evaluates via regex statements\n",
        "  \"\"\"\n",
        "\n",
        "  PEXPECT_PROMPT = r'^\\>\\s'\n",
        "  # no-match regex\n",
        "  #this class had some kind of bug with continuation prompts atm it raises an error\n",
        "  #TODO: Understand the EOF error on continue statment\n",
        "  PEXPECT_CONTINUATION_PROMPT = r'a^'\n",
        "  def _expect_prompt(self, timeout=-1, async_=False):\n",
        "    cpl = self.child.compile_pattern_list([self.prompt, self.continuation_prompt])\n",
        "    return self.child.expect_list(cpl,timeout=timeout, async_=async_) "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cpVzMT4LTK2m"
      },
      "source": [
        "#Running the program\n",
        "to initialize the metamath program instantiate a RegexREPLWrapper as shown below. The paramaters attempt to ensure that no special 'interaction' is required after command execution.  \n",
        "Note: If a partial command is provided the program may fail.\n",
        "\n",
        "to run a command simply input the string as it would be typed into the interactive shell without pressing enter.\n",
        "```python\n",
        "m.run_command(\"set scroll CONTINUOUS\")\n",
        "m.run_command(\"r set.mm\")\n",
        "m.run_command(\"show proof sqrt2irr\")\n",
        "```\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fJMpKZ_aLHiu",
        "outputId": "3c63ddcd-308d-481b-99f7-f6b9fb82cbc8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        }
      },
      "source": [
        "m = RegexREPLWrapper(\"./metamath\",r\"MM> |TOOLS> |MM-PA> \",None,continuation_prompt=r\"(?<=\\S\\?)\\s\")\n",
        "#Alternative options(Doesn't error on continuation? prompt)\n",
        "#m = RegexREPLWrapper(\"./metamath\",r\"MM> |TOOLS> |MM-PA> |(?<=\\S\\?)\\s\",None,continuation_prompt=r\"a^\")\n",
        "#try it with:\n",
        "#m.run_command(\"show proof\")\n",
        "\n",
        "m.run_command(\"set scroll CONTINUOUS\")\n",
        "m.run_command(\"set WIDTH 1000000\")\n",
        "m.run_command(\"r set.mm\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Reading source file \"set.mm\"... 39668530 bytes\\r\\n39668530 bytes were read into the source buffer.\\r\\nThe source has 185080 statements; 2583 are $a and 36636 are $p.\\r\\nNo errors were found.  However, proofs were not checked.  Type VERIFY PROOF * if you want to check them.\\r\\n'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ij7gbVtfg55T"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EqWiDIejJll8"
      },
      "source": [
        "def showProof(self,proof,*,lemmon=False,renumber=False,all=False):\n",
        "  \"\"\"Returns the [proof] as provided in metamath as a single string. this may contain \\r\\n or \\n\n",
        "  >>> showProof(m,\"sqrt2irr\")\n",
        "  \"\"\"\n",
        "  #TODO: add sanitization of proof input and optional paramaters\n",
        "  return self.run_command(\"show proof {}\".format(proof))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ApCRjIhBJn8V"
      },
      "source": [
        "import re\n",
        "def showLabels(self,pattern,*,all=False):\n",
        "  \"\"\"Shows labels based on patterns, returns a list, could be empty\n",
        "  to show all available labels:\n",
        "  >>> showLabels(m,\"*\")\n",
        "  \"\"\"\n",
        "  #the linear options could fail at timeout?, need to check that out.\n",
        "  #first line indicates output results\n",
        "  return self.run_command(\"show label {} /linear\".format(pattern)).splitlines()[1:]\n",
        "  #out = self.run_command(\"show label {}\".format(pattern))\n",
        "  #out = out.replace(\"The assertions that match are shown with statement number, label, and type.\",\"\").replace(\"\\r\",\"\").replace(\"\\n\",\"\").strip()\n",
        "  #out = re.split(r\"\\s\\s+\",out)\n",
        "  #return out"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7eUxlftMUjLv"
      },
      "source": [
        "## Additional Settings\n",
        "the metamath shell provides settings worth mentioning, SCROLL, WIDTH.  \n",
        "SCROLL sets/avoid interactive prompts for scrolling  \n",
        "WIDTH the length of each line. default 79. (this can ease string output parsing for now)  \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bsaqUyMRUiG4",
        "outputId": "4cd89646-576a-4c04-bb31-806e244f152b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 357
        }
      },
      "source": [
        "!./metamath 'show settings' exit"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Metamath - Version 0.188 23-Aug-2020          Type HELP for help, EXIT to exit.\n",
            "MM> show settings\n",
            "Metamath settings on 27-Aug-2020 at 1:13 PM:\n",
            "(SET ECHO...) Command ECHO is OFF.\n",
            "(SET SCROLL...) SCROLLing mode is PROMPTED.\n",
            "(SET WIDTH...) Screen display WIDTH is 79.\n",
            "(SET HEIGHT...) Screen display HEIGHT is 24.\n",
            "(READ...) No source file has been read in yet.\n",
            "(SET ROOT_DIRECTORY...) Root directory is \"\".\n",
            "(SET DISCOURAGEMENT...) Blocking based on \"discouraged\" tags is ON.\n",
            "(SET CONTRIBUTOR...) The current contributor is \"?who?\".\n",
            "(SET UNDO...) The maximum number of UNDOs is 19.\n",
            "(SET UNIFICATION_TIMEOUT...) The unification timeout parameter is 100000.\n",
            "(SET SEARCH_LIMIT...) The SEARCH_LIMIT for the IMPROVE command is 50000.\n",
            "(SET EMPTY_SUBSTITUTION...) EMPTY_SUBSTITUTION is not allowed (OFF).\n",
            "(SET JEREMY_HENTY_FILTER...) The Henty filter is turned ON.\n",
            "(OPEN LOG...) No log file is currently open.\n",
            "(SHOW STATEMENT.../[TEX,HTML,ALT_HTML]) Current output mode is TEX (LaTeX).\n",
            "The program is compiled for a 64-bit CPU.\n",
            "MM> exit\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ro3Jx-mEXPTx"
      },
      "source": [
        "##To see a proof:\n",
        "for the moment the is no sanitization of the text thus this function can fail easily and make the entire program stuck requiring reinisialization via the above code block.  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mjl45b6SYEcf",
        "outputId": "44797a3c-60a4-4adf-ef40-1fa9f2a21246",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "!./metamath 'help show proof' exit"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Metamath - Version 0.188 23-Aug-2020          Type HELP for help, EXIT to exit.\n",
            "MM> help show proof\n",
            "Syntax:  SHOW PROOF <label-match> [<qualifiers (see below)>]\n",
            "\n",
            "This command displays the proof of the specified $p statement various\n",
            "formats.  The <label-match> may contain \"*\" (0-or-more-character match) and\n",
            "\"?\" (single-character match) wildcard characters to match multiple\n",
            "statements.  See HELP SEARCH for other label matching conventions.\n",
            "Without any qualifiers, only the logical steps will be shown (i.e.\n",
            "syntax construction steps will be omitted), in indented format.\n",
            "\n",
            "Note that a compressed proof will have references to repeated parts of\n",
            "the proof with \"local labels\" prefixed with \"@\".  To show all steps\n",
            "in the original RPN proof, you must SAVE PROOF <label-match> / NORMAL before\n",
            "using SHOW PROOF.\n",
            "\n",
            "Most of the time, you will use\n",
            "    SHOW PROOF <label-match>\n",
            "to see just the proof steps corresponding to logical deduction.\n",
            "\n",
            "Optional qualifiers:\n",
            "    / ESSENTIAL - the proof tree is trimmed of all $f hypotheses before\n",
            "        being displayed.  (This is the default, and it is redundant to\n",
            "        specify it.)\n",
            "    / ALL - the proof tree is not trimmed of all $f hypotheses before\n",
            "        being displayed.  / ESSENTIAL and / ALL are mutually exclusive.\n",
            "    / FROM_STEP <step> - the display starts at the specified step.  If\n",
            "        this qualifier is omitted, the display starts at the first step.\n",
            "    / TO_STEP <step> - the display ends at the specified step.  If this\n",
            "        qualifier is omitted, the display ends at the last step.\n",
            "    / DEPTH <number> - Only steps at less than the specified proof\n",
            "        tree depth are displayed.  Useful for obtaining an overview of\n",
            "        the proof.\n",
            "    / REVERSE - the steps are displayed in reverse order.\n",
            "    / RENUMBER - when used with / ESSENTIAL, the steps are renumbered\n",
            "        to correspond only to the essential steps.\n",
            "    / TEX - the proof is converted to LaTeX and stored in the file opened\n",
            "        with OPEN TEX.  Tip:  SET WIDTH 120 (or so) to to fit equations\n",
            "        to LaTeX line.  Then use SHOW PROOF / TEX / LEMMON / RENUMBER.\n",
            "    / OLD_TEX - same as TEX but uses macros to fit line.  Obsolete and\n",
            "        will be removed eventually.\n",
            "    / LEMMON - The proof is displayed in a non-indented format known\n",
            "        as Lemmon style, with explicit previous step number references.\n",
            "        If this qualifier is omitted, steps are indented in a tree format.\n",
            "    / START_COLUMN <number> - Overrides the default column at which\n",
            "        the formula display starts in a Lemmon style display.  Affects\n",
            "        only displays using the / LEMMON qualifier.\n",
            "    / NO_REPEATED_STEPS - When a proof step is identical to an earlier\n",
            "        step, it will not be repeated.  Instead, a reference to it will be\n",
            "        changed to a reference to the earlier step.  In particular,\n",
            "        SHOW PROOF <label-match> / LEMMON / RENUMBER / NO_REPEATED_STEPS\n",
            "        will have the same proof step numbering as the web page proof\n",
            "        generated by SHOW STATEMENT  <label-match> / HTML, rather than\n",
            "        the proof step numbering of the indented format\n",
            "        SHOW PROOF <label-match> / RENUMBER.  This qualifier affects only\n",
            "        displays also using the / LEMMON qualifier.\n",
            "    / STATEMENT_SUMMARY - Summarizes all statements (like a brief SHOW\n",
            "        STATEMENT) used by the proof.  May not be used with any other\n",
            "        qualifier except / ESSENTIAL.\n",
            "    / SIZE - Shows size of the proof in the source.  The size depends on\n",
            "        how it was last SAVEd (compressed or normal).\n",
            "    / DETAILED_STEP <step> - Shows the details of what is happening at\n",
            "        a specific proof step.  May not be used with any other qualifier.\n",
            "    / NORMAL, / COMPRESSED, / EXPLICIT, / PACKED, / FAST,\n",
            "        / OLD_COMPRESSION - These qualifiers are the same as for\n",
            "        SAVE PROOF except that the proof is displayed on the screen in\n",
            "        a format suitable for manual inclusion in a source file.  See\n",
            "        HELP SAVE PROOF.\n",
            "\n",
            "MM> exit\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j_mohqFrScPj",
        "outputId": "553cf3c0-d3c1-4796-85c8-51c41ef95d63",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "print(showProof(m,\"sqrt2irr\"))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " 61           syl.1=peano2nn       $p |- ( y e. NN -> ( y + 1 ) e. NN )\r\n",
            "110                 imbid.1=breq2        $p |- ( n = 1 -> ( z < n <-> z < 1 ) )\r\n",
            "111               ralbidv.1=imbi1d     $p |- ( n = 1 -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "112             nnind.1=ralbidv      $p |- ( n = 1 -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "128                 imbid.1=breq2        $p |- ( n = y -> ( z < n <-> z < y ) )\r\n",
            "129               ralbidv.1=imbi1d     $p |- ( n = y -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "130             nnind.2=ralbidv      $p |- ( n = y -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "146                 imbid.1=breq2        $p |- ( n = ( y + 1 ) -> ( z < n <-> z < ( y + 1 ) ) )\r\n",
            "147               ralbidv.1=imbi1d     $p |- ( n = ( y + 1 ) -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "148         148:nnind.3=ralbidv      $p |- ( n = ( y + 1 ) -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "149             nnind.4=148          $p |- ( n = ( y + 1 ) -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "159                 pm2.21d.1=nnnlt1     $p |- ( z e. NN -> -. z < 1 )\r\n",
            "160               rgen.1=pm2.21d       $p |- ( z e. NN -> ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )\r\n",
            "161             nnind.5=rgen         $p |- A. z e. NN ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) )\r\n",
            "232                           syl.1=nnrp           $p |- ( y e. NN -> y e. RR+ )\r\n",
            "234                           syl.2=rphalflt       $p |- ( y e. RR+ -> ( y / 2 ) < y )\r\n",
            "235                         syl.1=syl            $p |- ( y e. NN -> ( y / 2 ) < y )\r\n",
            "258                               imbi12d.1=breq1      $p |- ( z = ( y / 2 ) -> ( z < y <-> ( y / 2 ) < y ) )\r\n",
            "272                                   neeq1d.1=oveq2       $p |- ( z = ( y / 2 ) -> ( x / z ) = ( x / ( y / 2 ) ) )\r\n",
            "273                                 ralbidv.1=neeq2d     $p |- ( z = ( y / 2 ) -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )\r\n",
            "274                               imbi12d.2=ralbidv    $p |- ( z = ( y / 2 ) -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )\r\n",
            "275                             rspcv.1=imbi12d      $p |- ( z = ( y / 2 ) -> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( y / 2 ) < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "276                           com3.1=rspcv         $p |- ( ( y / 2 ) e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "277                         syl.2=com13          $p |- ( ( y / 2 ) < y -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "278                       syld.1=syl           $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "317                             317:eqtr4d.1=simpr       $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( z / y ) )\r\n",
            "329                                     ad2ant.1=zcn         $p |- ( z e. ZZ -> z e. CC )\r\n",
            "330                                   div1d.1=ad2antlr     $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> z e. CC )\r\n",
            "338                                     ad2ant.1=nncn        $p |- ( y e. NN -> y e. CC )\r\n",
            "339                                   divcld.2=ad2antrr    $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y e. CC )\r\n",
            "341                                   divmuld.3=2cnd       $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> 2 e. CC )\r\n",
            "349                                     ad2ant.1=nnne0       $p |- ( y e. NN -> y =/= 0 )\r\n",
            "350                                   divmuld.4=ad2antrr   $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y =/= 0 )\r\n",
            "355                                     a1i.1=2ne0           $p |- 2 =/= 0\r\n",
            "356                                   divdiv23d.5=a1i      $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> 2 =/= 0 )\r\n",
            "357                                 eqtr4d.2=divcan7d    $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) / ( y / 2 ) ) = ( z / y ) )\r\n",
            "358                               mpd.1=eqtr4d         $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( ( z / 2 ) / ( y / 2 ) ) )\r\n",
            "380                                       sqr2irrlem.1=simplr  $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> z e. ZZ )\r\n",
            "384                                       sqr2irrlem.2=simpll  $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y e. NN )\r\n",
            "385                                       sqrt2irrlem.3=317    $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( z / y ) )\r\n",
            "386                                 386:simprd.1=sqr2irrlem  $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) e. ZZ /\\ ( y / 2 ) e. NN ) )\r\n",
            "387                                   embantd.1=simprd     $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( y / 2 ) e. NN )\r\n",
            "396                                       simpld.1=386         $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) e. ZZ /\\ ( y / 2 ) e. NN ) )\r\n",
            "397                                     syl.1=simpld         $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( z / 2 ) e. ZZ )\r\n",
            "413                                         neeq1d.1=oveq1       $p |- ( x = ( z / 2 ) -> ( x / ( y / 2 ) ) = ( ( z / 2 ) / ( y / 2 ) ) )\r\n",
            "414                                       rspcv.1=neeq2d       $p |- ( x = ( z / 2 ) -> ( ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) <-> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )\r\n",
            "415                                     syl.2=rspcv          $p |- ( ( z / 2 ) e. ZZ -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )\r\n",
            "416                                   embantd.2=syl        $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )\r\n",
            "417                                 necon2bd.1=embantd   $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )\r\n",
            "418                               mpd.2=necon2bd       $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( sqrt ` 2 ) = ( ( z / 2 ) / ( y / 2 ) ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "419                             ex.1=mpd             $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )\r\n",
            "420                           necon2ad.1=ex        $p |- ( ( y e. NN /\\ z e. ZZ ) -> ( ( sqrt ` 2 ) = ( z / y ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "421                         ralrimdva.1=necon2ad $p |- ( ( y e. NN /\\ z e. ZZ ) -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> ( sqrt ` 2 ) =/= ( z / y ) ) )\r\n",
            "422                       syld.2=ralrimdva     $p |- ( y e. NN -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) ) )\r\n",
            "423                     syl6ibr.1=syld       $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) ) )\r\n",
            "439                         neeq1d.1=oveq1       $p |- ( x = z -> ( x / y ) = ( z / y ) )\r\n",
            "440                       cbvralv.1=neeq2d     $p |- ( x = z -> ( ( sqrt ` 2 ) =/= ( x / y ) <-> ( sqrt ` 2 ) =/= ( z / y ) ) )\r\n",
            "441                     syl6ibr.2=cbvralv    $p |- ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) <-> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) )\r\n",
            "442                   sylibrd.1=syl6ibr    $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )\r\n",
            "461                         neeq1d.1=oveq2       $p |- ( z = y -> ( x / z ) = ( x / y ) )\r\n",
            "462                   462:ralbidv.1=neeq2d     $p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / y ) ) )\r\n",
            "463                     ceqsralv.2=ralbidv   $p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )\r\n",
            "464                   sylibrd.2=ceqsralv   $p |- ( y e. NN -> ( A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )\r\n",
            "465                 ancld.1=sylibrd      $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "466               sylibrd.1=ancld      $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )\r\n",
            "511                           bitr3d.1=nnleltp1    $p |- ( ( z e. NN /\\ y e. NN ) -> ( z <_ y <-> z < ( y + 1 ) ) )\r\n",
            "524                             syl2an.1=nnre        $p |- ( z e. NN -> z e. RR )\r\n",
            "526                         526:syl2an.2=nnre        $p |- ( y e. NN -> y e. RR )\r\n",
            "529                             syl2an.3=leloe       $p |- ( ( z e. RR /\\ y e. RR ) -> ( z <_ y <-> ( z < y \\/ z = y ) ) )\r\n",
            "530                           bitr3d.2=syl2an      $p |- ( ( z e. NN /\\ y e. NN ) -> ( z <_ y <-> ( z < y \\/ z = y ) ) )\r\n",
            "531                         ancoms.1=bitr3d      $p |- ( ( z e. NN /\\ y e. NN ) -> ( z < ( y + 1 ) <-> ( z < y \\/ z = y ) ) )\r\n",
            "532                       imbid.1=ancoms       $p |- ( ( y e. NN /\\ z e. NN ) -> ( z < ( y + 1 ) <-> ( z < y \\/ z = y ) ) )\r\n",
            "533                     syl6bb.1=imbi1d      $p |- ( ( y e. NN /\\ z e. NN ) -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y \\/ z = y ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "537                     syl6bb.2=jaob        $p |- ( ( ( z < y \\/ z = y ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "538                   ralbidva.1=syl6bb    $p |- ( ( y e. NN /\\ z e. NN ) -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )\r\n",
            "539                 syl6bb.1=ralbidva    $p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )\r\n",
            "544                 syl6bb.2=r19.26      $p |- ( A. z e. NN ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) <-> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "545               sylibrd.2=syl6bb     $p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )\r\n",
            "546             nnind.6=sylibrd      $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "547           syl.2=nnind          $p |- ( ( y + 1 ) e. NN -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )\r\n",
            "548         mp2d.1=syl           $p |- ( y e. NN -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )\r\n",
            "551           ltp1d.1=526          $p |- ( y e. NN -> y e. RR )\r\n",
            "552         mp2d.2=ltp1d         $p |- ( y e. NN -> y < ( y + 1 ) )\r\n",
            "569             imbi12d.1=breq1      $p |- ( z = y -> ( z < ( y + 1 ) <-> y < ( y + 1 ) ) )\r\n",
            "587                   syl6bb.1=462         $p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / y ) ) )\r\n",
            "590                   syl6bb.2=df-ne       $a |- ( ( sqrt ` 2 ) =/= ( x / y ) <-> -. ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "591                 ralbidv.1=syl6bb     $p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> -. ( sqrt ` 2 ) = ( x / y ) ) )\r\n",
            "592               syl6bb.1=ralbidv     $p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ -. ( sqrt ` 2 ) = ( x / y ) ) )\r\n",
            "596               syl6bb.2=ralnex      $p |- ( A. x e. ZZ -. ( sqrt ` 2 ) = ( x / y ) <-> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "597             imbi12d.2=syl6bb     $p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) )\r\n",
            "598           rspcv.1=imbi12d      $p |- ( z = y -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( y < ( y + 1 ) -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) ) )\r\n",
            "599         mp2d.3=rspcv         $p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( y < ( y + 1 ) -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) ) )\r\n",
            "600       nrex.1=mp2d          $p |- ( y e. NN -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "601     mtbir.1=nrex         $p |- -. E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y )\r\n",
            "614       bitri.1=elq          $p |- ( ( sqrt ` 2 ) e. QQ <-> E. x e. ZZ E. y e. NN ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "620       bitri.2=rexcom       $p |- ( E. x e. ZZ E. y e. NN ( sqrt ` 2 ) = ( x / y ) <-> E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "621     mtbir.2=bitri        $p |- ( ( sqrt ` 2 ) e. QQ <-> E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "622   nelir.1=mtbir        $p |- -. ( sqrt ` 2 ) e. QQ\r\n",
            "623 sqrt2irr=nelir       $p |- ( sqrt ` 2 ) e/ QQ\r\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jc0tG8leYiYI"
      },
      "source": [
        "Exactly like in the metamath shell it is possible to print the proof in different formats:  \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IM7cenOaY3x3",
        "outputId": "767debdc-9a22-4c37-ea3f-97ffab5a8c2a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "print(showProof(m,\"sqrt2irr /LEMMON/RENUMBER/NO_REPEATED_STEPS\"))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            " 1 peano2nn      $p |- ( y e. NN -> ( y + 1 ) e. NN )\r\n",
            " 2 breq2         $p |- ( n = 1 -> ( z < n <-> z < 1 ) )\r\n",
            " 3 2 imbi1d      $p |- ( n = 1 -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            " 4 3 ralbidv     $p |- ( n = 1 -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            " 5 breq2         $p |- ( n = y -> ( z < n <-> z < y ) )\r\n",
            " 6 5 imbi1d      $p |- ( n = y -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            " 7 6 ralbidv     $p |- ( n = y -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            " 8 breq2         $p |- ( n = ( y + 1 ) -> ( z < n <-> z < ( y + 1 ) ) )\r\n",
            " 9 8 imbi1d      $p |- ( n = ( y + 1 ) -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "10 9 ralbidv     $p |- ( n = ( y + 1 ) -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "11 nnnlt1        $p |- ( z e. NN -> -. z < 1 )\r\n",
            "12 11 pm2.21d    $p |- ( z e. NN -> ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )\r\n",
            "13 12 rgen       $p |- A. z e. NN ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) )\r\n",
            "14 nnrp          $p |- ( y e. NN -> y e. RR+ )\r\n",
            "15 rphalflt      $p |- ( y e. RR+ -> ( y / 2 ) < y )\r\n",
            "16 14,15 syl     $p |- ( y e. NN -> ( y / 2 ) < y )\r\n",
            "17 breq1         $p |- ( z = ( y / 2 ) -> ( z < y <-> ( y / 2 ) < y ) )\r\n",
            "18 oveq2         $p |- ( z = ( y / 2 ) -> ( x / z ) = ( x / ( y / 2 ) ) )\r\n",
            "19 18 neeq2d     $p |- ( z = ( y / 2 ) -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )\r\n",
            "20 19 ralbidv    $p |- ( z = ( y / 2 ) -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )\r\n",
            "21 17,20 imbi12d  $p |- ( z = ( y / 2 ) -> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( y / 2 ) < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "22 21 rspcv      $p |- ( ( y / 2 ) e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "23 22 com13      $p |- ( ( y / 2 ) < y -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "24 16,23 syl     $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "25 simpr         $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( z / y ) )\r\n",
            "26 zcn           $p |- ( z e. ZZ -> z e. CC )\r\n",
            "27 26 ad2antlr   $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> z e. CC )\r\n",
            "28 nncn          $p |- ( y e. NN -> y e. CC )\r\n",
            "29 28 ad2antrr   $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y e. CC )\r\n",
            "30 2cnd          $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> 2 e. CC )\r\n",
            "31 nnne0         $p |- ( y e. NN -> y =/= 0 )\r\n",
            "32 31 ad2antrr   $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y =/= 0 )\r\n",
            "33 2ne0          $p |- 2 =/= 0\r\n",
            "34 33 a1i        $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> 2 =/= 0 )\r\n",
            "35 27,29,30,32,34 divcan7d  $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) / ( y / 2 ) ) = ( z / y ) )\r\n",
            "36 25,35 eqtr4d  $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( ( z / 2 ) / ( y / 2 ) ) )\r\n",
            "37 simplr        $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> z e. ZZ )\r\n",
            "38 simpll        $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> y e. NN )\r\n",
            "39 37,38,25 sqr2irrlem  $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) e. ZZ /\\ ( y / 2 ) e. NN ) )\r\n",
            "40 39 simprd     $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( y / 2 ) e. NN )\r\n",
            "41 39 simpld     $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( z / 2 ) e. ZZ )\r\n",
            "42 oveq1         $p |- ( x = ( z / 2 ) -> ( x / ( y / 2 ) ) = ( ( z / 2 ) / ( y / 2 ) ) )\r\n",
            "43 42 neeq2d     $p |- ( x = ( z / 2 ) -> ( ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) <-> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )\r\n",
            "44 43 rspcv      $p |- ( ( z / 2 ) e. ZZ -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )\r\n",
            "45 41,44 syl     $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )\r\n",
            "46 40,45 embantd  $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )\r\n",
            "47 46 necon2bd   $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( sqrt ` 2 ) = ( ( z / 2 ) / ( y / 2 ) ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "48 36,47 mpd     $p |- ( ( ( y e. NN /\\ z e. ZZ ) /\\ ( sqrt ` 2 ) = ( z / y ) ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )\r\n",
            "49 48 ex         $p |- ( ( y e. NN /\\ z e. ZZ ) -> ( ( sqrt ` 2 ) = ( z / y ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )\r\n",
            "50 49 necon2ad   $p |- ( ( y e. NN /\\ z e. ZZ ) -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> ( sqrt ` 2 ) =/= ( z / y ) ) )\r\n",
            "51 50 ralrimdva  $p |- ( y e. NN -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) ) )\r\n",
            "52 24,51 syld    $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) ) )\r\n",
            "53 oveq1         $p |- ( x = z -> ( x / y ) = ( z / y ) )\r\n",
            "54 53 neeq2d     $p |- ( x = z -> ( ( sqrt ` 2 ) =/= ( x / y ) <-> ( sqrt ` 2 ) =/= ( z / y ) ) )\r\n",
            "55 54 cbvralv    $p |- ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) <-> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) )\r\n",
            "56 52,55 syl6ibr  $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )\r\n",
            "57 oveq2         $p |- ( z = y -> ( x / z ) = ( x / y ) )\r\n",
            "58 57 neeq2d     $p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / y ) ) )\r\n",
            "59 58 ralbidv    $p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )\r\n",
            "60 59 ceqsralv   $p |- ( y e. NN -> ( A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )\r\n",
            "61 56,60 sylibrd  $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "62 61 ancld      $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )\r\n",
            "63 nnleltp1      $p |- ( ( z e. NN /\\ y e. NN ) -> ( z <_ y <-> z < ( y + 1 ) ) )\r\n",
            "64 nnre          $p |- ( z e. NN -> z e. RR )\r\n",
            "65 nnre          $p |- ( y e. NN -> y e. RR )\r\n",
            "66 leloe         $p |- ( ( z e. RR /\\ y e. RR ) -> ( z <_ y <-> ( z < y \\/ z = y ) ) )\r\n",
            "67 64,65,66 syl2an  $p |- ( ( z e. NN /\\ y e. NN ) -> ( z <_ y <-> ( z < y \\/ z = y ) ) )\r\n",
            "68 63,67 bitr3d  $p |- ( ( z e. NN /\\ y e. NN ) -> ( z < ( y + 1 ) <-> ( z < y \\/ z = y ) ) )\r\n",
            "69 68 ancoms     $p |- ( ( y e. NN /\\ z e. NN ) -> ( z < ( y + 1 ) <-> ( z < y \\/ z = y ) ) )\r\n",
            "70 69 imbi1d     $p |- ( ( y e. NN /\\ z e. NN ) -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y \\/ z = y ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "71 jaob          $p |- ( ( ( z < y \\/ z = y ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "72 70,71 syl6bb  $p |- ( ( y e. NN /\\ z e. NN ) -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )\r\n",
            "73 72 ralbidva   $p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )\r\n",
            "74 r19.26        $p |- ( A. z e. NN ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) <-> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "75 73,74 syl6bb  $p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )\r\n",
            "76 62,75 sylibrd  $p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )\r\n",
            "77 4,7,10,10,13,76 nnind  $p |- ( ( y + 1 ) e. NN -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )\r\n",
            "78 1,77 syl      $p |- ( y e. NN -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )\r\n",
            "79 65 ltp1d      $p |- ( y e. NN -> y < ( y + 1 ) )\r\n",
            "80 breq1         $p |- ( z = y -> ( z < ( y + 1 ) <-> y < ( y + 1 ) ) )\r\n",
            "81 df-ne         $a |- ( ( sqrt ` 2 ) =/= ( x / y ) <-> -. ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "82 58,81 syl6bb  $p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> -. ( sqrt ` 2 ) = ( x / y ) ) )\r\n",
            "83 82 ralbidv    $p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ -. ( sqrt ` 2 ) = ( x / y ) ) )\r\n",
            "84 ralnex        $p |- ( A. x e. ZZ -. ( sqrt ` 2 ) = ( x / y ) <-> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "85 83,84 syl6bb  $p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) )\r\n",
            "86 80,85 imbi12d  $p |- ( z = y -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( y < ( y + 1 ) -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) ) )\r\n",
            "87 86 rspcv      $p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( y < ( y + 1 ) -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) ) )\r\n",
            "88 78,79,87 mp2d  $p |- ( y e. NN -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "89 88 nrex       $p |- -. E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y )\r\n",
            "90 elq           $p |- ( ( sqrt ` 2 ) e. QQ <-> E. x e. ZZ E. y e. NN ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "91 rexcom        $p |- ( E. x e. ZZ E. y e. NN ( sqrt ` 2 ) = ( x / y ) <-> E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "92 90,91 bitri   $p |- ( ( sqrt ` 2 ) e. QQ <-> E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )\r\n",
            "93 89,92 mtbir   $p |- -. ( sqrt ` 2 ) e. QQ\r\n",
            "94 93 nelir      $p |- ( sqrt ` 2 ) e/ QQ\r\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3bVzgpueZ861"
      },
      "source": [
        "#Parsing a proof into a tree like structure.\n",
        "Ultimately now that we can have the textual output of proofs in python it would be useful to parse them into useful object such as Trees and [DAG](https://en.wikipedia.org/wiki/Directed_acyclic_graph)'s  \n",
        "this has been left as an exercise for the user.\n",
        "Good Luck!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d20tJCaAC8VI"
      },
      "source": [
        "import re\n",
        "proof = showProof(m,\"sqrt2irr /LEMMON/RENUMBER/NO_REPEATED_STEPS\")\n",
        "#Assuming table-row like of the form Line-number Hyp{Optional} Ref{Optional} $Statement\n",
        "pattern = r\"^\\s*(\\d+)\\s(?:((?:\\d+\\,*)*)\\s)?(\\S+)\\s+(\\$.*)$\" \n",
        "#                 id    hyp1,hyp2,hyp3      ref    statment\n",
        "unpacked = [re.search(pattern,line).groups() for line in proof.splitlines()]\n",
        "raw_nodes = [{\n",
        "              \"id\":id,\n",
        "              \"hypotheses\":(hyps.split(\",\") if hyps is not None else None),\n",
        "              \"reference\":ref,\n",
        "              \"statement\":statement\n",
        "              } for (id,hyps,ref,statement) in unpacked]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QTwHH1px9IpW"
      },
      "source": [
        "import re\n",
        "def raw_nodes_proof(self,str):\n",
        "  proof = showProof(self,str+\" /LEMMON/RENUMBER/NO_REPEATED_STEPS\")\n",
        "  #Assuming table-row like of the form Line-number Hyp{Optional} Ref{Optional} $Statement\n",
        "  pattern = r\"^\\s*(\\d+)\\s(?:((?:\\d+\\,*)*)\\s)?(\\S+)\\s+(\\$.*)$\" \n",
        "  #                 id    hyp1,hyp2,hyp3      ref    statment\n",
        "  unpacked = [re.search(pattern,line).groups() for line in proof.splitlines()]\n",
        "  raw_nodes = [{\n",
        "                \"id\":id,\n",
        "                \"hypotheses\":(hyps.split(\",\") if hyps is not None else None),\n",
        "                \"reference\":ref,\n",
        "                \"statement\":statement\n",
        "                } for (id,hyps,ref,statement) in unpacked]\n",
        "  return raw_nodes"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oGK29dYIGq-f",
        "outputId": "582c0b0d-800f-4cfc-fc25-50f17cfba63b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "raw_nodes"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[{'hypotheses': None,\n",
              "  'id': '1',\n",
              "  'reference': 'peano2nn',\n",
              "  'statement': '$p |- ( y e. NN -> ( y + 1 ) e. NN )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '2',\n",
              "  'reference': 'breq2',\n",
              "  'statement': '$p |- ( n = 1 -> ( z < n <-> z < 1 ) )'},\n",
              " {'hypotheses': ['2'],\n",
              "  'id': '3',\n",
              "  'reference': 'imbi1d',\n",
              "  'statement': '$p |- ( n = 1 -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': ['3'],\n",
              "  'id': '4',\n",
              "  'reference': 'ralbidv',\n",
              "  'statement': '$p |- ( n = 1 -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '5',\n",
              "  'reference': 'breq2',\n",
              "  'statement': '$p |- ( n = y -> ( z < n <-> z < y ) )'},\n",
              " {'hypotheses': ['5'],\n",
              "  'id': '6',\n",
              "  'reference': 'imbi1d',\n",
              "  'statement': '$p |- ( n = y -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': ['6'],\n",
              "  'id': '7',\n",
              "  'reference': 'ralbidv',\n",
              "  'statement': '$p |- ( n = y -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '8',\n",
              "  'reference': 'breq2',\n",
              "  'statement': '$p |- ( n = ( y + 1 ) -> ( z < n <-> z < ( y + 1 ) ) )'},\n",
              " {'hypotheses': ['8'],\n",
              "  'id': '9',\n",
              "  'reference': 'imbi1d',\n",
              "  'statement': '$p |- ( n = ( y + 1 ) -> ( ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': ['9'],\n",
              "  'id': '10',\n",
              "  'reference': 'ralbidv',\n",
              "  'statement': '$p |- ( n = ( y + 1 ) -> ( A. z e. NN ( z < n -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '11',\n",
              "  'reference': 'nnnlt1',\n",
              "  'statement': '$p |- ( z e. NN -> -. z < 1 )'},\n",
              " {'hypotheses': ['11'],\n",
              "  'id': '12',\n",
              "  'reference': 'pm2.21d',\n",
              "  'statement': '$p |- ( z e. NN -> ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )'},\n",
              " {'hypotheses': ['12'],\n",
              "  'id': '13',\n",
              "  'reference': 'rgen',\n",
              "  'statement': '$p |- A. z e. NN ( z < 1 -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '14',\n",
              "  'reference': 'nnrp',\n",
              "  'statement': '$p |- ( y e. NN -> y e. RR+ )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '15',\n",
              "  'reference': 'rphalflt',\n",
              "  'statement': '$p |- ( y e. RR+ -> ( y / 2 ) < y )'},\n",
              " {'hypotheses': ['14', '15'],\n",
              "  'id': '16',\n",
              "  'reference': 'syl',\n",
              "  'statement': '$p |- ( y e. NN -> ( y / 2 ) < y )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '17',\n",
              "  'reference': 'breq1',\n",
              "  'statement': '$p |- ( z = ( y / 2 ) -> ( z < y <-> ( y / 2 ) < y ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '18',\n",
              "  'reference': 'oveq2',\n",
              "  'statement': '$p |- ( z = ( y / 2 ) -> ( x / z ) = ( x / ( y / 2 ) ) )'},\n",
              " {'hypotheses': ['18'],\n",
              "  'id': '19',\n",
              "  'reference': 'neeq2d',\n",
              "  'statement': '$p |- ( z = ( y / 2 ) -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )'},\n",
              " {'hypotheses': ['19'],\n",
              "  'id': '20',\n",
              "  'reference': 'ralbidv',\n",
              "  'statement': '$p |- ( z = ( y / 2 ) -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )'},\n",
              " {'hypotheses': ['17', '20'],\n",
              "  'id': '21',\n",
              "  'reference': 'imbi12d',\n",
              "  'statement': '$p |- ( z = ( y / 2 ) -> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( y / 2 ) < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )'},\n",
              " {'hypotheses': ['21'],\n",
              "  'id': '22',\n",
              "  'reference': 'rspcv',\n",
              "  'statement': '$p |- ( ( y / 2 ) e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )'},\n",
              " {'hypotheses': ['22'],\n",
              "  'id': '23',\n",
              "  'reference': 'com13',\n",
              "  'statement': '$p |- ( ( y / 2 ) < y -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )'},\n",
              " {'hypotheses': ['16', '23'],\n",
              "  'id': '24',\n",
              "  'reference': 'syl',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '25',\n",
              "  'reference': 'simpr',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( z / y ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '26',\n",
              "  'reference': 'zcn',\n",
              "  'statement': '$p |- ( z e. ZZ -> z e. CC )'},\n",
              " {'hypotheses': ['26'],\n",
              "  'id': '27',\n",
              "  'reference': 'ad2antlr',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> z e. CC )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '28',\n",
              "  'reference': 'nncn',\n",
              "  'statement': '$p |- ( y e. NN -> y e. CC )'},\n",
              " {'hypotheses': ['28'],\n",
              "  'id': '29',\n",
              "  'reference': 'ad2antrr',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> y e. CC )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '30',\n",
              "  'reference': '2cnd',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> 2 e. CC )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '31',\n",
              "  'reference': 'nnne0',\n",
              "  'statement': '$p |- ( y e. NN -> y =/= 0 )'},\n",
              " {'hypotheses': ['31'],\n",
              "  'id': '32',\n",
              "  'reference': 'ad2antrr',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> y =/= 0 )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '33',\n",
              "  'reference': '2ne0',\n",
              "  'statement': '$p |- 2 =/= 0'},\n",
              " {'hypotheses': ['33'],\n",
              "  'id': '34',\n",
              "  'reference': 'a1i',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> 2 =/= 0 )'},\n",
              " {'hypotheses': ['27', '29', '30', '32', '34'],\n",
              "  'id': '35',\n",
              "  'reference': 'divcan7d',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) / ( y / 2 ) ) = ( z / y ) )'},\n",
              " {'hypotheses': ['25', '35'],\n",
              "  'id': '36',\n",
              "  'reference': 'eqtr4d',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( sqrt ` 2 ) = ( ( z / 2 ) / ( y / 2 ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '37',\n",
              "  'reference': 'simplr',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> z e. ZZ )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '38',\n",
              "  'reference': 'simpll',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> y e. NN )'},\n",
              " {'hypotheses': ['37', '38', '25'],\n",
              "  'id': '39',\n",
              "  'reference': 'sqr2irrlem',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( z / 2 ) e. ZZ /\\\\ ( y / 2 ) e. NN ) )'},\n",
              " {'hypotheses': ['39'],\n",
              "  'id': '40',\n",
              "  'reference': 'simprd',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( y / 2 ) e. NN )'},\n",
              " {'hypotheses': ['39'],\n",
              "  'id': '41',\n",
              "  'reference': 'simpld',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( z / 2 ) e. ZZ )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '42',\n",
              "  'reference': 'oveq1',\n",
              "  'statement': '$p |- ( x = ( z / 2 ) -> ( x / ( y / 2 ) ) = ( ( z / 2 ) / ( y / 2 ) ) )'},\n",
              " {'hypotheses': ['42'],\n",
              "  'id': '43',\n",
              "  'reference': 'neeq2d',\n",
              "  'statement': '$p |- ( x = ( z / 2 ) -> ( ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) <-> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )'},\n",
              " {'hypotheses': ['43'],\n",
              "  'id': '44',\n",
              "  'reference': 'rspcv',\n",
              "  'statement': '$p |- ( ( z / 2 ) e. ZZ -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )'},\n",
              " {'hypotheses': ['41', '44'],\n",
              "  'id': '45',\n",
              "  'reference': 'syl',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )'},\n",
              " {'hypotheses': ['40', '45'],\n",
              "  'id': '46',\n",
              "  'reference': 'embantd',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> ( sqrt ` 2 ) =/= ( ( z / 2 ) / ( y / 2 ) ) ) )'},\n",
              " {'hypotheses': ['46'],\n",
              "  'id': '47',\n",
              "  'reference': 'necon2bd',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> ( ( sqrt ` 2 ) = ( ( z / 2 ) / ( y / 2 ) ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )'},\n",
              " {'hypotheses': ['36', '47'],\n",
              "  'id': '48',\n",
              "  'reference': 'mpd',\n",
              "  'statement': '$p |- ( ( ( y e. NN /\\\\ z e. ZZ ) /\\\\ ( sqrt ` 2 ) = ( z / y ) ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) )'},\n",
              " {'hypotheses': ['48'],\n",
              "  'id': '49',\n",
              "  'reference': 'ex',\n",
              "  'statement': '$p |- ( ( y e. NN /\\\\ z e. ZZ ) -> ( ( sqrt ` 2 ) = ( z / y ) -> -. ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) ) )'},\n",
              " {'hypotheses': ['49'],\n",
              "  'id': '50',\n",
              "  'reference': 'necon2ad',\n",
              "  'statement': '$p |- ( ( y e. NN /\\\\ z e. ZZ ) -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> ( sqrt ` 2 ) =/= ( z / y ) ) )'},\n",
              " {'hypotheses': ['50'],\n",
              "  'id': '51',\n",
              "  'reference': 'ralrimdva',\n",
              "  'statement': '$p |- ( y e. NN -> ( ( ( y / 2 ) e. NN -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / ( y / 2 ) ) ) -> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) ) )'},\n",
              " {'hypotheses': ['24', '51'],\n",
              "  'id': '52',\n",
              "  'reference': 'syld',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '53',\n",
              "  'reference': 'oveq1',\n",
              "  'statement': '$p |- ( x = z -> ( x / y ) = ( z / y ) )'},\n",
              " {'hypotheses': ['53'],\n",
              "  'id': '54',\n",
              "  'reference': 'neeq2d',\n",
              "  'statement': '$p |- ( x = z -> ( ( sqrt ` 2 ) =/= ( x / y ) <-> ( sqrt ` 2 ) =/= ( z / y ) ) )'},\n",
              " {'hypotheses': ['54'],\n",
              "  'id': '55',\n",
              "  'reference': 'cbvralv',\n",
              "  'statement': '$p |- ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) <-> A. z e. ZZ ( sqrt ` 2 ) =/= ( z / y ) )'},\n",
              " {'hypotheses': ['52', '55'],\n",
              "  'id': '56',\n",
              "  'reference': 'syl6ibr',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '57',\n",
              "  'reference': 'oveq2',\n",
              "  'statement': '$p |- ( z = y -> ( x / z ) = ( x / y ) )'},\n",
              " {'hypotheses': ['57'],\n",
              "  'id': '58',\n",
              "  'reference': 'neeq2d',\n",
              "  'statement': '$p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> ( sqrt ` 2 ) =/= ( x / y ) ) )'},\n",
              " {'hypotheses': ['58'],\n",
              "  'id': '59',\n",
              "  'reference': 'ralbidv',\n",
              "  'statement': '$p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )'},\n",
              " {'hypotheses': ['59'],\n",
              "  'id': '60',\n",
              "  'reference': 'ceqsralv',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / y ) ) )'},\n",
              " {'hypotheses': ['56', '60'],\n",
              "  'id': '61',\n",
              "  'reference': 'sylibrd',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': ['61'],\n",
              "  'id': '62',\n",
              "  'reference': 'ancld',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '63',\n",
              "  'reference': 'nnleltp1',\n",
              "  'statement': '$p |- ( ( z e. NN /\\\\ y e. NN ) -> ( z <_ y <-> z < ( y + 1 ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '64',\n",
              "  'reference': 'nnre',\n",
              "  'statement': '$p |- ( z e. NN -> z e. RR )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '65',\n",
              "  'reference': 'nnre',\n",
              "  'statement': '$p |- ( y e. NN -> y e. RR )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '66',\n",
              "  'reference': 'leloe',\n",
              "  'statement': '$p |- ( ( z e. RR /\\\\ y e. RR ) -> ( z <_ y <-> ( z < y \\\\/ z = y ) ) )'},\n",
              " {'hypotheses': ['64', '65', '66'],\n",
              "  'id': '67',\n",
              "  'reference': 'syl2an',\n",
              "  'statement': '$p |- ( ( z e. NN /\\\\ y e. NN ) -> ( z <_ y <-> ( z < y \\\\/ z = y ) ) )'},\n",
              " {'hypotheses': ['63', '67'],\n",
              "  'id': '68',\n",
              "  'reference': 'bitr3d',\n",
              "  'statement': '$p |- ( ( z e. NN /\\\\ y e. NN ) -> ( z < ( y + 1 ) <-> ( z < y \\\\/ z = y ) ) )'},\n",
              " {'hypotheses': ['68'],\n",
              "  'id': '69',\n",
              "  'reference': 'ancoms',\n",
              "  'statement': '$p |- ( ( y e. NN /\\\\ z e. NN ) -> ( z < ( y + 1 ) <-> ( z < y \\\\/ z = y ) ) )'},\n",
              " {'hypotheses': ['69'],\n",
              "  'id': '70',\n",
              "  'reference': 'imbi1d',\n",
              "  'statement': '$p |- ( ( y e. NN /\\\\ z e. NN ) -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y \\\\/ z = y ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '71',\n",
              "  'reference': 'jaob',\n",
              "  'statement': '$p |- ( ( ( z < y \\\\/ z = y ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': ['70', '71'],\n",
              "  'id': '72',\n",
              "  'reference': 'syl6bb',\n",
              "  'statement': '$p |- ( ( y e. NN /\\\\ z e. NN ) -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )'},\n",
              " {'hypotheses': ['72'],\n",
              "  'id': '73',\n",
              "  'reference': 'ralbidva',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> A. z e. NN ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '74',\n",
              "  'reference': 'r19.26',\n",
              "  'statement': '$p |- ( A. z e. NN ( ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\\\ ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) <-> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': ['73', '74'],\n",
              "  'id': '75',\n",
              "  'reference': 'syl6bb',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) /\\\\ A. z e. NN ( z = y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) ) )'},\n",
              " {'hypotheses': ['62', '75'],\n",
              "  'id': '76',\n",
              "  'reference': 'sylibrd',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z < y -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) ) )'},\n",
              " {'hypotheses': ['4', '7', '10', '10', '13', '76'],\n",
              "  'id': '77',\n",
              "  'reference': 'nnind',\n",
              "  'statement': '$p |- ( ( y + 1 ) e. NN -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )'},\n",
              " {'hypotheses': ['1', '77'],\n",
              "  'id': '78',\n",
              "  'reference': 'syl',\n",
              "  'statement': '$p |- ( y e. NN -> A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) )'},\n",
              " {'hypotheses': ['65'],\n",
              "  'id': '79',\n",
              "  'reference': 'ltp1d',\n",
              "  'statement': '$p |- ( y e. NN -> y < ( y + 1 ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '80',\n",
              "  'reference': 'breq1',\n",
              "  'statement': '$p |- ( z = y -> ( z < ( y + 1 ) <-> y < ( y + 1 ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '81',\n",
              "  'reference': 'df-ne',\n",
              "  'statement': '$a |- ( ( sqrt ` 2 ) =/= ( x / y ) <-> -. ( sqrt ` 2 ) = ( x / y ) )'},\n",
              " {'hypotheses': ['58', '81'],\n",
              "  'id': '82',\n",
              "  'reference': 'syl6bb',\n",
              "  'statement': '$p |- ( z = y -> ( ( sqrt ` 2 ) =/= ( x / z ) <-> -. ( sqrt ` 2 ) = ( x / y ) ) )'},\n",
              " {'hypotheses': ['82'],\n",
              "  'id': '83',\n",
              "  'reference': 'ralbidv',\n",
              "  'statement': '$p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> A. x e. ZZ -. ( sqrt ` 2 ) = ( x / y ) ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '84',\n",
              "  'reference': 'ralnex',\n",
              "  'statement': '$p |- ( A. x e. ZZ -. ( sqrt ` 2 ) = ( x / y ) <-> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )'},\n",
              " {'hypotheses': ['83', '84'],\n",
              "  'id': '85',\n",
              "  'reference': 'syl6bb',\n",
              "  'statement': '$p |- ( z = y -> ( A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) <-> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) )'},\n",
              " {'hypotheses': ['80', '85'],\n",
              "  'id': '86',\n",
              "  'reference': 'imbi12d',\n",
              "  'statement': '$p |- ( z = y -> ( ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) <-> ( y < ( y + 1 ) -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) ) )'},\n",
              " {'hypotheses': ['86'],\n",
              "  'id': '87',\n",
              "  'reference': 'rspcv',\n",
              "  'statement': '$p |- ( y e. NN -> ( A. z e. NN ( z < ( y + 1 ) -> A. x e. ZZ ( sqrt ` 2 ) =/= ( x / z ) ) -> ( y < ( y + 1 ) -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) ) ) )'},\n",
              " {'hypotheses': ['78', '79', '87'],\n",
              "  'id': '88',\n",
              "  'reference': 'mp2d',\n",
              "  'statement': '$p |- ( y e. NN -> -. E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )'},\n",
              " {'hypotheses': ['88'],\n",
              "  'id': '89',\n",
              "  'reference': 'nrex',\n",
              "  'statement': '$p |- -. E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '90',\n",
              "  'reference': 'elq',\n",
              "  'statement': '$p |- ( ( sqrt ` 2 ) e. QQ <-> E. x e. ZZ E. y e. NN ( sqrt ` 2 ) = ( x / y ) )'},\n",
              " {'hypotheses': None,\n",
              "  'id': '91',\n",
              "  'reference': 'rexcom',\n",
              "  'statement': '$p |- ( E. x e. ZZ E. y e. NN ( sqrt ` 2 ) = ( x / y ) <-> E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )'},\n",
              " {'hypotheses': ['90', '91'],\n",
              "  'id': '92',\n",
              "  'reference': 'bitri',\n",
              "  'statement': '$p |- ( ( sqrt ` 2 ) e. QQ <-> E. y e. NN E. x e. ZZ ( sqrt ` 2 ) = ( x / y ) )'},\n",
              " {'hypotheses': ['89', '92'],\n",
              "  'id': '93',\n",
              "  'reference': 'mtbir',\n",
              "  'statement': '$p |- -. ( sqrt ` 2 ) e. QQ'},\n",
              " {'hypotheses': ['93'],\n",
              "  'id': '94',\n",
              "  'reference': 'nelir',\n",
              "  'statement': '$p |- ( sqrt ` 2 ) e/ QQ'}]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BaXmtegriSle"
      },
      "source": [
        "## Constructing a tree like structure out of the list"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ecq_2E3yD5Q6"
      },
      "source": [
        "import weakref\n",
        "\n",
        "class Node():\n",
        "  #Note that dictionaries are not weak referencable\n",
        "  def __init__(self,* ,id:int, hypotheses:list=None, reference:str=None, statement:str):\n",
        "    self.id=id\n",
        "    if hypotheses:\n",
        "      self.hypotheses = hypotheses #list of nodes\n",
        "    else :\n",
        "      self.hypotheses = []\n",
        "    self.reference = reference\n",
        "    self.statement = statement\n",
        "  def __str__(self):\n",
        "    outstring = \"<Node: Line Number: {}, Hypotheses: {}, Reference: {}, Statement:  {}>\"\n",
        "    return outstring.format(self.id,self.hypotheses,self.reference,self.statement)\n",
        "  def __repr__(self):\n",
        "    return self.__str__()\n",
        "\n",
        "node_dict = {node[\"id\"]:Node(id=node[\"id\"],hypotheses=node[\"hypotheses\"],reference=node[\"reference\"],statement=node[\"statement\"]) for node in raw_nodes}\n",
        "for node in node_dict.values():\n",
        "  #update ids to weak references\n",
        "  node.hypotheses = [weakref.proxy(node_dict[hypothesis_id]) for hypothesis_id in node.hypotheses]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4SNYALKO92k7"
      },
      "source": [
        "def create_node_dict(raw_nodes):\n",
        "  node_dict = {node[\"id\"]:Node(id=node[\"id\"],hypotheses=node[\"hypotheses\"],reference=node[\"reference\"],statement=node[\"statement\"]) for node in raw_nodes}\n",
        "  for node in node_dict.values():\n",
        "    #update ids to weak references\n",
        "    node.hypotheses = [weakref.proxy(node_dict[hypothesis_id]) for hypothesis_id in node.hypotheses]\n",
        "  return node_dict"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-u5eeLgM7SqH"
      },
      "source": [
        "##Visualizing the graph like structure\n",
        "https://stackoverflow.com/questions/7670280/tree-plotting-in-python\n",
        "networkx matplotlib graphviz http://etetoolkit.org/"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iCItskE_8J3P",
        "outputId": "b0082f23-6a57-44f2-a07e-af1662df27c1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "#https://graphviz.readthedocs.io/en/stable/manual.html#jupyter-notebooks\n",
        "from graphviz import Graph\n",
        "g = Graph(format='svg')\n",
        "for node in node_dict.values():\n",
        "  for hypothesis in node.hypotheses:\n",
        "    g.edge(node.id,hypothesis.id)\n",
        "#to save a file use g.render()\n",
        "g"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Graph at 0x7fc9dec40780>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: %3 Pages: 1 -->\n<svg width=\"824pt\" height=\"1484pt\"\n viewBox=\"0.00 0.00 824.00 1484.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 1480)\">\n<title>%3</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-1480 820,-1480 820,4 -4,4\"/>\n<!-- 3 -->\n<g id=\"node1\" class=\"node\">\n<title>3</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"154\" cy=\"-954\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"154\" y=\"-950.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">3</text>\n</g>\n<!-- 2 -->\n<g id=\"node2\" class=\"node\">\n<title>2</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"154\" cy=\"-882\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"154\" y=\"-878.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">2</text>\n</g>\n<!-- 3&#45;&#45;2 -->\n<g id=\"edge1\" class=\"edge\">\n<title>3&#45;&#45;2</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M154,-935.8314C154,-925 154,-911.2876 154,-900.4133\"/>\n</g>\n<!-- 4 -->\n<g id=\"node3\" class=\"node\">\n<title>4</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"154\" cy=\"-1026\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"154\" y=\"-1022.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">4</text>\n</g>\n<!-- 4&#45;&#45;3 -->\n<g id=\"edge2\" class=\"edge\">\n<title>4&#45;&#45;3</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M154,-1007.8314C154,-997 154,-983.2876 154,-972.4133\"/>\n</g>\n<!-- 6 -->\n<g id=\"node4\" class=\"node\">\n<title>6</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"370\" cy=\"-954\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"370\" y=\"-950.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">6</text>\n</g>\n<!-- 5 -->\n<g id=\"node5\" class=\"node\">\n<title>5</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"442\" cy=\"-882\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"442\" y=\"-878.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">5</text>\n</g>\n<!-- 6&#45;&#45;5 -->\n<g id=\"edge3\" class=\"edge\">\n<title>6&#45;&#45;5</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M385.2693,-938.7307C397.488,-926.512 414.5398,-909.4602 426.7527,-897.2473\"/>\n</g>\n<!-- 7 -->\n<g id=\"node6\" class=\"node\">\n<title>7</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"298\" cy=\"-1026\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"298\" y=\"-1022.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">7</text>\n</g>\n<!-- 7&#45;&#45;6 -->\n<g id=\"edge4\" class=\"edge\">\n<title>7&#45;&#45;6</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M313.2693,-1010.7307C325.488,-998.512 342.5398,-981.4602 354.7527,-969.2473\"/>\n</g>\n<!-- 9 -->\n<g id=\"node7\" class=\"node\">\n<title>9</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"442\" cy=\"-954\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"442\" y=\"-950.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">9</text>\n</g>\n<!-- 8 -->\n<g id=\"node8\" class=\"node\">\n<title>8</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"514\" cy=\"-882\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"514\" y=\"-878.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">8</text>\n</g>\n<!-- 9&#45;&#45;8 -->\n<g id=\"edge5\" class=\"edge\">\n<title>9&#45;&#45;8</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M457.2693,-938.7307C469.488,-926.512 486.5398,-909.4602 498.7527,-897.2473\"/>\n</g>\n<!-- 10 -->\n<g id=\"node9\" class=\"node\">\n<title>10</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"370\" cy=\"-1026\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"370\" y=\"-1022.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">10</text>\n</g>\n<!-- 10&#45;&#45;9 -->\n<g id=\"edge6\" class=\"edge\">\n<title>10&#45;&#45;9</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M385.2693,-1010.7307C397.488,-998.512 414.5398,-981.4602 426.7527,-969.2473\"/>\n</g>\n<!-- 12 -->\n<g id=\"node10\" class=\"node\">\n<title>12</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"82\" cy=\"-954\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"82\" y=\"-950.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">12</text>\n</g>\n<!-- 11 -->\n<g id=\"node11\" class=\"node\">\n<title>11</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"82\" cy=\"-882\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"82\" y=\"-878.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">11</text>\n</g>\n<!-- 12&#45;&#45;11 -->\n<g id=\"edge7\" class=\"edge\">\n<title>12&#45;&#45;11</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M82,-935.8314C82,-925 82,-911.2876 82,-900.4133\"/>\n</g>\n<!-- 13 -->\n<g id=\"node12\" class=\"node\">\n<title>13</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"82\" cy=\"-1026\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"82\" y=\"-1022.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">13</text>\n</g>\n<!-- 13&#45;&#45;12 -->\n<g id=\"edge8\" class=\"edge\">\n<title>13&#45;&#45;12</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M82,-1007.8314C82,-997 82,-983.2876 82,-972.4133\"/>\n</g>\n<!-- 16 -->\n<g id=\"node13\" class=\"node\">\n<title>16</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"387\" cy=\"-594\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"387\" y=\"-590.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">16</text>\n</g>\n<!-- 14 -->\n<g id=\"node14\" class=\"node\">\n<title>14</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"444\" cy=\"-522\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"444\" y=\"-518.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">14</text>\n</g>\n<!-- 16&#45;&#45;14 -->\n<g id=\"edge9\" class=\"edge\">\n<title>16&#45;&#45;14</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M399.6501,-578.0209C409.096,-566.0892 421.9479,-549.8553 431.3852,-537.9345\"/>\n</g>\n<!-- 15 -->\n<g id=\"node15\" class=\"node\">\n<title>15</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"372\" cy=\"-522\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"372\" y=\"-518.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">15</text>\n</g>\n<!-- 16&#45;&#45;15 -->\n<g id=\"edge10\" class=\"edge\">\n<title>16&#45;&#45;15</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M383.2149,-575.8314C380.9236,-564.8334 378.0135,-550.865 375.732,-539.9134\"/>\n</g>\n<!-- 19 -->\n<g id=\"node16\" class=\"node\">\n<title>19</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"169\" cy=\"-306\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"169\" y=\"-302.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">19</text>\n</g>\n<!-- 18 -->\n<g id=\"node17\" class=\"node\">\n<title>18</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"166\" cy=\"-234\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"166\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">18</text>\n</g>\n<!-- 19&#45;&#45;18 -->\n<g id=\"edge11\" class=\"edge\">\n<title>19&#45;&#45;18</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M168.243,-287.8314C167.7917,-277 167.2203,-263.2876 166.7672,-252.4133\"/>\n</g>\n<!-- 20 -->\n<g id=\"node18\" class=\"node\">\n<title>20</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"175\" cy=\"-378\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"175\" y=\"-374.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">20</text>\n</g>\n<!-- 20&#45;&#45;19 -->\n<g id=\"edge12\" class=\"edge\">\n<title>20&#45;&#45;19</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M173.4859,-359.8314C172.5833,-349 171.4406,-335.2876 170.5344,-324.4133\"/>\n</g>\n<!-- 21 -->\n<g id=\"node19\" class=\"node\">\n<title>21</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"259\" cy=\"-450\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"259\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">21</text>\n</g>\n<!-- 21&#45;&#45;20 -->\n<g id=\"edge14\" class=\"edge\">\n<title>21&#45;&#45;20</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M242.4043,-435.7751C227.7736,-423.2345 206.5548,-405.047 191.8487,-392.4418\"/>\n</g>\n<!-- 17 -->\n<g id=\"node20\" class=\"node\">\n<title>17</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"259\" cy=\"-378\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"259\" y=\"-374.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">17</text>\n</g>\n<!-- 21&#45;&#45;17 -->\n<g id=\"edge13\" class=\"edge\">\n<title>21&#45;&#45;17</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M259,-431.8314C259,-421 259,-407.2876 259,-396.4133\"/>\n</g>\n<!-- 22 -->\n<g id=\"node21\" class=\"node\">\n<title>22</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"286\" cy=\"-522\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"286\" y=\"-518.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">22</text>\n</g>\n<!-- 22&#45;&#45;21 -->\n<g id=\"edge15\" class=\"edge\">\n<title>22&#45;&#45;21</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M279.3258,-504.2022C275.1407,-493.0419 269.7679,-478.7143 265.5974,-467.593\"/>\n</g>\n<!-- 23 -->\n<g id=\"node22\" class=\"node\">\n<title>23</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"315\" cy=\"-594\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"315\" y=\"-590.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">23</text>\n</g>\n<!-- 23&#45;&#45;22 -->\n<g id=\"edge16\" class=\"edge\">\n<title>23&#45;&#45;22</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M307.9799,-576.5708C303.4539,-565.3339 297.589,-550.7727 293.056,-539.5182\"/>\n</g>\n<!-- 24 -->\n<g id=\"node23\" class=\"node\">\n<title>24</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"375\" cy=\"-666\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"375\" y=\"-662.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">24</text>\n</g>\n<!-- 24&#45;&#45;16 -->\n<g id=\"edge17\" class=\"edge\">\n<title>24&#45;&#45;16</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M378.0281,-647.8314C379.8611,-636.8334 382.1892,-622.865 384.0144,-611.9134\"/>\n</g>\n<!-- 24&#45;&#45;23 -->\n<g id=\"edge18\" class=\"edge\">\n<title>24&#45;&#45;23</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M361.6841,-650.0209C351.741,-638.0892 338.2128,-621.8553 328.2787,-609.9345\"/>\n</g>\n<!-- 27 -->\n<g id=\"node24\" class=\"node\">\n<title>27</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"310\" cy=\"-234\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"310\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">27</text>\n</g>\n<!-- 26 -->\n<g id=\"node25\" class=\"node\">\n<title>26</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"310\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"310\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">26</text>\n</g>\n<!-- 27&#45;&#45;26 -->\n<g id=\"edge19\" class=\"edge\">\n<title>27&#45;&#45;26</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M310,-215.8314C310,-205 310,-191.2876 310,-180.4133\"/>\n</g>\n<!-- 29 -->\n<g id=\"node26\" class=\"node\">\n<title>29</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"382\" cy=\"-234\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"382\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">29</text>\n</g>\n<!-- 28 -->\n<g id=\"node27\" class=\"node\">\n<title>28</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"382\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"382\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">28</text>\n</g>\n<!-- 29&#45;&#45;28 -->\n<g id=\"edge20\" class=\"edge\">\n<title>29&#45;&#45;28</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M382,-215.8314C382,-205 382,-191.2876 382,-180.4133\"/>\n</g>\n<!-- 32 -->\n<g id=\"node28\" class=\"node\">\n<title>32</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"454\" cy=\"-234\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"454\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">32</text>\n</g>\n<!-- 31 -->\n<g id=\"node29\" class=\"node\">\n<title>31</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"454\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"454\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">31</text>\n</g>\n<!-- 32&#45;&#45;31 -->\n<g id=\"edge21\" class=\"edge\">\n<title>32&#45;&#45;31</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M454,-215.8314C454,-205 454,-191.2876 454,-180.4133\"/>\n</g>\n<!-- 34 -->\n<g id=\"node30\" class=\"node\">\n<title>34</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"526\" cy=\"-234\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"526\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">34</text>\n</g>\n<!-- 33 -->\n<g id=\"node31\" class=\"node\">\n<title>33</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"526\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"526\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">33</text>\n</g>\n<!-- 34&#45;&#45;33 -->\n<g id=\"edge22\" class=\"edge\">\n<title>34&#45;&#45;33</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M526,-215.8314C526,-205 526,-191.2876 526,-180.4133\"/>\n</g>\n<!-- 35 -->\n<g id=\"node32\" class=\"node\">\n<title>35</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"418\" cy=\"-306\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"418\" y=\"-302.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">35</text>\n</g>\n<!-- 35&#45;&#45;27 -->\n<g id=\"edge23\" class=\"edge\">\n<title>35&#45;&#45;27</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M398.6918,-293.1278C379.0337,-280.0225 348.7386,-259.8257 329.1411,-246.7607\"/>\n</g>\n<!-- 35&#45;&#45;29 -->\n<g id=\"edge24\" class=\"edge\">\n<title>35&#45;&#45;29</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M409.2854,-288.5708C403.6253,-277.2506 396.2784,-262.5568 390.6343,-251.2687\"/>\n</g>\n<!-- 35&#45;&#45;32 -->\n<g id=\"edge26\" class=\"edge\">\n<title>35&#45;&#45;32</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M426.7146,-288.5708C432.3747,-277.2506 439.7216,-262.5568 445.3657,-251.2687\"/>\n</g>\n<!-- 35&#45;&#45;34 -->\n<g id=\"edge27\" class=\"edge\">\n<title>35&#45;&#45;34</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M437.3082,-293.1278C456.9663,-280.0225 487.2614,-259.8257 506.8589,-246.7607\"/>\n</g>\n<!-- 30 -->\n<g id=\"node33\" class=\"node\">\n<title>30</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"238\" cy=\"-234\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"238\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">30</text>\n</g>\n<!-- 35&#45;&#45;30 -->\n<g id=\"edge25\" class=\"edge\">\n<title>35&#45;&#45;30</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M393.7416,-297.7783C364.869,-287.7927 315.3615,-270.0365 274,-252 269.2601,-249.9331 264.2525,-247.5571 259.5278,-245.2234\"/>\n</g>\n<!-- 36 -->\n<g id=\"node34\" class=\"node\">\n<title>36</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"578\" cy=\"-378\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"578\" y=\"-374.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">36</text>\n</g>\n<!-- 36&#45;&#45;35 -->\n<g id=\"edge29\" class=\"edge\">\n<title>36&#45;&#45;35</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M555.4153,-367.8369C524.9214,-354.1146 470.9045,-329.807 440.4699,-316.1114\"/>\n</g>\n<!-- 25 -->\n<g id=\"node35\" class=\"node\">\n<title>25</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"573\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"573\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">25</text>\n</g>\n<!-- 36&#45;&#45;25 -->\n<g id=\"edge28\" class=\"edge\">\n<title>36&#45;&#45;25</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M578.6216,-359.8172C579.5003,-332.504 581,-279.2598 581,-234 581,-234 581,-234 581,-162 581,-116.6802 577.0009,-63.4608 574.6576,-36.1674\"/>\n</g>\n<!-- 39 -->\n<g id=\"node36\" class=\"node\">\n<title>39</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"717\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"717\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">39</text>\n</g>\n<!-- 39&#45;&#45;25 -->\n<g id=\"edge32\" class=\"edge\">\n<title>39&#45;&#45;25</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M695.1295,-79.0647C667.9066,-65.4533 621.703,-42.3515 594.6045,-28.8022\"/>\n</g>\n<!-- 37 -->\n<g id=\"node37\" class=\"node\">\n<title>37</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"717\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"717\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">37</text>\n</g>\n<!-- 39&#45;&#45;37 -->\n<g id=\"edge30\" class=\"edge\">\n<title>39&#45;&#45;37</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M717,-71.8314C717,-61 717,-47.2876 717,-36.4133\"/>\n</g>\n<!-- 38 -->\n<g id=\"node38\" class=\"node\">\n<title>38</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"789\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"789\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">38</text>\n</g>\n<!-- 39&#45;&#45;38 -->\n<g id=\"edge31\" class=\"edge\">\n<title>39&#45;&#45;38</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M732.2693,-74.7307C744.488,-62.512 761.5398,-45.4602 773.7527,-33.2473\"/>\n</g>\n<!-- 40 -->\n<g id=\"node39\" class=\"node\">\n<title>40</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"782\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"782\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">40</text>\n</g>\n<!-- 40&#45;&#45;39 -->\n<g id=\"edge33\" class=\"edge\">\n<title>40&#45;&#45;39</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M767.896,-146.3771C756.9933,-134.3003 741.9722,-117.6616 731.0765,-105.5924\"/>\n</g>\n<!-- 41 -->\n<g id=\"node40\" class=\"node\">\n<title>41</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"710\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"710\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">41</text>\n</g>\n<!-- 41&#45;&#45;39 -->\n<g id=\"edge34\" class=\"edge\">\n<title>41&#45;&#45;39</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M711.7664,-143.8314C712.8194,-133 714.1526,-119.2876 715.2098,-108.4133\"/>\n</g>\n<!-- 43 -->\n<g id=\"node41\" class=\"node\">\n<title>43</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"642\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"642\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">43</text>\n</g>\n<!-- 42 -->\n<g id=\"node42\" class=\"node\">\n<title>42</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"645\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"645\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">42</text>\n</g>\n<!-- 43&#45;&#45;42 -->\n<g id=\"edge35\" class=\"edge\">\n<title>43&#45;&#45;42</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M642.757,-71.8314C643.2083,-61 643.7797,-47.2876 644.2328,-36.4133\"/>\n</g>\n<!-- 44 -->\n<g id=\"node43\" class=\"node\">\n<title>44</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"638\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"638\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">44</text>\n</g>\n<!-- 44&#45;&#45;43 -->\n<g id=\"edge36\" class=\"edge\">\n<title>44&#45;&#45;43</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M639.0094,-143.8314C639.6111,-133 640.3729,-119.2876 640.977,-108.4133\"/>\n</g>\n<!-- 45 -->\n<g id=\"node44\" class=\"node\">\n<title>45</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"672\" cy=\"-234\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"672\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">45</text>\n</g>\n<!-- 45&#45;&#45;41 -->\n<g id=\"edge37\" class=\"edge\">\n<title>45&#45;&#45;41</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M681.0055,-216.937C686.9752,-205.626 694.7851,-190.8282 700.7952,-179.4407\"/>\n</g>\n<!-- 45&#45;&#45;44 -->\n<g id=\"edge38\" class=\"edge\">\n<title>45&#45;&#45;44</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M663.7695,-216.5708C658.4239,-205.2506 651.4852,-190.5568 646.1547,-179.2687\"/>\n</g>\n<!-- 46 -->\n<g id=\"node45\" class=\"node\">\n<title>46</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"672\" cy=\"-306\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"672\" y=\"-302.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">46</text>\n</g>\n<!-- 46&#45;&#45;40 -->\n<g id=\"edge39\" class=\"edge\">\n<title>46&#45;&#45;40</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M684.4046,-289.7613C705.5309,-262.105 748.2618,-206.1664 769.472,-178.4003\"/>\n</g>\n<!-- 46&#45;&#45;45 -->\n<g id=\"edge40\" class=\"edge\">\n<title>46&#45;&#45;45</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M672,-287.8314C672,-277 672,-263.2876 672,-252.4133\"/>\n</g>\n<!-- 47 -->\n<g id=\"node46\" class=\"node\">\n<title>47</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"665\" cy=\"-378\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"665\" y=\"-374.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">47</text>\n</g>\n<!-- 47&#45;&#45;46 -->\n<g id=\"edge41\" class=\"edge\">\n<title>47&#45;&#45;46</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M666.7664,-359.8314C667.8194,-349 669.1526,-335.2876 670.2098,-324.4133\"/>\n</g>\n<!-- 48 -->\n<g id=\"node47\" class=\"node\">\n<title>48</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"578\" cy=\"-450\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"578\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">48</text>\n</g>\n<!-- 48&#45;&#45;36 -->\n<g id=\"edge42\" class=\"edge\">\n<title>48&#45;&#45;36</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M578,-431.8314C578,-421 578,-407.2876 578,-396.4133\"/>\n</g>\n<!-- 48&#45;&#45;47 -->\n<g id=\"edge43\" class=\"edge\">\n<title>48&#45;&#45;47</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M595.1884,-435.7751C610.4407,-423.1525 632.6058,-404.809 647.8473,-392.1953\"/>\n</g>\n<!-- 49 -->\n<g id=\"node48\" class=\"node\">\n<title>49</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"523\" cy=\"-522\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"523\" y=\"-518.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">49</text>\n</g>\n<!-- 49&#45;&#45;48 -->\n<g id=\"edge44\" class=\"edge\">\n<title>49&#45;&#45;48</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M535.4804,-505.6621C544.4814,-493.8788 556.5793,-478.0416 565.569,-466.2733\"/>\n</g>\n<!-- 50 -->\n<g id=\"node49\" class=\"node\">\n<title>50</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"459\" cy=\"-594\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"459\" y=\"-590.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">50</text>\n</g>\n<!-- 50&#45;&#45;49 -->\n<g id=\"edge45\" class=\"edge\">\n<title>50&#45;&#45;49</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M472.887,-578.3771C483.622,-566.3003 498.4119,-549.6616 509.1401,-537.5924\"/>\n</g>\n<!-- 51 -->\n<g id=\"node50\" class=\"node\">\n<title>51</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"455\" cy=\"-666\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"455\" y=\"-662.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">51</text>\n</g>\n<!-- 51&#45;&#45;50 -->\n<g id=\"edge46\" class=\"edge\">\n<title>51&#45;&#45;50</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M456.0094,-647.8314C456.6111,-637 457.3729,-623.2876 457.977,-612.4133\"/>\n</g>\n<!-- 52 -->\n<g id=\"node51\" class=\"node\">\n<title>52</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"375\" cy=\"-738\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"375\" y=\"-734.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">52</text>\n</g>\n<!-- 52&#45;&#45;24 -->\n<g id=\"edge47\" class=\"edge\">\n<title>52&#45;&#45;24</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M375,-719.8314C375,-709 375,-695.2876 375,-684.4133\"/>\n</g>\n<!-- 52&#45;&#45;51 -->\n<g id=\"edge48\" class=\"edge\">\n<title>52&#45;&#45;51</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M391.1892,-723.4297C405.0688,-710.938 424.9622,-693.034 438.8349,-680.5486\"/>\n</g>\n<!-- 54 -->\n<g id=\"node52\" class=\"node\">\n<title>54</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"284\" cy=\"-666\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"284\" y=\"-662.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">54</text>\n</g>\n<!-- 53 -->\n<g id=\"node53\" class=\"node\">\n<title>53</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"243\" cy=\"-594\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"243\" y=\"-590.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">53</text>\n</g>\n<!-- 54&#45;&#45;53 -->\n<g id=\"edge49\" class=\"edge\">\n<title>54&#45;&#45;53</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M274.2836,-648.937C267.7478,-637.4596 259.1678,-622.3922 252.6467,-610.9405\"/>\n</g>\n<!-- 55 -->\n<g id=\"node54\" class=\"node\">\n<title>55</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"292\" cy=\"-738\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"292\" y=\"-734.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">55</text>\n</g>\n<!-- 55&#45;&#45;54 -->\n<g id=\"edge50\" class=\"edge\">\n<title>55&#45;&#45;54</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M289.9813,-719.8314C288.7778,-709 287.2542,-695.2876 286.0459,-684.4133\"/>\n</g>\n<!-- 56 -->\n<g id=\"node55\" class=\"node\">\n<title>56</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"370\" cy=\"-810\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"370\" y=\"-806.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">56</text>\n</g>\n<!-- 56&#45;&#45;52 -->\n<g id=\"edge51\" class=\"edge\">\n<title>56&#45;&#45;52</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M371.2617,-791.8314C372.0139,-781 372.9661,-767.2876 373.7213,-756.4133\"/>\n</g>\n<!-- 56&#45;&#45;55 -->\n<g id=\"edge52\" class=\"edge\">\n<title>56&#45;&#45;55</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M353.8383,-795.0816C340.3624,-782.6422 321.2693,-765.0178 307.8741,-752.653\"/>\n</g>\n<!-- 58 -->\n<g id=\"node56\" class=\"node\">\n<title>58</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"531\" cy=\"-666\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"531\" y=\"-662.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">58</text>\n</g>\n<!-- 57 -->\n<g id=\"node57\" class=\"node\">\n<title>57</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"531\" cy=\"-594\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"531\" y=\"-590.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">57</text>\n</g>\n<!-- 58&#45;&#45;57 -->\n<g id=\"edge53\" class=\"edge\">\n<title>58&#45;&#45;57</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M531,-647.8314C531,-637 531,-623.2876 531,-612.4133\"/>\n</g>\n<!-- 59 -->\n<g id=\"node58\" class=\"node\">\n<title>59</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"468\" cy=\"-738\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"468\" y=\"-734.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">59</text>\n</g>\n<!-- 59&#45;&#45;58 -->\n<g id=\"edge54\" class=\"edge\">\n<title>59&#45;&#45;58</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M481.6701,-722.3771C492.2373,-710.3003 506.7961,-693.6616 517.3566,-681.5924\"/>\n</g>\n<!-- 60 -->\n<g id=\"node59\" class=\"node\">\n<title>60</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"459\" cy=\"-810\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"459\" y=\"-806.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">60</text>\n</g>\n<!-- 60&#45;&#45;59 -->\n<g id=\"edge55\" class=\"edge\">\n<title>60&#45;&#45;59</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M461.2711,-791.8314C462.625,-781 464.3391,-767.2876 465.6983,-756.4133\"/>\n</g>\n<!-- 61 -->\n<g id=\"node60\" class=\"node\">\n<title>61</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"370\" cy=\"-882\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"370\" y=\"-878.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">61</text>\n</g>\n<!-- 61&#45;&#45;56 -->\n<g id=\"edge56\" class=\"edge\">\n<title>61&#45;&#45;56</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M370,-863.8314C370,-853 370,-839.2876 370,-828.4133\"/>\n</g>\n<!-- 61&#45;&#45;60 -->\n<g id=\"edge57\" class=\"edge\">\n<title>61&#45;&#45;60</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M387.5835,-867.7751C403.2878,-855.0706 426.1559,-836.5705 441.7558,-823.9503\"/>\n</g>\n<!-- 62 -->\n<g id=\"node61\" class=\"node\">\n<title>62</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"298\" cy=\"-954\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"298\" y=\"-950.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">62</text>\n</g>\n<!-- 62&#45;&#45;61 -->\n<g id=\"edge58\" class=\"edge\">\n<title>62&#45;&#45;61</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M313.2693,-938.7307C325.488,-926.512 342.5398,-909.4602 354.7527,-897.2473\"/>\n</g>\n<!-- 67 -->\n<g id=\"node62\" class=\"node\">\n<title>67</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"99\" cy=\"-522\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-518.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">67</text>\n</g>\n<!-- 64 -->\n<g id=\"node63\" class=\"node\">\n<title>64</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"99\" cy=\"-450\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">64</text>\n</g>\n<!-- 67&#45;&#45;64 -->\n<g id=\"edge59\" class=\"edge\">\n<title>67&#45;&#45;64</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M99,-503.8314C99,-493 99,-479.2876 99,-468.4133\"/>\n</g>\n<!-- 65 -->\n<g id=\"node64\" class=\"node\">\n<title>65</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-450\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">65</text>\n</g>\n<!-- 67&#45;&#45;65 -->\n<g id=\"edge60\" class=\"edge\">\n<title>67&#45;&#45;65</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M83.7307,-506.7307C71.512,-494.512 54.4602,-477.4602 42.2473,-465.2473\"/>\n</g>\n<!-- 66 -->\n<g id=\"node65\" class=\"node\">\n<title>66</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"171\" cy=\"-450\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"171\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">66</text>\n</g>\n<!-- 67&#45;&#45;66 -->\n<g id=\"edge61\" class=\"edge\">\n<title>67&#45;&#45;66</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M114.2693,-506.7307C126.488,-494.512 143.5398,-477.4602 155.7527,-465.2473\"/>\n</g>\n<!-- 68 -->\n<g id=\"node66\" class=\"node\">\n<title>68</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"171\" cy=\"-594\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"171\" y=\"-590.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">68</text>\n</g>\n<!-- 68&#45;&#45;67 -->\n<g id=\"edge63\" class=\"edge\">\n<title>68&#45;&#45;67</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M155.7307,-578.7307C143.512,-566.512 126.4602,-549.4602 114.2473,-537.2473\"/>\n</g>\n<!-- 63 -->\n<g id=\"node67\" class=\"node\">\n<title>63</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"171\" cy=\"-522\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"171\" y=\"-518.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">63</text>\n</g>\n<!-- 68&#45;&#45;63 -->\n<g id=\"edge62\" class=\"edge\">\n<title>68&#45;&#45;63</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M171,-575.8314C171,-565 171,-551.2876 171,-540.4133\"/>\n</g>\n<!-- 69 -->\n<g id=\"node68\" class=\"node\">\n<title>69</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"198\" cy=\"-666\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"198\" y=\"-662.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">69</text>\n</g>\n<!-- 69&#45;&#45;68 -->\n<g id=\"edge64\" class=\"edge\">\n<title>69&#45;&#45;68</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M191.3258,-648.2022C187.1407,-637.0419 181.7679,-622.7143 177.5974,-611.593\"/>\n</g>\n<!-- 70 -->\n<g id=\"node69\" class=\"node\">\n<title>70</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"218\" cy=\"-738\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"218\" y=\"-734.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">70</text>\n</g>\n<!-- 70&#45;&#45;69 -->\n<g id=\"edge65\" class=\"edge\">\n<title>70&#45;&#45;69</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M213.0562,-720.2022C209.9792,-709.1252 206.0356,-694.928 202.9563,-683.8425\"/>\n</g>\n<!-- 72 -->\n<g id=\"node70\" class=\"node\">\n<title>72</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"218\" cy=\"-810\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"218\" y=\"-806.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">72</text>\n</g>\n<!-- 72&#45;&#45;70 -->\n<g id=\"edge66\" class=\"edge\">\n<title>72&#45;&#45;70</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M218,-791.8314C218,-781 218,-767.2876 218,-756.4133\"/>\n</g>\n<!-- 71 -->\n<g id=\"node71\" class=\"node\">\n<title>71</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"146\" cy=\"-738\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"146\" y=\"-734.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">71</text>\n</g>\n<!-- 72&#45;&#45;71 -->\n<g id=\"edge67\" class=\"edge\">\n<title>72&#45;&#45;71</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M202.7307,-794.7307C190.512,-782.512 173.4602,-765.4602 161.2473,-753.2473\"/>\n</g>\n<!-- 73 -->\n<g id=\"node72\" class=\"node\">\n<title>73</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"226\" cy=\"-882\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"226\" y=\"-878.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">73</text>\n</g>\n<!-- 73&#45;&#45;72 -->\n<g id=\"edge68\" class=\"edge\">\n<title>73&#45;&#45;72</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M223.9813,-863.8314C222.7778,-853 221.2542,-839.2876 220.0459,-828.4133\"/>\n</g>\n<!-- 75 -->\n<g id=\"node73\" class=\"node\">\n<title>75</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"226\" cy=\"-954\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"226\" y=\"-950.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">75</text>\n</g>\n<!-- 75&#45;&#45;73 -->\n<g id=\"edge69\" class=\"edge\">\n<title>75&#45;&#45;73</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M226,-935.8314C226,-925 226,-911.2876 226,-900.4133\"/>\n</g>\n<!-- 74 -->\n<g id=\"node74\" class=\"node\">\n<title>74</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"298\" cy=\"-882\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"298\" y=\"-878.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">74</text>\n</g>\n<!-- 75&#45;&#45;74 -->\n<g id=\"edge70\" class=\"edge\">\n<title>75&#45;&#45;74</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M241.2693,-938.7307C253.488,-926.512 270.5398,-909.4602 282.7527,-897.2473\"/>\n</g>\n<!-- 76 -->\n<g id=\"node75\" class=\"node\">\n<title>76</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"226\" cy=\"-1026\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"226\" y=\"-1022.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">76</text>\n</g>\n<!-- 76&#45;&#45;62 -->\n<g id=\"edge71\" class=\"edge\">\n<title>76&#45;&#45;62</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M241.2693,-1010.7307C253.488,-998.512 270.5398,-981.4602 282.7527,-969.2473\"/>\n</g>\n<!-- 76&#45;&#45;75 -->\n<g id=\"edge72\" class=\"edge\">\n<title>76&#45;&#45;75</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M226,-1007.8314C226,-997 226,-983.2876 226,-972.4133\"/>\n</g>\n<!-- 77 -->\n<g id=\"node76\" class=\"node\">\n<title>77</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"262\" cy=\"-1098\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"262\" y=\"-1094.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">77</text>\n</g>\n<!-- 77&#45;&#45;4 -->\n<g id=\"edge73\" class=\"edge\">\n<title>77&#45;&#45;4</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M242.6918,-1085.1278C223.0337,-1072.0225 192.7386,-1051.8257 173.1411,-1038.7607\"/>\n</g>\n<!-- 77&#45;&#45;7 -->\n<g id=\"edge74\" class=\"edge\">\n<title>77&#45;&#45;7</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M270.7146,-1080.5708C276.3747,-1069.2506 283.7216,-1054.5568 289.3657,-1043.2687\"/>\n</g>\n<!-- 77&#45;&#45;10 -->\n<g id=\"edge75\" class=\"edge\">\n<title>77&#45;&#45;10</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M278.3068,-1083.4297C297.1325,-1069.7053 327.6939,-1049.4476 348.4446,-1037.021\"/>\n</g>\n<!-- 77&#45;&#45;10 -->\n<g id=\"edge76\" class=\"edge\">\n<title>77&#45;&#45;10</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M283.6743,-1086.9078C304.4767,-1074.4427 335.0623,-1054.1632 353.8398,-1040.4634\"/>\n</g>\n<!-- 77&#45;&#45;13 -->\n<g id=\"edge77\" class=\"edge\">\n<title>77&#45;&#45;13</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M240.5289,-1086.643C235.8008,-1084.3177 230.7773,-1081.9788 226,-1080 179.255,-1060.6376 164.745,-1063.3624 118,-1044 113.2227,-1042.0212 108.1992,-1039.6823 103.4711,-1037.357\"/>\n</g>\n<!-- 77&#45;&#45;76 -->\n<g id=\"edge78\" class=\"edge\">\n<title>77&#45;&#45;76</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M253.2854,-1080.5708C247.6253,-1069.2506 240.2784,-1054.5568 234.6343,-1043.2687\"/>\n</g>\n<!-- 78 -->\n<g id=\"node77\" class=\"node\">\n<title>78</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"226\" cy=\"-1170\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"226\" y=\"-1166.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">78</text>\n</g>\n<!-- 78&#45;&#45;77 -->\n<g id=\"edge80\" class=\"edge\">\n<title>78&#45;&#45;77</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M234.7146,-1152.5708C240.3747,-1141.2506 247.7216,-1126.5568 253.3657,-1115.2687\"/>\n</g>\n<!-- 1 -->\n<g id=\"node78\" class=\"node\">\n<title>1</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"190\" cy=\"-1098\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"190\" y=\"-1094.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">1</text>\n</g>\n<!-- 78&#45;&#45;1 -->\n<g id=\"edge79\" class=\"edge\">\n<title>78&#45;&#45;1</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M217.2854,-1152.5708C211.6253,-1141.2506 204.2784,-1126.5568 198.6343,-1115.2687\"/>\n</g>\n<!-- 79 -->\n<g id=\"node79\" class=\"node\">\n<title>79</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"91\" cy=\"-1170\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"91\" y=\"-1166.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">79</text>\n</g>\n<!-- 79&#45;&#45;65 -->\n<g id=\"edge81\" class=\"edge\">\n<title>79&#45;&#45;65</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M78.3557,-1153.7632C59.7041,-1128.1369 27,-1076.065 27,-1026 27,-1026 27,-1026 27,-594 27,-548.75 27,-495.5017 27,-468.1854\"/>\n</g>\n<!-- 82 -->\n<g id=\"node80\" class=\"node\">\n<title>82</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"586\" cy=\"-882\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"586\" y=\"-878.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">82</text>\n</g>\n<!-- 82&#45;&#45;58 -->\n<g id=\"edge82\" class=\"edge\">\n<title>82&#45;&#45;58</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M572.4564,-866.0904C564.544,-855.8797 555.1331,-841.959 550,-828 531.7239,-778.2995 530.01,-714.7676 530.4137,-684.1306\"/>\n</g>\n<!-- 81 -->\n<g id=\"node81\" class=\"node\">\n<title>81</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"586\" cy=\"-810\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"586\" y=\"-806.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">81</text>\n</g>\n<!-- 82&#45;&#45;81 -->\n<g id=\"edge83\" class=\"edge\">\n<title>82&#45;&#45;81</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M586,-863.8314C586,-853 586,-839.2876 586,-828.4133\"/>\n</g>\n<!-- 83 -->\n<g id=\"node82\" class=\"node\">\n<title>83</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"586\" cy=\"-954\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"586\" y=\"-950.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">83</text>\n</g>\n<!-- 83&#45;&#45;82 -->\n<g id=\"edge84\" class=\"edge\">\n<title>83&#45;&#45;82</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M586,-935.8314C586,-925 586,-911.2876 586,-900.4133\"/>\n</g>\n<!-- 85 -->\n<g id=\"node83\" class=\"node\">\n<title>85</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"514\" cy=\"-1026\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"514\" y=\"-1022.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">85</text>\n</g>\n<!-- 85&#45;&#45;83 -->\n<g id=\"edge85\" class=\"edge\">\n<title>85&#45;&#45;83</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M529.2693,-1010.7307C541.488,-998.512 558.5398,-981.4602 570.7527,-969.2473\"/>\n</g>\n<!-- 84 -->\n<g id=\"node84\" class=\"node\">\n<title>84</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"514\" cy=\"-954\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"514\" y=\"-950.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">84</text>\n</g>\n<!-- 85&#45;&#45;84 -->\n<g id=\"edge86\" class=\"edge\">\n<title>85&#45;&#45;84</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M514,-1007.8314C514,-997 514,-983.2876 514,-972.4133\"/>\n</g>\n<!-- 86 -->\n<g id=\"node85\" class=\"node\">\n<title>86</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"442\" cy=\"-1098\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"442\" y=\"-1094.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">86</text>\n</g>\n<!-- 86&#45;&#45;85 -->\n<g id=\"edge88\" class=\"edge\">\n<title>86&#45;&#45;85</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M457.2693,-1082.7307C469.488,-1070.512 486.5398,-1053.4602 498.7527,-1041.2473\"/>\n</g>\n<!-- 80 -->\n<g id=\"node86\" class=\"node\">\n<title>80</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"442\" cy=\"-1026\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"442\" y=\"-1022.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">80</text>\n</g>\n<!-- 86&#45;&#45;80 -->\n<g id=\"edge87\" class=\"edge\">\n<title>86&#45;&#45;80</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M442,-1079.8314C442,-1069 442,-1055.2876 442,-1044.4133\"/>\n</g>\n<!-- 87 -->\n<g id=\"node87\" class=\"node\">\n<title>87</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"370\" cy=\"-1170\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"370\" y=\"-1166.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">87</text>\n</g>\n<!-- 87&#45;&#45;86 -->\n<g id=\"edge89\" class=\"edge\">\n<title>87&#45;&#45;86</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M385.2693,-1154.7307C397.488,-1142.512 414.5398,-1125.4602 426.7527,-1113.2473\"/>\n</g>\n<!-- 88 -->\n<g id=\"node88\" class=\"node\">\n<title>88</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"226\" cy=\"-1242\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"226\" y=\"-1238.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">88</text>\n</g>\n<!-- 88&#45;&#45;78 -->\n<g id=\"edge90\" class=\"edge\">\n<title>88&#45;&#45;78</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M226,-1223.8314C226,-1213 226,-1199.2876 226,-1188.4133\"/>\n</g>\n<!-- 88&#45;&#45;79 -->\n<g id=\"edge91\" class=\"edge\">\n<title>88&#45;&#45;79</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M204.9063,-1230.75C179.6926,-1217.3027 137.7356,-1194.9256 112.3912,-1181.4086\"/>\n</g>\n<!-- 88&#45;&#45;87 -->\n<g id=\"edge92\" class=\"edge\">\n<title>88&#45;&#45;87</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M247.8705,-1231.0647C275.0934,-1217.4533 321.297,-1194.3515 348.3955,-1180.8022\"/>\n</g>\n<!-- 89 -->\n<g id=\"node89\" class=\"node\">\n<title>89</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"226\" cy=\"-1314\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"226\" y=\"-1310.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">89</text>\n</g>\n<!-- 89&#45;&#45;88 -->\n<g id=\"edge93\" class=\"edge\">\n<title>89&#45;&#45;88</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M226,-1295.8314C226,-1285 226,-1271.2876 226,-1260.4133\"/>\n</g>\n<!-- 92 -->\n<g id=\"node90\" class=\"node\">\n<title>92</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"298\" cy=\"-1314\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"298\" y=\"-1310.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">92</text>\n</g>\n<!-- 90 -->\n<g id=\"node91\" class=\"node\">\n<title>90</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"370\" cy=\"-1242\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"370\" y=\"-1238.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">90</text>\n</g>\n<!-- 92&#45;&#45;90 -->\n<g id=\"edge94\" class=\"edge\">\n<title>92&#45;&#45;90</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M313.2693,-1298.7307C325.488,-1286.512 342.5398,-1269.4602 354.7527,-1257.2473\"/>\n</g>\n<!-- 91 -->\n<g id=\"node92\" class=\"node\">\n<title>91</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"298\" cy=\"-1242\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"298\" y=\"-1238.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">91</text>\n</g>\n<!-- 92&#45;&#45;91 -->\n<g id=\"edge95\" class=\"edge\">\n<title>92&#45;&#45;91</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M298,-1295.8314C298,-1285 298,-1271.2876 298,-1260.4133\"/>\n</g>\n<!-- 93 -->\n<g id=\"node93\" class=\"node\">\n<title>93</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"262\" cy=\"-1386\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"262\" y=\"-1382.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">93</text>\n</g>\n<!-- 93&#45;&#45;89 -->\n<g id=\"edge96\" class=\"edge\">\n<title>93&#45;&#45;89</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M253.2854,-1368.5708C247.6253,-1357.2506 240.2784,-1342.5568 234.6343,-1331.2687\"/>\n</g>\n<!-- 93&#45;&#45;92 -->\n<g id=\"edge97\" class=\"edge\">\n<title>93&#45;&#45;92</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M270.7146,-1368.5708C276.3747,-1357.2506 283.7216,-1342.5568 289.3657,-1331.2687\"/>\n</g>\n<!-- 94 -->\n<g id=\"node94\" class=\"node\">\n<title>94</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"262\" cy=\"-1458\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"262\" y=\"-1454.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">94</text>\n</g>\n<!-- 94&#45;&#45;93 -->\n<g id=\"edge98\" class=\"edge\">\n<title>94&#45;&#45;93</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M262,-1439.8314C262,-1429 262,-1415.2876 262,-1404.4133\"/>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L7f2b4s3Kw6H"
      },
      "source": [
        "##Collapsable graph!\n",
        "for tutorial open the tutorial branch at: https://github.com/jupyter-widgets with colab\n",
        "\n",
        "https://ipython-books.github.io/64-visualizing-a-networkx-graph-in-the-notebook-with-d3js/\n",
        "This code is a python to javascript transformation that allows to create dynamic and interactive visualizations that can later be adaptable to regular \n",
        "web pages\n",
        "https://jakevdp.github.io/blog/2013/06/01/ipython-notebook-javascript-python-communication/\n",
        "\n",
        "https://github.com/timbr-io/jupyter-react-example"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EkLa5MbleKdC"
      },
      "source": [
        "This is a test setup for \"stacked\" widget, it doesn't seem to work hopefully i'll get an answer at:\n",
        "https://github.com/jupyter-widgets/ipywidgets/issues/2789#issuecomment-681108216"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b5N3pVFW-JMN"
      },
      "source": [
        "def AccordionProof(self,str):\n",
        "  node_dict = create_node_dict(raw_nodes_proof(self,str))\n",
        "  return AccordionTree(self, node_dict[max(node_dict.keys())])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xePIQ_fAJJLl"
      },
      "source": [
        "import ipywidgets as widgets\n",
        "def AccordionTree(self,root):\n",
        "  def create_Accordion(node):\n",
        "    accordion = widgets.Accordion(children=[])\n",
        "    if node.hypotheses:\n",
        "      hypotheses_children = [create_Accordion(node_hypothesis) for node_hypothesis in node.hypotheses]\n",
        "      accordion.children = list(accordion.children) + hypotheses_children\n",
        "      for i,node_hypothesis in enumerate(node.hypotheses):\n",
        "        accordion.set_title(i,\" \".join([node_hypothesis.id+\":\", node_hypothesis.statement]))\n",
        "    if node.reference:\n",
        "    #temporary placeholder for title - should be show_acoordion(label)\n",
        "      reference_children = [widgets.Output()]#[AccordionProof(self,node.reference)]\n",
        "      accordion.children = list(accordion.children) + reference_children\n",
        "      accordion.set_title(len(accordion.children)-1,node.reference)\n",
        "    return accordion\n",
        "  accordion = widgets.Accordion(children = [create_Accordion(root)])\n",
        "  accordion.set_title(0,\" \".join([root.id+\":\", root.statement]))\n",
        "  return accordion"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0KUysKTjDdha",
        "outputId": "e37c2a65-ff7f-4b07-cc95-9db89ebcb5df",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 60,
          "referenced_widgets": [
            "eb7d1eea496d4594a0e0399686cb6b70",
            "fa9c610609f04d39b7fff8635a2ab6c8",
            "1126521135f249bf80292e0bab4d8170",
            "76666286b6c94707bd6c59ccc55a8c9a",
            "1b7bf44235164790b9709beb4b89ab60",
            "fa09acafc2c444979a6ca3ffe56fd4b8",
            "59b464b47fb0439885d825573a0d2e89",
            "fb367081d44c4824b54a42aae3a4dc4b",
            "386e060617e14842b1e917a15b13a5d1",
            "6de100041a3345db823b95732aebe6f0",
            "699eccabcee6408186a5a4a49542cc06",
            "5cc4e6fe2ba64887b06e6f3bdeb97129",
            "54637d86f40340dcbbe196486dd8be88",
            "7c83b3089faa401a853eb6e51b8122b0",
            "b0f4d7ab1bf747bc836fdbd20585dfd2",
            "ccfa3adc4ed84986925a196d8b79b650",
            "daf7d20692044184b99706056ef1e64a",
            "62428fc7b7fa41a593867558c4515601",
            "496790ed6a5549d5ae82e89123afed68",
            "f4c22954561243c796492ae89dd4ad0b",
            "1ac087c254a74fadafde9a34ccbcdd31",
            "778742cd39a94ae3a52a58bb78d9ed9d",
            "dcdbe53e251e4d0c88f6c3abcf440e92",
            "e9312a74f1cc4557a99260eba723f3ba",
            "9f3c6e60f76648ea803327cdaeba6161",
            "ab0434e642014b349f13f3f61788a863",
            "c3ebd29271e2410f8139ca8007d672de",
            "8a86836a6a0b4039977fdce87cffecf1",
            "04ff01b5e2ac44bdbd1794c19f6ef573",
            "214ec5b92d1943c78a28ed8d1f9925d2",
            "b14ac893bf4f4e99b58c52fa194bdda5",
            "458db5a5542043c786b820e56887ba20",
            "71aa2af25ce643adab0ea79be9d668fd",
            "3f420072e6704381814ac3754936870e",
            "9cb1955bbaef46a49bbb7c02141ec730",
            "be246052bd184e759289f25724081123",
            "8fa99e47b5ed42879f4dc60a3ce5d5a9",
            "893a5cf455744c7787aa927189bb5b8e",
            "ef8138e4822c41118b5dca22fa861c5d",
            "2a35aac81dbd4e9c9f6313f4f32d84c2",
            "23e79fe7f6434853aa20b396d27766de",
            "f8bdcb0f32d44bac9b5519b2738375b3",
            "3707d6625a044178bf912f954d52dfe5",
            "1f42a614d60541e894fdacb165de73d3",
            "2a58534ef617403b83823f220702c856",
            "4d0098b7e217406dbdcd6d43526e546f",
            "6f6107a05c1749b0b6c15f68a8464e4b",
            "0df6de36b0d644c5bf625307e46b5a60",
            "0bdbb7e07bd94f3b8c02a20f1e89b0fb",
            "498f397ae99f41618e0f6c8b5027791c",
            "b9c16c33924c4c32a0f2772040e1c12a",
            "5311c1bda5b24b7fbc3c7d402e67b55f",
            "60aa3b071b3c4318bb524b6a2d0dc709",
            "12148052ad7f48d2b44cfb46a66495eb",
            "c0947a83531242d78e89921c51162f0d",
            "3e0d8371e3044ab7a05a81a237966aed",
            "cb24e596b5734eb89f9543ea2a12f83b",
            "7bdb703f549046459682aa3c2fbfbb86",
            "fddda069a6574829a0cda893bae591ed",
            "00d3207e02f54b85b2189622dfa4fd3e",
            "0fa79a33b245499b991c40fdb7192f6c",
            "3cb1b1db0432441f9dc7d3cc878ad6f4",
            "4e14f15cca054bb18aeb8ce9b59dd4b9",
            "cc66c359e7014f71ac2d1ce2bb4ac582",
            "b5305f40e94e4674be69ca6f18612bc9",
            "89a0cb6d4eb14048aeba5a56894f8c60",
            "18dceb1223c0468994194b23fa499166",
            "3badfed6e4dd4d6f9698b905a77a45b8",
            "32aedc1570384c0f859391bffa56614d",
            "940887318126479e90bd7c60eaafa95f",
            "6228d8d603274f6bb9c80f7f94e191bf",
            "ad066f3374794cd4a571b4239182afc3",
            "f7822e491531488c972fcee5ad82605a",
            "c9a8b151afa54c7ca67388d4a9838ed4",
            "ac312c9a5009443e872f306cd2da9855",
            "18c2e27f48874b128ab5162e67ea08af",
            "b4885793b05d4668aa5d6a715f34a6de",
            "e2b3eebbbe57486e8e22a7d4b310f318",
            "216b46e436c14b34bb79c1db0e596c17",
            "7114627467204ce0927aec5304808e49",
            "5d9ef2260366448eb524d917ca4d1e9a",
            "999e5f1668854e00ba6a75cf40660497",
            "2288082df357495d8fdada7992a98aa6",
            "e8ceff3b76bc477b917d2c923923fded",
            "14f75d27f0564f86b2ebbd3653bb733d",
            "8e088c5bc9da4f73959082b01245234d",
            "316a79fb29b7438aa5af0902d8e9b9ff",
            "1967dd6621914c6c8d51f6918b531aa4",
            "fd21b4ebd3fc43c591544230d53cfb67",
            "c3bb812e368a4aca9ffcac08e02671a6",
            "4ad26d9f83a94e61b07542473e7c9ccd",
            "9a176de9f8bb4ae6980ec4da1c9b9628",
            "7310ed5c1799406aa1c794bcf165cf93",
            "0c3a2b220e5649d4aa29d7223c375a40",
            "1619090a74e641d5afcf5e799c81fa82",
            "33b11c456f5649739c326ad88b19d923",
            "cdda06cccfc140e8a1d0c0c05cdd7f52",
            "699688103d074e9d903021d5676f262f",
            "046bc185913340a49fca128705c48445",
            "698f40278b174e3ba939ccaf030fc88f",
            "f5a9d2db9549464eaac3b97e8b163421",
            "dc2818efbafa4ed092abd5b4b561dd6b",
            "bfe53e5ec5cd47f5a6a0b5cf4e1e9e02",
            "f64c27c9f6ac4ef3a00fa996c83b8ddb",
            "e8cbf1ea18eb49a39da6e004d8b6c4e5",
            "cf29a6e4b6354c46876dfad635408c22",
            "b7495b0bd59c483eb14acbcd48a98f84",
            "4fa4bd517bdc49548ec94a482e86bfe3",
            "5fe946c796f6479f8d7aee0ced89735f",
            "9a83db1f1e834bae81a39d02babbcf7e",
            "58c838132b8a45b78bd44efa1ee7d811",
            "805b6810abae4eddb2fa5a87c481e7dd",
            "7b9c9056330f46509c4b8019f58b8c5c",
            "dbc1c305df92419d865d1f6cef4b4c37",
            "6593b51845e24a6ca058f069e42aeb24",
            "909c86dfb15341b8adfcf507425a97c2",
            "f47204c3cfce45179af31367364431cf",
            "e1ee20ddac734dd0bfb69cb2189ce883",
            "ad97bfb30bfc481bb61320a0d3048586",
            "da6fb3ea7eed4f24ae64b4e9e217ebf0",
            "dd3dc1f96f16430b8fa9ea0418d8bcc3",
            "8df4dd25b78a4b5da2a2b35e3a168fbb",
            "a3556fba60fe491a81d73607aebbedbb",
            "623c0af26f40499c8267d5d1cbd15cbe",
            "ce60a20e3847481cb6a7c8ab208a0964",
            "0a6452d283264d6e8e44e97a1477daa2",
            "1648370d4ab743ce9bc42dc334f5b7c9",
            "2ea4369368b14272a6f331f07655e04e",
            "fb6272247d5b44ee8064806dbd73ca86",
            "851046fdf6114a67b113ebde0a2e287b",
            "5e19d23e2cb5431aa46da97749b93ef0",
            "c69a028e6ac541c4940ef26bb2ad5668",
            "485e32bbb12f44b793e0c8c6b19a6757",
            "c695e0e4c25644a0bf10a935d8a0e155",
            "3d5be39f5cee48358d0daa79f531fb28",
            "cbbb58ba5a384b8f9571a0904e2004c7",
            "289a8eb2e761498ab36c7314078fe6c4",
            "725a7e12e50b4d29b968668d7a29436a",
            "5eb769a46111407493a268b2438e8dff",
            "ac53775b2a2c42e98c6b16dc30c302f9",
            "6413673951bd45088ae0a4faf931e3e4",
            "def35a7829b742a886f19596220273d6",
            "9f6c663753264868acdc928d219eab1f",
            "50675553fc7643da8390f546d1b90f6b",
            "af76efc8e675406ea67be8cbe9d7769b",
            "7eb2d2c1a9684f6b9c327141a67b84fd",
            "26e8bb1ddd3e4ad2b88e2baf6ddcf45b",
            "9f368524c7044529b09e418901b98246",
            "7a8a655344b1461585a77d120850c9aa",
            "7e9d769f80e84e578abbff75f7d88f52",
            "cf0d823004854d9890c55b64d23b70b1",
            "2cb7cd402bf140f3a1608a991dc4fb90",
            "5ec55cbbb0fe46dd8bacdb93b687b929",
            "04362f6a05374ae9b67c3afec9b29ab9",
            "e835096a202945f6992515115fc9fae9",
            "7feb79450299421ba7d77b27a7c5771a",
            "7993a1d452a44ab7b278c18d4a74b144",
            "9c81493b38fa4ec68663b493ed27e87e",
            "1b5c00a8310446789a84c3492c0d16b1",
            "c4df935143af4eacad07cdf7b29003d5",
            "bb9c567a3fca4a938e42ecd979f07618",
            "12423bc67d7a485c9d6a325758caa686",
            "829dada504484021909ef0fa759adeef",
            "2c8bc4f4491b4ba68ac9bb5f23cbacaa",
            "c96721d34a1a4c34b9609c454e83f08d",
            "3724812f9d8f4527b7acc222da8109fa",
            "ac41ebd0d0c64fa58d1ded3398b542ce",
            "3a9ab159702549049194b623ef5c3f0f",
            "5ce4861da8b14887af6d554b39f2a0ab",
            "2230bc961cd2415aa767d707927ba40c",
            "c693c94ae1124d9c91331762c6a5b5c1",
            "7d26947b51c74ac8b75444ebe8ee0cd7",
            "48fbbb94c67b418f90752151a6de6730",
            "5f684ff8e51940be939a7c0ace4d70fb",
            "37342a7a9ae34e558687b55f9bad76a7",
            "ec21b4a4122a4a3a8ee68b74305b7a5e",
            "b13a2471adf542b9925886a79fb6d78b",
            "e14b0d2420564c0daba93663d2ce8f33",
            "8788ce32b59c47aca82a921038c5a051",
            "1842b0297e8a4e8d870daccde9f1475b",
            "5b13dc62998e4a5a829991ff6744d9fc",
            "09daf6cb91994570ab2430b26bef0c5a",
            "ab8903570fbd44d097ee94d6b73da377",
            "f106aef5c116477fbf865cd6c529588f",
            "2cc0e1fabd83426cb95b238b93f2bc86",
            "76b0ac20fee642c3a4ec6c585dc4fbc9",
            "c2784e1350e543e3b000a02bb03e7b7d",
            "35ce6f9665f14b4b8b0f3ee3ff8a45e4",
            "eb22cc46da4a4dd4826437cd6d129f6d",
            "eb2a7e2b91a44993a7251de45f50c54a",
            "27e2cbc348d14465bf3702afa92bbd03",
            "b9b10ea09d0d4459adecb477a4692b04",
            "c920219b0d8b482c8c2a7082cf612587",
            "83c88731597c4d24b282ac3588bafc4f",
            "ac67b954b0134c44829530575d69bf13",
            "011c156cc1a34eaeb07b6c1df06ec42f",
            "1aac9a0e930142f0a6bbf2ccbecb767d",
            "c72d70cb56da468087560322d62443a6",
            "fb21275d5f954de18a6f09040e93715f",
            "1fba51aa73934c9b86540ffa22cd005c",
            "334d6db0e70e448da350fab34609b0f0",
            "2da34768afe94d15991106b095b29eb0",
            "9e4b19dfd58b457db13b25d0a4e3f600",
            "6616b185dc4c420a897371ad25456764",
            "c781adb4509441fa94c0d0357f6f80de",
            "dbd2633955b249939e615ea51b33f601",
            "a82a476444e9489d846e4ae234d30458",
            "88dd612dfebb4c67b2ae6a1dc0b44785",
            "64bb76d6195b463ba4b80b5ce05742c1",
            "1b79c9e7549543c39571b19e86d02fd3",
            "1c8590cb32f04615a3f697d9189e4c8d",
            "fefc8c3317f340e4ab4f286878f81eec",
            "cc4a6e3c40f34e3295ad89c9f086ed7c",
            "97a55f5beda94c3aa0946a233d847d01",
            "39fb64fdf8af4a47a0c2e6067a38889b",
            "a44c389b0eea4da49caf597621f53706",
            "31994644c59c46eabe7b22ca3921d9ac",
            "822ef94976e8433796c3656d2e6ff332",
            "ee41d05000ec4cd297de3d180c6c9925",
            "9c1d7fe68a7a45b1b2868bcc23eb106d",
            "ca1395ca24c04970ae1dc0b8ba81d5be",
            "ee9e8f97164b444bb14bc5e2a480e879",
            "f133043b6de147df8365eafb945b422b",
            "16e0510bf0ed4078a704d1791bc335fb",
            "bd81db6b1736424997856caf5622fad2",
            "61e7d9381452473fbccb9b6710dfcec5",
            "31f03884d784402f9c30bf98539c6556",
            "3b9e993d0c1b40d0938a67da525eb0a6",
            "36156f0669f6428ca7452aa9bec86df0",
            "eb6a5674bf0c471597447cd3e5365ec6",
            "4180859288044f61b39bc87d757475c7",
            "3d447bd161f14fd0b522b18e806b345f",
            "3f2eef516868442680bd942057dbff73",
            "5a14f936aece4e1abd343709c7e6fed6",
            "d268b391d5bb4c5ea78b871970f36d77",
            "595cf14c613d48f1aff9cf0b9540140a",
            "3af490d18c7049dd8c8c95cd74ca0c23",
            "ebc36affc27b47d3b15834bc25ad4aa5",
            "38eac5688ec34f9ea35707bcdb2e3d6d",
            "54c66c59aaf4463bb4e969ef4f2613b2",
            "fcde836d90844d47a553e4541ea2846c",
            "f825abd68df946cc9e8f1c90e2821e49",
            "bd6fc778119d49efb269c35071e5ba08",
            "324461a06b2342b982156061eb8b7250",
            "4821f4b955074e8ca1ad80cd6ff2a9fd",
            "10bbe43fe4734bba97ec77240da399ae",
            "8b3fd42ff7b041c29211a30845fcea1d",
            "c3853d17ad564a01811d7cb947e7f76b",
            "6671d84187b64427a5b91e0e81c8085a",
            "2a529124a41b4455a5e651f2b4ec110b",
            "9afc7939120a4e84a149697edb3275df",
            "75c70d044f824925aa582469f1091533",
            "3bfa8ed979374a948e39108f69464876",
            "22261645d0ee45d28376d4cc04c8b20e",
            "c3bc79c6930b4ece9d8fb71084abd1d5",
            "8023671e49a24e8e87cb755d6e85f4b3",
            "64db0fe21ccb4051ae29df1ef2cef9ca",
            "dba115c4cab74729aa4bff54b676de3d",
            "ccb5c9e40ec24a748a073ff677e110ce",
            "74d80d5af9b1467db89f0f129fb90ccf",
            "81157ce531cb4359abb87427d0c5da1d",
            "20c77f3d86ff4227bbfcbbed57345b28",
            "99c21dbdb08a43d2bacb8c56bfe202c0",
            "39ca9f0d50b44039988d0bff3accc57f",
            "b07f9c49392c4b3088b0c6a47957ce5a",
            "19fdc16a04174583a5183b55aef13420",
            "067d86a57f3f404883ad543c9178b60b",
            "feb44f273c6a44eaa446cd368afba39b",
            "cdf8c72a190f4fd5ad9f23c0a3207876",
            "1f62166dda5842f98cf346df6833f0e9",
            "f7ede39ecd9647299fd7df1e4811529b",
            "479678c2b7f04553a20117bdc15c4471",
            "ab1ab38ce09a4addb5024086be8eefc3",
            "569fc2a727af4a018a60754db0e834d3",
            "c4dd92b63f114a59878296257cf78bc1",
            "d07df7e5136940a6bee989e3a62d1319",
            "ca4ed642f2a84f099e14bcb4bbd96213",
            "769c4521b80245e999ee62d8e9c555aa",
            "44c0cbbfb5f44cd4989fadb982c299ff",
            "77c9c489556849d898f2ce36861021e5",
            "f3f5f0ca9dc946de96d3eb95556f9d33",
            "2df6125b19bf46229e88bb7a91f93686",
            "a3ff2b680f4043a4bf473805410d0869",
            "7f58f34a3e9d4d698454e6396349c438",
            "81caa3e3626944458ac8ef50683a94bb",
            "7bba29319d7a4e9faa21c56f8d6dcbeb",
            "f1438f9292114e31a60f3e8cf535d29b",
            "a14d20b9d344464b852fa11d7b1ac4ee",
            "b99f9f513f8c48e585df3686f577e23a",
            "4d01b6ea0bb943f98ad1ef5fa8ec24b2",
            "3240f02597734e8b9266b2b2b5fbeff5",
            "52e14363e9df4f9db0a91a7c948304b9",
            "eba9dcfef33143029328d7f7b71b2925",
            "1ced4d8de5924ae39a454e8043ee475d",
            "45a1a0aaad3d46629e4df0a233b679b1",
            "5286c096febd4779901d64b6d06951c7",
            "297f212515e548a48030860d32f15d02",
            "7c19400e925945d3b2e83ae068bc31ce",
            "884ec1a268884de0a523e07eeeeb5b2f",
            "3649cb6f78f34265b7793a0637106229",
            "4857cf719f06446aac0d01082ad8f24e",
            "9e8f951afaa945aaaecd04626112806b",
            "2a508579261a4dea9ba168343f056144",
            "0ec04acda6144323ac0e036d4c1e0779",
            "e0b950db1d6e458eb241cb2d84e5269f",
            "a5a3aec96cd549cfa2f834cf4bb37ea1",
            "864580e4501b483da2b6ff5ccc116677",
            "7ca401ff9a0a4f558d04d7561c299f47",
            "3630197f830e4fe9a9846a5b30c6a03f",
            "989d55d0c1ff455fac40fdd8a26e0ae9",
            "343fdcb8416d4903addb5181b77b892c",
            "ab223753ec4047a28f14b8e4b0d52c6a",
            "51b7cb872c0a42df98fe31e1a8d5c214",
            "854b79919b954677879b1799f1d8cbad",
            "b88daff41ff24eb9845abab63f3db736",
            "3e5470c8978b401ea93d9f1acd5ce02d",
            "4e51086126954f7c961394a6b8cb2d56",
            "b392de99d58140358435710bd8c8af94",
            "2aa3cf28ccb145eaa8381fbdb85dc302",
            "975c98f167004057a06624876b9fdb46",
            "7766ab8032764cc0a282324c70391abe",
            "9ecf86e97b4f4d158c7ecf59064b3f3e",
            "d847e2604ec74683a4133294697d080d",
            "e33aa8a69bf3472c8b098b0b9bf19973",
            "6d31d2448a9e44f5b2dbb5235eae9e46",
            "4f51b13a1c544222bb942e4f410216a0",
            "37478058407640f1bb4af980f1c7e0b6",
            "ed0b691edf0e450caa2aa55fc45bfa0e",
            "57fe6e4df4044a7b9848cac70b15eaa2",
            "c190fd1b64df44069110a61728862628",
            "06e98b14eb174d2fb1184f86dad2b0d3",
            "2e48bb1862da47489261fb0bbd5a6ffd",
            "cfd85dc1ea2e4d11affd4bc7fae7f69d",
            "d380d6abfb6e4136b4fd977219ba4199",
            "7d1c752a93084411961b787c7389932a",
            "fdbd5dcad1ba4e5b8e5fa762ec6c9107",
            "3fe1b6f2278941b1805de7ee4a1d8c44",
            "0dff734e4b224018acea5e47b66d6e79",
            "3069db68eff04468ab5661e2170ada40",
            "0b03c4e324e64f48bfe070de3977dd39",
            "0531b4d51690404988fea9a5f1d9b27c",
            "9bf61733584045e4bffa8d07eed0033c",
            "50253b3cefdd47d59430f3255e00d1fa",
            "0e9415e854c6477b9701617652ba3258",
            "d014ce05f3934497bf616a8c20b2391f",
            "a7fadebfc46b43778df526aaf1b03610",
            "c86cfeaed61f40d49f0970432a3ac6ed",
            "1aea7b4d2d33419bb4669e2b0b523a1c",
            "033e3f8dfc1c4c40a85db561e6f25a3f",
            "c2d9e046a56144e682685d78ca94cb31",
            "424543c9ab844d7f8ce238bca1606dc2",
            "80fa7df8d9704cd492bf9e0fdbe6b556",
            "fa2eb0ca79bd46d68ea07bb7f71e690f",
            "92e861209e1f4a468315f972b312dcd2",
            "79a73dfe3d9848e4b07eddcf60e7368f",
            "b0f1ab7267394171bf88590d897e0673",
            "11bbc54884c544bba813bb3663401d23",
            "23e869b31ea0485ca76a08aa1bcbc527",
            "7b87c844691945aeac88c5e61807b51e",
            "2b752e11dd6a41c395a4378e3a2faa2e",
            "0fae406b95c3410a90187476cd38fa73",
            "88866bd04954449b89e8104bce421b2d",
            "583cb59bae8a4b788b87c27e48b59d29",
            "d2a21ef301c24193966885243eace121",
            "78c609f3c1e54ba6bebba6b645cdbd51",
            "15a3ece0cd3c49189f1c246f50fa226b",
            "b6b16d28c6814dcdaf30d3dbda458405",
            "ec4fddaaafba41879ef7a6bcb380cd79",
            "ab60a9b840c640088eaa529a5fd4d1e1",
            "403179bf179c423da000ba720dfb607a",
            "d44954be68dc4af98176897a5c089a79",
            "b2ddbf571033407c953e974a4ef3e2ca",
            "68954f14f6f7460289d8077ee20b29c0",
            "6ebfd58bfd6642a6a10ec9c4ac5ee5eb",
            "7947d99d5eb74148bbe8974f2cc9911d",
            "d5c6b8755a044afc8bcd9f9d95dba8a0",
            "be1d4ba9b41e403b82535e4e54c4866d",
            "999f839e8b9c41bea74067b380fb5737",
            "7664d62652694f76a09038f2bd57679f",
            "c5496e372e1547608f6c2ae92eb9d14a",
            "b5a06d90d6c942639f8e03d4d925960d",
            "ee6b540900c3434fb608f2b24479190c",
            "30004fb0232b44588dd2dbaf6a1cf0d4",
            "9a973f5c2abb481a9aff8ceea7763697",
            "cd2d3daa97aa4df79ecfb605ad94f0a9",
            "ad63940e41d545ef86e64e5745f1a260",
            "a1f9b6b9bc274d088dd90032cc4ec7e2",
            "c7d5e80ed0c6410e836626b962084640",
            "6385fe3f1fca436e88b17fe38b147758",
            "78c98f35800c4e188be2b29a137189a0",
            "1271f0de0e364049a50ec5d2c2d5fd45",
            "31c4af548119456e9cc6c2568139d703",
            "69446a27ea674474ad541270efd38a1f",
            "ab62cfd6c39e4e5eb6e7335136bdfa67",
            "6153c29c6fe440dbb3c1765a19ea405f",
            "319a9eae798441fa8579598318564e00",
            "3e9b9696b58f4920825276fb0b4cbef4",
            "435bbeb9e61940a2abbfd37e6cf79812",
            "6cdcd46595194e2599d23b5caf4c18b5",
            "0b36a386e7ac40f39060df07e182bed6",
            "02b65cd9df294673a5642a19ccc8e8a1",
            "0a280549c9e84552a3ca518f67688501",
            "aa4fa170c8bd4002a4098c60cb46346e",
            "6f2299b54cf447f0aac026ea2efadb3e",
            "6c8bd8a457fe4039a205767e10675346",
            "eb92714ff27a422d8d3e617ab9cea909",
            "f5116f6d71c54959a6e27ef89e83032a",
            "9a72479801e244a6b4bd8a719603339b",
            "9a64c056559c4627bd3a7bd302884584",
            "a1e0c13446c24eb298657c00928ad2fc",
            "1d6e54b9aca24b71a5e6b9ef005f3e78",
            "14727d51f6a4430ebe96329b466fb89b",
            "42a4a2681e264d889e93a8b3c48d3a7b",
            "b15f2d03e4cb4a1ebcbe148a51cc3a3b",
            "8f1aeffc00304c18a369bacbe488844c",
            "2b9f4c1b07844757add5aec16c2dacfa",
            "f8bd77ec49674be896a7e3117ea4bedc",
            "271d2e1728aa4fb9af38730779bf60f6",
            "b229f7df9e6d430b9affa5905c78f608",
            "85f4728ed36a4071a276cf9457b1d151",
            "a5279777fa104167806bbb4ebd54f832",
            "3a6510b5df6a46b79a3e4c833abd545c"
          ]
        }
      },
      "source": [
        "AccordionProof(m,\"sqrt2irr\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "eb7d1eea496d4594a0e0399686cb6b70",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "Accordion(children=(Accordion(children=(Accordion(children=(Accordion(children=(Accordion(children=(Accordion(…"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F-6lPSra-xeM",
        "outputId": "8bb63215-d9cd-40aa-9c2c-5cd91c13376c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 60,
          "referenced_widgets": [
            "62bc4d18b7344f838f979a5bcb9fb498",
            "e715efb80a804f59970993b770e74334",
            "32805d3a100c4f7cb000e7c269cfcc04",
            "81e9f3825bbd49179d0f55017f8abac9",
            "5296ce6a8d66449aa52ac2f4e9dd71de",
            "bd01792309cd4ec19d98c1098aa0c3df",
            "3efcf3d89479413f84d9f26fcac2b980",
            "ab44e93e38874a51b177cfc4b80b4968",
            "fb95e0c7afc042f1997d51db8b053653",
            "8ae7193d5b43412aa6cce3cc1075d6ea",
            "a61040a5ee9b4e5d892275fb4d08dc67",
            "3dcce0dda0154d6abbb228484d3c0c67",
            "385a893106494fad9fecdb9f12fc90dc",
            "908f6b8e4664460cb0c87968b13ca737"
          ]
        }
      },
      "source": [
        "AccordionProof(m,\"ovex\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "62bc4d18b7344f838f979a5bcb9fb498",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "Accordion(children=(Accordion(children=(Accordion(children=(Output(),), _titles={'0': 'df-ov'}), Accordion(chi…"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IoVzZ9uiNt_n"
      },
      "source": [
        "# Statistics on proofs and lemmas\n",
        "TODO\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fy4uKMK0N4W2"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}