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Data.List.Relation.Unary.Any.Properties.html
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<!DOCTYPE HTML>
<html><head><meta charset="utf-8"><title>Data.List.Relation.Unary.Any.Properties</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Comment">------------------------------------------------------------------------</a>
<a id="74" class="Comment">-- The Agda standard library</a>
<a id="103" class="Comment">--</a>
<a id="106" class="Comment">-- Properties related to Any</a>
<a id="135" class="Comment">------------------------------------------------------------------------</a>
<a id="209" class="Symbol">{-#</a> <a id="213" class="Keyword">OPTIONS</a> <a id="221" class="Pragma">--without-K</a> <a id="233" class="Pragma">--safe</a> <a id="240" class="Symbol">#-}</a>
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<a id="1881" class="Keyword">open</a> <a id="1886" class="Keyword">import</a> <a id="1893" href="Level.html" class="Module">Level</a> <a id="1899" class="Keyword">using</a> <a id="1905" class="Symbol">(</a><a id="1906" href="Agda.Primitive.html#597" class="Postulate">Level</a><a id="1911" class="Symbol">)</a>
<a id="1913" class="Keyword">open</a> <a id="1918" class="Keyword">import</a> <a id="1925" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="1941" class="Symbol">as</a> <a id="1944" class="Module">B</a> <a id="1946" class="Keyword">hiding</a> <a id="1953" class="Symbol">(</a><a id="1954" href="Relation.Binary.Core.html#1325" class="Function Operator">_⇔_</a><a id="1957" class="Symbol">)</a>
<a id="1959" class="Keyword">open</a> <a id="1964" class="Keyword">import</a> <a id="1971" href="Relation.Binary.PropositionalEquality.html" class="Module">Relation.Binary.PropositionalEquality</a> <a id="2009" class="Symbol">as</a> <a id="2012" class="Module">P</a>
<a id="2016" class="Keyword">using</a> <a id="2022" class="Symbol">(</a><a id="2023" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">_≡_</a><a id="2026" class="Symbol">;</a> <a id="2028" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a><a id="2032" class="Symbol">;</a> <a id="2034" href="Relation.Binary.PropositionalEquality.html#2382" class="Function">inspect</a><a id="2041" class="Symbol">)</a>
<a id="2043" class="Keyword">open</a> <a id="2048" class="Keyword">import</a> <a id="2055" href="Relation.Unary.html" class="Module">Relation.Unary</a> <a id="2070" class="Symbol">as</a> <a id="2073" class="Module">U</a>
<a id="2077" class="Keyword">using</a> <a id="2083" class="Symbol">(</a><a id="2084" href="Relation.Unary.html#1101" class="Function">Pred</a><a id="2088" class="Symbol">;</a> <a id="2090" href="Relation.Unary.html#5466" class="Function Operator">_⟨×⟩_</a><a id="2095" class="Symbol">;</a> <a id="2097" href="Relation.Unary.html#5766" class="Function Operator">_⟨→⟩_</a><a id="2102" class="Symbol">)</a> <a id="2104" class="Keyword">renaming</a> <a id="2113" class="Symbol">(</a><a id="2114" href="Relation.Unary.html#1742" class="Function Operator">_⊆_</a> <a id="2118" class="Symbol">to</a> <a id="2121" class="Function Operator">_⋐_</a><a id="2124" class="Symbol">)</a>
<a id="2126" class="Keyword">open</a> <a id="2131" class="Keyword">import</a> <a id="2138" href="Relation.Nullary.html" class="Module">Relation.Nullary</a> <a id="2155" class="Keyword">using</a> <a id="2161" class="Symbol">(</a><a id="2162" href="Relation.Nullary.html#656" class="Function Operator">¬_</a><a id="2164" class="Symbol">;</a> <a id="2166" href="Relation.Nullary.html#1559" class="InductiveConstructor Operator">_because_</a><a id="2175" class="Symbol">;</a> <a id="2177" href="Relation.Nullary.html#1581" class="Field">does</a><a id="2181" class="Symbol">;</a> <a id="2183" href="Relation.Nullary.html#902" class="InductiveConstructor">ofʸ</a><a id="2186" class="Symbol">;</a> <a id="2188" href="Relation.Nullary.html#939" class="InductiveConstructor">ofⁿ</a><a id="2191" class="Symbol">;</a> <a id="2193" href="Relation.Nullary.html#1648" class="InductiveConstructor">yes</a><a id="2196" class="Symbol">;</a> <a id="2198" href="Relation.Nullary.html#1685" class="InductiveConstructor">no</a><a id="2200" class="Symbol">)</a>
<a id="2202" class="Keyword">open</a> <a id="2207" class="Keyword">import</a> <a id="2214" href="Relation.Nullary.Negation.html" class="Module">Relation.Nullary.Negation</a> <a id="2240" class="Keyword">using</a> <a id="2246" class="Symbol">(</a><a id="2247" href="Relation.Nullary.Negation.Core.html#778" class="Function">contradiction</a><a id="2260" class="Symbol">;</a> <a id="2262" href="Relation.Nullary.Negation.Core.html#1355" class="Function">¬?</a><a id="2264" class="Symbol">;</a> <a id="2266" href="Relation.Nullary.Negation.html#1052" class="Function">decidable-stable</a><a id="2282" class="Symbol">)</a>
<a id="2285" class="Keyword">private</a>
<a id="2295" class="Keyword">open</a> <a id="2300" class="Keyword">module</a> <a id="ListMonad"></a><a id="2307" href="Data.List.Relation.Unary.Any.Properties.html#2307" class="Module">ListMonad</a> <a id="2317" class="Symbol">{</a><a id="2318" href="Data.List.Relation.Unary.Any.Properties.html#2318" class="Bound">ℓ</a><a id="2319" class="Symbol">}</a> <a id="2321" class="Symbol">=</a> <a id="2323" href="Category.Monad.html#832" class="Module">RawMonad</a> <a id="2332" class="Symbol">(</a><a id="2333" href="Data.List.Categorical.html#1276" class="Function">monad</a> <a id="2339" class="Symbol">{</a><a id="2340" class="Argument">ℓ</a> <a id="2342" class="Symbol">=</a> <a id="2344" href="Data.List.Relation.Unary.Any.Properties.html#2318" class="Bound">ℓ</a><a id="2345" class="Symbol">})</a>
<a id="2349" class="Keyword">private</a>
<a id="2359" class="Keyword">variable</a>
<a id="2372" href="Data.List.Relation.Unary.Any.Properties.html#2372" class="Generalizable">a</a> <a id="2374" href="Data.List.Relation.Unary.Any.Properties.html#2374" class="Generalizable">b</a> <a id="2376" href="Data.List.Relation.Unary.Any.Properties.html#2376" class="Generalizable">c</a> <a id="2378" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a> <a id="2380" href="Data.List.Relation.Unary.Any.Properties.html#2380" class="Generalizable">q</a> <a id="2382" href="Data.List.Relation.Unary.Any.Properties.html#2382" class="Generalizable">r</a> <a id="2384" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a> <a id="2386" class="Symbol">:</a> <a id="2388" href="Agda.Primitive.html#597" class="Postulate">Level</a>
<a id="2398" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="2400" class="Symbol">:</a> <a id="2402" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="2406" href="Data.List.Relation.Unary.Any.Properties.html#2372" class="Generalizable">a</a>
<a id="2412" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="2414" class="Symbol">:</a> <a id="2416" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="2420" href="Data.List.Relation.Unary.Any.Properties.html#2374" class="Generalizable">b</a>
<a id="2426" href="Data.List.Relation.Unary.Any.Properties.html#2426" class="Generalizable">C</a> <a id="2428" class="Symbol">:</a> <a id="2430" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="2434" href="Data.List.Relation.Unary.Any.Properties.html#2376" class="Generalizable">c</a>
<a id="2440" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="2442" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="2444" href="Data.List.Relation.Unary.Any.Properties.html#2444" class="Generalizable">R</a> <a id="2446" class="Symbol">:</a> <a id="2448" href="Relation.Unary.html#1101" class="Function">Pred</a> <a id="2453" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="2455" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a>
<a id="2461" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="2463" href="Data.List.Relation.Unary.Any.Properties.html#2463" class="Generalizable">y</a> <a id="2465" class="Symbol">:</a> <a id="2467" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a>
<a id="2473" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="2476" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a> <a id="2479" class="Symbol">:</a> <a id="2481" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="2486" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a>
<a id="2489" class="Comment">------------------------------------------------------------------------</a>
<a id="2562" class="Comment">-- Equality properties</a>
<a id="lift-resp"></a><a id="2586" href="Data.List.Relation.Unary.Any.Properties.html#2586" class="Function">lift-resp</a> <a id="2596" class="Symbol">:</a> <a id="2598" class="Symbol">∀</a> <a id="2600" class="Symbol">{</a><a id="2601" href="Data.List.Relation.Unary.Any.Properties.html#2601" class="Bound Operator">_≈_</a> <a id="2605" class="Symbol">:</a> <a id="2607" href="Relation.Binary.Core.html#882" class="Function">Rel</a> <a id="2611" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="2613" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="2614" class="Symbol">}</a> <a id="2616" class="Symbol">→</a> <a id="2618" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="2620" href="Relation.Binary.Definitions.html#3593" class="Function Operator">Respects</a> <a id="2629" href="Data.List.Relation.Unary.Any.Properties.html#2601" class="Bound Operator">_≈_</a> <a id="2633" class="Symbol">→</a>
<a id="2647" class="Symbol">(</a><a id="2648" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="2652" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a><a id="2653" class="Symbol">)</a> <a id="2655" href="Relation.Binary.Definitions.html#3593" class="Function Operator">Respects</a> <a id="2664" class="Symbol">(</a><a id="2665" href="Data.List.Relation.Binary.Pointwise.Base.html#775" class="Datatype">Pointwise</a> <a id="2675" href="Data.List.Relation.Unary.Any.Properties.html#2601" class="Bound Operator">_≈_</a><a id="2678" class="Symbol">)</a>
<a id="2680" href="Data.List.Relation.Unary.Any.Properties.html#2586" class="Function">lift-resp</a> <a id="2690" href="Data.List.Relation.Unary.Any.Properties.html#2690" class="Bound">resp</a> <a id="2695" class="Symbol">(</a><a id="2696" href="Data.List.Relation.Unary.Any.Properties.html#2696" class="Bound">x≈y</a> <a id="2700" href="Data.List.Relation.Binary.Pointwise.Base.html#910" class="InductiveConstructor Operator">∷</a> <a id="2702" href="Data.List.Relation.Unary.Any.Properties.html#2702" class="Bound">xs≈ys</a><a id="2707" class="Symbol">)</a> <a id="2709" class="Symbol">(</a><a id="2710" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="2715" href="Data.List.Relation.Unary.Any.Properties.html#2715" class="Bound">px</a><a id="2717" class="Symbol">)</a> <a id="2721" class="Symbol">=</a> <a id="2723" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="2728" class="Symbol">(</a><a id="2729" href="Data.List.Relation.Unary.Any.Properties.html#2690" class="Bound">resp</a> <a id="2734" href="Data.List.Relation.Unary.Any.Properties.html#2696" class="Bound">x≈y</a> <a id="2738" href="Data.List.Relation.Unary.Any.Properties.html#2715" class="Bound">px</a><a id="2740" class="Symbol">)</a>
<a id="2742" href="Data.List.Relation.Unary.Any.Properties.html#2586" class="Function">lift-resp</a> <a id="2752" href="Data.List.Relation.Unary.Any.Properties.html#2752" class="Bound">resp</a> <a id="2757" class="Symbol">(</a><a id="2758" href="Data.List.Relation.Unary.Any.Properties.html#2758" class="Bound">x≈y</a> <a id="2762" href="Data.List.Relation.Binary.Pointwise.Base.html#910" class="InductiveConstructor Operator">∷</a> <a id="2764" href="Data.List.Relation.Unary.Any.Properties.html#2764" class="Bound">xs≈ys</a><a id="2769" class="Symbol">)</a> <a id="2771" class="Symbol">(</a><a id="2772" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="2778" href="Data.List.Relation.Unary.Any.Properties.html#2778" class="Bound">pxs</a><a id="2781" class="Symbol">)</a> <a id="2783" class="Symbol">=</a> <a id="2785" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="2791" class="Symbol">(</a><a id="2792" href="Data.List.Relation.Unary.Any.Properties.html#2586" class="Function">lift-resp</a> <a id="2802" href="Data.List.Relation.Unary.Any.Properties.html#2752" class="Bound">resp</a> <a id="2807" href="Data.List.Relation.Unary.Any.Properties.html#2764" class="Bound">xs≈ys</a> <a id="2813" href="Data.List.Relation.Unary.Any.Properties.html#2778" class="Bound">pxs</a><a id="2816" class="Symbol">)</a>
<a id="here-injective"></a><a id="2819" href="Data.List.Relation.Unary.Any.Properties.html#2819" class="Function">here-injective</a> <a id="2834" class="Symbol">:</a> <a id="2836" class="Symbol">∀</a> <a id="2838" class="Symbol">{</a><a id="2839" href="Data.List.Relation.Unary.Any.Properties.html#2839" class="Bound">p</a> <a id="2841" href="Data.List.Relation.Unary.Any.Properties.html#2841" class="Bound">q</a> <a id="2843" class="Symbol">:</a> <a id="2845" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="2847" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a><a id="2848" class="Symbol">}</a> <a id="2850" class="Symbol">→</a> <a id="2852" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="2857" class="Symbol">{</a><a id="2858" class="Argument">P</a> <a id="2860" class="Symbol">=</a> <a id="2862" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a><a id="2863" class="Symbol">}</a> <a id="2865" class="Symbol">{</a><a id="2866" class="Argument">xs</a> <a id="2869" class="Symbol">=</a> <a id="2871" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="2873" class="Symbol">}</a> <a id="2875" href="Data.List.Relation.Unary.Any.Properties.html#2839" class="Bound">p</a> <a id="2877" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="2879" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="2884" href="Data.List.Relation.Unary.Any.Properties.html#2841" class="Bound">q</a> <a id="2886" class="Symbol">→</a> <a id="2888" href="Data.List.Relation.Unary.Any.Properties.html#2839" class="Bound">p</a> <a id="2890" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="2892" href="Data.List.Relation.Unary.Any.Properties.html#2841" class="Bound">q</a>
<a id="2894" href="Data.List.Relation.Unary.Any.Properties.html#2819" class="Function">here-injective</a> <a id="2909" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a> <a id="2914" class="Symbol">=</a> <a id="2916" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="there-injective"></a><a id="2922" href="Data.List.Relation.Unary.Any.Properties.html#2922" class="Function">there-injective</a> <a id="2938" class="Symbol">:</a> <a id="2940" class="Symbol">∀</a> <a id="2942" class="Symbol">{</a><a id="2943" href="Data.List.Relation.Unary.Any.Properties.html#2943" class="Bound">p</a> <a id="2945" href="Data.List.Relation.Unary.Any.Properties.html#2945" class="Bound">q</a> <a id="2947" class="Symbol">:</a> <a id="2949" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="2953" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="2955" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="2957" class="Symbol">}</a> <a id="2959" class="Symbol">→</a> <a id="2961" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="2967" class="Symbol">{</a><a id="2968" class="Argument">x</a> <a id="2970" class="Symbol">=</a> <a id="2972" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a><a id="2973" class="Symbol">}</a> <a id="2975" href="Data.List.Relation.Unary.Any.Properties.html#2943" class="Bound">p</a> <a id="2977" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="2979" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="2985" href="Data.List.Relation.Unary.Any.Properties.html#2945" class="Bound">q</a> <a id="2987" class="Symbol">→</a> <a id="2989" href="Data.List.Relation.Unary.Any.Properties.html#2943" class="Bound">p</a> <a id="2991" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="2993" href="Data.List.Relation.Unary.Any.Properties.html#2945" class="Bound">q</a>
<a id="2995" href="Data.List.Relation.Unary.Any.Properties.html#2922" class="Function">there-injective</a> <a id="3011" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a> <a id="3016" class="Symbol">=</a> <a id="3018" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="3024" class="Comment">------------------------------------------------------------------------</a>
<a id="3097" class="Comment">-- Misc</a>
<a id="¬Any[]"></a><a id="3106" href="Data.List.Relation.Unary.Any.Properties.html#3106" class="Function">¬Any[]</a> <a id="3113" class="Symbol">:</a> <a id="3115" href="Relation.Nullary.html#656" class="Function Operator">¬</a> <a id="3117" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="3121" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="3123" class="InductiveConstructor">[]</a>
<a id="3126" href="Data.List.Relation.Unary.Any.Properties.html#3106" class="Function">¬Any[]</a> <a id="3133" class="Symbol">()</a>
<a id="3137" class="Comment">------------------------------------------------------------------------</a>
<a id="3210" class="Comment">-- Any is a congruence</a>
<a id="Any-cong"></a><a id="3234" href="Data.List.Relation.Unary.Any.Properties.html#3234" class="Function">Any-cong</a> <a id="3243" class="Symbol">:</a> <a id="3245" class="Symbol">∀</a> <a id="3247" class="Symbol">{</a><a id="3248" href="Data.List.Relation.Unary.Any.Properties.html#3248" class="Bound">k</a> <a id="3250" class="Symbol">:</a> <a id="3252" href="Function.Related.html#1654" class="Datatype">Kind</a><a id="3256" class="Symbol">}</a> <a id="3258" class="Symbol">→</a> <a id="3260" class="Symbol">(∀</a> <a id="3263" href="Data.List.Relation.Unary.Any.Properties.html#3263" class="Bound">x</a> <a id="3265" class="Symbol">→</a> <a id="3267" href="Function.Related.html#2599" class="Function">Related</a> <a id="3275" href="Data.List.Relation.Unary.Any.Properties.html#3248" class="Bound">k</a> <a id="3277" class="Symbol">(</a><a id="3278" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="3280" href="Data.List.Relation.Unary.Any.Properties.html#3263" class="Bound">x</a><a id="3281" class="Symbol">)</a> <a id="3283" class="Symbol">(</a><a id="3284" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="3286" href="Data.List.Relation.Unary.Any.Properties.html#3263" class="Bound">x</a><a id="3287" class="Symbol">))</a> <a id="3290" class="Symbol">→</a>
<a id="3303" class="Symbol">(∀</a> <a id="3306" class="Symbol">{</a><a id="3307" href="Data.List.Relation.Unary.Any.Properties.html#3307" class="Bound">z</a><a id="3308" class="Symbol">}</a> <a id="3310" class="Symbol">→</a> <a id="3312" href="Function.Related.html#2599" class="Function">Related</a> <a id="3320" href="Data.List.Relation.Unary.Any.Properties.html#3248" class="Bound">k</a> <a id="3322" class="Symbol">(</a><a id="3323" href="Data.List.Relation.Unary.Any.Properties.html#3307" class="Bound">z</a> <a id="3325" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="3327" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="3329" class="Symbol">)</a> <a id="3331" class="Symbol">(</a><a id="3332" href="Data.List.Relation.Unary.Any.Properties.html#3307" class="Bound">z</a> <a id="3334" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="3336" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="3338" class="Symbol">))</a> <a id="3341" class="Symbol">→</a>
<a id="3354" href="Function.Related.html#2599" class="Function">Related</a> <a id="3362" href="Data.List.Relation.Unary.Any.Properties.html#3248" class="Bound">k</a> <a id="3364" class="Symbol">(</a><a id="3365" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="3369" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="3371" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="3373" class="Symbol">)</a> <a id="3375" class="Symbol">(</a><a id="3376" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="3380" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="3382" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="3384" class="Symbol">)</a>
<a id="3386" href="Data.List.Relation.Unary.Any.Properties.html#3234" class="Function">Any-cong</a> <a id="3395" class="Symbol">{</a><a id="3396" class="Argument">P</a> <a id="3398" class="Symbol">=</a> <a id="3400" href="Data.List.Relation.Unary.Any.Properties.html#3400" class="Bound">P</a><a id="3401" class="Symbol">}</a> <a id="3403" class="Symbol">{</a><a id="3404" class="Argument">Q</a> <a id="3406" class="Symbol">=</a> <a id="3408" href="Data.List.Relation.Unary.Any.Properties.html#3408" class="Bound">Q</a><a id="3409" class="Symbol">}</a> <a id="3411" class="Symbol">{</a><a id="3412" class="Argument">xs</a> <a id="3415" class="Symbol">=</a> <a id="3417" href="Data.List.Relation.Unary.Any.Properties.html#3417" class="Bound">xs</a><a id="3419" class="Symbol">}</a> <a id="3421" class="Symbol">{</a><a id="3422" href="Data.List.Relation.Unary.Any.Properties.html#3422" class="Bound">ys</a><a id="3424" class="Symbol">}</a> <a id="3426" href="Data.List.Relation.Unary.Any.Properties.html#3426" class="Bound">P↔Q</a> <a id="3430" href="Data.List.Relation.Unary.Any.Properties.html#3430" class="Bound">xs≈ys</a> <a id="3436" class="Symbol">=</a>
<a id="3440" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="3444" href="Data.List.Relation.Unary.Any.Properties.html#3400" class="Bound">P</a> <a id="3446" href="Data.List.Relation.Unary.Any.Properties.html#3417" class="Bound">xs</a> <a id="3464" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="3467" href="Function.Related.html#8883" class="Function">SK-sym</a> <a id="3474" href="Data.List.Membership.Propositional.Properties.Core.html#2748" class="Function">Any↔</a> <a id="3479" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="3483" class="Symbol">(</a><a id="3484" href="Data.Product.html#1369" class="Function">∃</a> <a id="3486" class="Symbol">λ</a> <a id="3488" href="Data.List.Relation.Unary.Any.Properties.html#3488" class="Bound">x</a> <a id="3490" class="Symbol">→</a> <a id="3492" href="Data.List.Relation.Unary.Any.Properties.html#3488" class="Bound">x</a> <a id="3494" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="3496" href="Data.List.Relation.Unary.Any.Properties.html#3417" class="Bound">xs</a> <a id="3499" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="3501" href="Data.List.Relation.Unary.Any.Properties.html#3400" class="Bound">P</a> <a id="3503" href="Data.List.Relation.Unary.Any.Properties.html#3488" class="Bound">x</a><a id="3504" class="Symbol">)</a> <a id="3507" href="Function.Related.html#9856" class="Function Operator">∼⟨</a> <a id="3510" href="Data.Product.Function.Dependent.Propositional.html#14156" class="Function">Σ.cong</a> <a id="3517" href="Function.Inverse.html#3662" class="Function">Inv.id</a> <a id="3524" class="Symbol">(</a><a id="3525" href="Data.List.Relation.Unary.Any.Properties.html#3430" class="Bound">xs≈ys</a> <a id="3531" href="Data.Product.Function.NonDependent.Propositional.html#2526" class="Function Operator">×-cong</a> <a id="3538" href="Data.List.Relation.Unary.Any.Properties.html#3426" class="Bound">P↔Q</a> <a id="3542" class="Symbol">_)</a> <a id="3545" href="Function.Related.html#9856" class="Function Operator">⟩</a>
<a id="3549" class="Symbol">(</a><a id="3550" href="Data.Product.html#1369" class="Function">∃</a> <a id="3552" class="Symbol">λ</a> <a id="3554" href="Data.List.Relation.Unary.Any.Properties.html#3554" class="Bound">x</a> <a id="3556" class="Symbol">→</a> <a id="3558" href="Data.List.Relation.Unary.Any.Properties.html#3554" class="Bound">x</a> <a id="3560" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="3562" href="Data.List.Relation.Unary.Any.Properties.html#3422" class="Bound">ys</a> <a id="3565" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="3567" href="Data.List.Relation.Unary.Any.Properties.html#3408" class="Bound">Q</a> <a id="3569" href="Data.List.Relation.Unary.Any.Properties.html#3554" class="Bound">x</a><a id="3570" class="Symbol">)</a> <a id="3573" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="3576" href="Data.List.Membership.Propositional.Properties.Core.html#2748" class="Function">Any↔</a> <a id="3581" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="3585" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="3589" href="Data.List.Relation.Unary.Any.Properties.html#3408" class="Bound">Q</a> <a id="3591" href="Data.List.Relation.Unary.Any.Properties.html#3422" class="Bound">ys</a> <a id="3609" href="Function.Related.html#10453" class="Function Operator">∎</a>
<a id="3613" class="Keyword">where</a> <a id="3619" class="Keyword">open</a> <a id="3624" href="Function.Related.html#9774" class="Module">Related.EquationalReasoning</a>
<a id="3653" class="Comment">------------------------------------------------------------------------</a>
<a id="3726" class="Comment">-- Any.map</a>
<a id="map-id"></a><a id="3738" href="Data.List.Relation.Unary.Any.Properties.html#3738" class="Function">map-id</a> <a id="3745" class="Symbol">:</a> <a id="3747" class="Symbol">∀</a> <a id="3749" class="Symbol">(</a><a id="3750" href="Data.List.Relation.Unary.Any.Properties.html#3750" class="Bound">f</a> <a id="3752" class="Symbol">:</a> <a id="3754" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="3756" href="Data.List.Relation.Unary.Any.Properties.html#2121" class="Function Operator">⋐</a> <a id="3758" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a><a id="3759" class="Symbol">)</a> <a id="3761" class="Symbol">→</a> <a id="3763" class="Symbol">(∀</a> <a id="3766" class="Symbol">{</a><a id="3767" href="Data.List.Relation.Unary.Any.Properties.html#3767" class="Bound">x</a><a id="3768" class="Symbol">}</a> <a id="3770" class="Symbol">(</a><a id="3771" href="Data.List.Relation.Unary.Any.Properties.html#3771" class="Bound">p</a> <a id="3773" class="Symbol">:</a> <a id="3775" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="3777" href="Data.List.Relation.Unary.Any.Properties.html#3767" class="Bound">x</a><a id="3778" class="Symbol">)</a> <a id="3780" class="Symbol">→</a> <a id="3782" href="Data.List.Relation.Unary.Any.Properties.html#3750" class="Bound">f</a> <a id="3784" href="Data.List.Relation.Unary.Any.Properties.html#3771" class="Bound">p</a> <a id="3786" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="3788" href="Data.List.Relation.Unary.Any.Properties.html#3771" class="Bound">p</a><a id="3789" class="Symbol">)</a> <a id="3791" class="Symbol">→</a>
<a id="3802" class="Symbol">(</a><a id="3803" href="Data.List.Relation.Unary.Any.Properties.html#3803" class="Bound">p</a> <a id="3805" class="Symbol">:</a> <a id="3807" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="3811" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="3813" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="3815" class="Symbol">)</a> <a id="3817" class="Symbol">→</a> <a id="3819" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="3827" href="Data.List.Relation.Unary.Any.Properties.html#3750" class="Bound">f</a> <a id="3829" href="Data.List.Relation.Unary.Any.Properties.html#3803" class="Bound">p</a> <a id="3831" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="3833" href="Data.List.Relation.Unary.Any.Properties.html#3803" class="Bound">p</a>
<a id="3835" href="Data.List.Relation.Unary.Any.Properties.html#3738" class="Function">map-id</a> <a id="3842" href="Data.List.Relation.Unary.Any.Properties.html#3842" class="Bound">f</a> <a id="3844" href="Data.List.Relation.Unary.Any.Properties.html#3844" class="Bound">hyp</a> <a id="3848" class="Symbol">(</a><a id="3849" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="3855" href="Data.List.Relation.Unary.Any.Properties.html#3855" class="Bound">p</a><a id="3856" class="Symbol">)</a> <a id="3858" class="Symbol">=</a> <a id="3860" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="3867" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="3872" class="Symbol">(</a><a id="3873" href="Data.List.Relation.Unary.Any.Properties.html#3844" class="Bound">hyp</a> <a id="3877" href="Data.List.Relation.Unary.Any.Properties.html#3855" class="Bound">p</a><a id="3878" class="Symbol">)</a>
<a id="3880" href="Data.List.Relation.Unary.Any.Properties.html#3738" class="Function">map-id</a> <a id="3887" href="Data.List.Relation.Unary.Any.Properties.html#3887" class="Bound">f</a> <a id="3889" href="Data.List.Relation.Unary.Any.Properties.html#3889" class="Bound">hyp</a> <a id="3893" class="Symbol">(</a><a id="3894" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="3900" href="Data.List.Relation.Unary.Any.Properties.html#3900" class="Bound">p</a><a id="3901" class="Symbol">)</a> <a id="3903" class="Symbol">=</a> <a id="3905" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="3912" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="3918" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="3920" href="Data.List.Relation.Unary.Any.Properties.html#3738" class="Function">map-id</a> <a id="3927" href="Data.List.Relation.Unary.Any.Properties.html#3887" class="Bound">f</a> <a id="3929" href="Data.List.Relation.Unary.Any.Properties.html#3889" class="Bound">hyp</a> <a id="3933" href="Data.List.Relation.Unary.Any.Properties.html#3900" class="Bound">p</a>
<a id="map-∘"></a><a id="3936" href="Data.List.Relation.Unary.Any.Properties.html#3936" class="Function">map-∘</a> <a id="3942" class="Symbol">:</a> <a id="3944" class="Symbol">∀</a> <a id="3946" class="Symbol">(</a><a id="3947" href="Data.List.Relation.Unary.Any.Properties.html#3947" class="Bound">f</a> <a id="3949" class="Symbol">:</a> <a id="3951" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="3953" href="Data.List.Relation.Unary.Any.Properties.html#2121" class="Function Operator">⋐</a> <a id="3955" href="Data.List.Relation.Unary.Any.Properties.html#2444" class="Generalizable">R</a><a id="3956" class="Symbol">)</a> <a id="3958" class="Symbol">(</a><a id="3959" href="Data.List.Relation.Unary.Any.Properties.html#3959" class="Bound">g</a> <a id="3961" class="Symbol">:</a> <a id="3963" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="3965" href="Data.List.Relation.Unary.Any.Properties.html#2121" class="Function Operator">⋐</a> <a id="3967" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a><a id="3968" class="Symbol">)</a> <a id="3970" class="Symbol">(</a><a id="3971" href="Data.List.Relation.Unary.Any.Properties.html#3971" class="Bound">p</a> <a id="3973" class="Symbol">:</a> <a id="3975" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="3979" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="3981" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="3983" class="Symbol">)</a> <a id="3985" class="Symbol">→</a>
<a id="3995" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="4003" class="Symbol">(</a><a id="4004" href="Data.List.Relation.Unary.Any.Properties.html#3947" class="Bound">f</a> <a id="4006" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="4008" href="Data.List.Relation.Unary.Any.Properties.html#3959" class="Bound">g</a><a id="4009" class="Symbol">)</a> <a id="4011" href="Data.List.Relation.Unary.Any.Properties.html#3971" class="Bound">p</a> <a id="4013" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="4015" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="4023" href="Data.List.Relation.Unary.Any.Properties.html#3947" class="Bound">f</a> <a id="4025" class="Symbol">(</a><a id="4026" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="4034" href="Data.List.Relation.Unary.Any.Properties.html#3959" class="Bound">g</a> <a id="4036" href="Data.List.Relation.Unary.Any.Properties.html#3971" class="Bound">p</a><a id="4037" class="Symbol">)</a>
<a id="4039" href="Data.List.Relation.Unary.Any.Properties.html#3936" class="Function">map-∘</a> <a id="4045" href="Data.List.Relation.Unary.Any.Properties.html#4045" class="Bound">f</a> <a id="4047" href="Data.List.Relation.Unary.Any.Properties.html#4047" class="Bound">g</a> <a id="4049" class="Symbol">(</a><a id="4050" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="4056" href="Data.List.Relation.Unary.Any.Properties.html#4056" class="Bound">p</a><a id="4057" class="Symbol">)</a> <a id="4059" class="Symbol">=</a> <a id="4061" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="4066" href="Data.List.Relation.Unary.Any.Properties.html#3936" class="Function">map-∘</a> <a id="4072" href="Data.List.Relation.Unary.Any.Properties.html#4072" class="Bound">f</a> <a id="4074" href="Data.List.Relation.Unary.Any.Properties.html#4074" class="Bound">g</a> <a id="4076" class="Symbol">(</a><a id="4077" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="4083" href="Data.List.Relation.Unary.Any.Properties.html#4083" class="Bound">p</a><a id="4084" class="Symbol">)</a> <a id="4086" class="Symbol">=</a> <a id="4088" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="4095" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="4101" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="4103" href="Data.List.Relation.Unary.Any.Properties.html#3936" class="Function">map-∘</a> <a id="4109" href="Data.List.Relation.Unary.Any.Properties.html#4072" class="Bound">f</a> <a id="4111" href="Data.List.Relation.Unary.Any.Properties.html#4074" class="Bound">g</a> <a id="4113" href="Data.List.Relation.Unary.Any.Properties.html#4083" class="Bound">p</a>
<a id="4116" class="Comment">------------------------------------------------------------------------</a>
<a id="4189" class="Comment">-- Any.lookup</a>
<a id="lookup-result"></a><a id="4204" href="Data.List.Relation.Unary.Any.Properties.html#4204" class="Function">lookup-result</a> <a id="4218" class="Symbol">:</a> <a id="4220" class="Symbol">∀</a> <a id="4222" class="Symbol">(</a><a id="4223" href="Data.List.Relation.Unary.Any.Properties.html#4223" class="Bound">p</a> <a id="4225" class="Symbol">:</a> <a id="4227" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="4231" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="4233" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="4235" class="Symbol">)</a> <a id="4237" class="Symbol">→</a> <a id="4239" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="4241" class="Symbol">(</a><a id="4242" href="Data.List.Relation.Unary.Any.html#1919" class="Function">Any.lookup</a> <a id="4253" href="Data.List.Relation.Unary.Any.Properties.html#4223" class="Bound">p</a><a id="4254" class="Symbol">)</a>
<a id="4256" href="Data.List.Relation.Unary.Any.Properties.html#4204" class="Function">lookup-result</a> <a id="4270" class="Symbol">(</a><a id="4271" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="4276" href="Data.List.Relation.Unary.Any.Properties.html#4276" class="Bound">px</a><a id="4278" class="Symbol">)</a> <a id="4280" class="Symbol">=</a> <a id="4282" href="Data.List.Relation.Unary.Any.Properties.html#4276" class="Bound">px</a>
<a id="4285" href="Data.List.Relation.Unary.Any.Properties.html#4204" class="Function">lookup-result</a> <a id="4299" class="Symbol">(</a><a id="4300" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="4306" href="Data.List.Relation.Unary.Any.Properties.html#4306" class="Bound">p</a><a id="4307" class="Symbol">)</a> <a id="4309" class="Symbol">=</a> <a id="4311" href="Data.List.Relation.Unary.Any.Properties.html#4204" class="Function">lookup-result</a> <a id="4325" href="Data.List.Relation.Unary.Any.Properties.html#4306" class="Bound">p</a>
<a id="lookup-index"></a><a id="4328" href="Data.List.Relation.Unary.Any.Properties.html#4328" class="Function">lookup-index</a> <a id="4341" class="Symbol">:</a> <a id="4343" class="Symbol">∀</a> <a id="4345" class="Symbol">(</a><a id="4346" href="Data.List.Relation.Unary.Any.Properties.html#4346" class="Bound">p</a> <a id="4348" class="Symbol">:</a> <a id="4350" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="4354" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="4356" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="4358" class="Symbol">)</a> <a id="4360" class="Symbol">→</a> <a id="4362" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="4364" class="Symbol">(</a><a id="4365" href="Data.List.Base.html#6106" class="Function">lookup</a> <a id="4372" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="4375" class="Symbol">(</a><a id="4376" href="Data.List.Relation.Unary.Any.html#1817" class="Function">Any.index</a> <a id="4386" href="Data.List.Relation.Unary.Any.Properties.html#4346" class="Bound">p</a><a id="4387" class="Symbol">))</a>
<a id="4390" href="Data.List.Relation.Unary.Any.Properties.html#4328" class="Function">lookup-index</a> <a id="4403" class="Symbol">(</a><a id="4404" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="4409" href="Data.List.Relation.Unary.Any.Properties.html#4409" class="Bound">px</a><a id="4411" class="Symbol">)</a> <a id="4415" class="Symbol">=</a> <a id="4417" href="Data.List.Relation.Unary.Any.Properties.html#4409" class="Bound">px</a>
<a id="4420" href="Data.List.Relation.Unary.Any.Properties.html#4328" class="Function">lookup-index</a> <a id="4433" class="Symbol">(</a><a id="4434" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="4440" href="Data.List.Relation.Unary.Any.Properties.html#4440" class="Bound">pxs</a><a id="4443" class="Symbol">)</a> <a id="4445" class="Symbol">=</a> <a id="4447" href="Data.List.Relation.Unary.Any.Properties.html#4328" class="Function">lookup-index</a> <a id="4460" href="Data.List.Relation.Unary.Any.Properties.html#4440" class="Bound">pxs</a>
<a id="4465" class="Comment">------------------------------------------------------------------------</a>
<a id="4538" class="Comment">-- Swapping</a>
<a id="4551" class="Comment">-- Nested occurrences of Any can sometimes be swapped. See also ×↔.</a>
<a id="swap"></a><a id="4620" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="4625" class="Symbol">:</a> <a id="4627" class="Symbol">∀</a> <a id="4629" class="Symbol">{</a><a id="4630" href="Data.List.Relation.Unary.Any.Properties.html#4630" class="Bound">P</a> <a id="4632" class="Symbol">:</a> <a id="4634" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="4636" class="Symbol">→</a> <a id="4638" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="4640" class="Symbol">→</a> <a id="4642" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="4646" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="4647" class="Symbol">}</a> <a id="4649" class="Symbol">→</a>
<a id="4658" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="4662" class="Symbol">(λ</a> <a id="4665" href="Data.List.Relation.Unary.Any.Properties.html#4665" class="Bound">x</a> <a id="4667" class="Symbol">→</a> <a id="4669" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="4673" class="Symbol">(</a><a id="4674" href="Data.List.Relation.Unary.Any.Properties.html#4630" class="Bound">P</a> <a id="4676" href="Data.List.Relation.Unary.Any.Properties.html#4665" class="Bound">x</a><a id="4677" class="Symbol">)</a> <a id="4679" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="4681" class="Symbol">)</a> <a id="4683" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="4686" class="Symbol">→</a> <a id="4688" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="4692" class="Symbol">(λ</a> <a id="4695" href="Data.List.Relation.Unary.Any.Properties.html#4695" class="Bound">y</a> <a id="4697" class="Symbol">→</a> <a id="4699" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="4703" class="Symbol">(</a><a id="4704" href="Function.Base.html#1554" class="Function">flip</a> <a id="4709" href="Data.List.Relation.Unary.Any.Properties.html#4630" class="Bound">P</a> <a id="4711" href="Data.List.Relation.Unary.Any.Properties.html#4695" class="Bound">y</a><a id="4712" class="Symbol">)</a> <a id="4714" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="4716" class="Symbol">)</a> <a id="4718" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a>
<a id="4721" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="4726" class="Symbol">(</a><a id="4727" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="4733" href="Data.List.Relation.Unary.Any.Properties.html#4733" class="Bound">pys</a><a id="4736" class="Symbol">)</a> <a id="4739" class="Symbol">=</a> <a id="4741" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="4749" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="4754" href="Data.List.Relation.Unary.Any.Properties.html#4733" class="Bound">pys</a>
<a id="4758" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="4763" class="Symbol">(</a><a id="4764" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="4770" href="Data.List.Relation.Unary.Any.Properties.html#4770" class="Bound">pxys</a><a id="4774" class="Symbol">)</a> <a id="4776" class="Symbol">=</a> <a id="4778" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="4786" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="4792" class="Symbol">(</a><a id="4793" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="4798" href="Data.List.Relation.Unary.Any.Properties.html#4770" class="Bound">pxys</a><a id="4802" class="Symbol">)</a>
<a id="swap-there"></a><a id="4805" href="Data.List.Relation.Unary.Any.Properties.html#4805" class="Function">swap-there</a> <a id="4816" class="Symbol">:</a> <a id="4818" class="Symbol">∀</a> <a id="4820" class="Symbol">{</a><a id="4821" href="Data.List.Relation.Unary.Any.Properties.html#4821" class="Bound">P</a> <a id="4823" class="Symbol">:</a> <a id="4825" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="4827" class="Symbol">→</a> <a id="4829" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="4831" class="Symbol">→</a> <a id="4833" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="4837" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="4838" class="Symbol">}</a> <a id="4840" class="Symbol">→</a>
<a id="4855" class="Symbol">(</a><a id="4856" href="Data.List.Relation.Unary.Any.Properties.html#4856" class="Bound">any</a> <a id="4860" class="Symbol">:</a> <a id="4862" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="4866" class="Symbol">(λ</a> <a id="4869" href="Data.List.Relation.Unary.Any.Properties.html#4869" class="Bound">x</a> <a id="4871" class="Symbol">→</a> <a id="4873" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="4877" class="Symbol">(</a><a id="4878" href="Data.List.Relation.Unary.Any.Properties.html#4821" class="Bound">P</a> <a id="4880" href="Data.List.Relation.Unary.Any.Properties.html#4869" class="Bound">x</a><a id="4881" class="Symbol">)</a> <a id="4883" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="4885" class="Symbol">)</a> <a id="4887" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="4889" class="Symbol">)</a> <a id="4891" class="Symbol">→</a>
<a id="4906" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="4911" class="Symbol">(</a><a id="4912" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="4920" class="Symbol">(</a><a id="4921" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="4927" class="Symbol">{</a><a id="4928" class="Argument">x</a> <a id="4930" class="Symbol">=</a> <a id="4932" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a><a id="4933" class="Symbol">})</a> <a id="4936" href="Data.List.Relation.Unary.Any.Properties.html#4856" class="Bound">any</a><a id="4939" class="Symbol">)</a> <a id="4941" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="4943" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="4949" class="Symbol">(</a><a id="4950" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="4955" href="Data.List.Relation.Unary.Any.Properties.html#4856" class="Bound">any</a><a id="4958" class="Symbol">)</a>
<a id="4960" href="Data.List.Relation.Unary.Any.Properties.html#4805" class="Function">swap-there</a> <a id="4971" class="Symbol">(</a><a id="4972" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="4978" href="Data.List.Relation.Unary.Any.Properties.html#4978" class="Bound">pys</a><a id="4981" class="Symbol">)</a> <a id="4984" class="Symbol">=</a> <a id="4986" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="4991" href="Data.List.Relation.Unary.Any.Properties.html#4805" class="Function">swap-there</a> <a id="5002" class="Symbol">(</a><a id="5003" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="5009" href="Data.List.Relation.Unary.Any.Properties.html#5009" class="Bound">pxys</a><a id="5013" class="Symbol">)</a> <a id="5015" class="Symbol">=</a> <a id="5017" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="5024" class="Symbol">(</a><a id="5025" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="5033" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a><a id="5038" class="Symbol">)</a> <a id="5040" class="Symbol">(</a><a id="5041" href="Data.List.Relation.Unary.Any.Properties.html#4805" class="Function">swap-there</a> <a id="5052" href="Data.List.Relation.Unary.Any.Properties.html#5009" class="Bound">pxys</a><a id="5056" class="Symbol">)</a>
<a id="swap-invol"></a><a id="5059" href="Data.List.Relation.Unary.Any.Properties.html#5059" class="Function">swap-invol</a> <a id="5070" class="Symbol">:</a> <a id="5072" class="Symbol">∀</a> <a id="5074" class="Symbol">{</a><a id="5075" href="Data.List.Relation.Unary.Any.Properties.html#5075" class="Bound">P</a> <a id="5077" class="Symbol">:</a> <a id="5079" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="5081" class="Symbol">→</a> <a id="5083" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="5085" class="Symbol">→</a> <a id="5087" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="5091" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="5092" class="Symbol">}</a> <a id="5094" class="Symbol">→</a>
<a id="5109" class="Symbol">(</a><a id="5110" href="Data.List.Relation.Unary.Any.Properties.html#5110" class="Bound">any</a> <a id="5114" class="Symbol">:</a> <a id="5116" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="5120" class="Symbol">(λ</a> <a id="5123" href="Data.List.Relation.Unary.Any.Properties.html#5123" class="Bound">x</a> <a id="5125" class="Symbol">→</a> <a id="5127" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="5131" class="Symbol">(</a><a id="5132" href="Data.List.Relation.Unary.Any.Properties.html#5075" class="Bound">P</a> <a id="5134" href="Data.List.Relation.Unary.Any.Properties.html#5123" class="Bound">x</a><a id="5135" class="Symbol">)</a> <a id="5137" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="5139" class="Symbol">)</a> <a id="5141" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="5143" class="Symbol">)</a> <a id="5145" class="Symbol">→</a>
<a id="5160" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="5165" class="Symbol">(</a><a id="5166" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="5171" href="Data.List.Relation.Unary.Any.Properties.html#5110" class="Bound">any</a><a id="5174" class="Symbol">)</a> <a id="5176" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="5178" href="Data.List.Relation.Unary.Any.Properties.html#5110" class="Bound">any</a>
<a id="5182" href="Data.List.Relation.Unary.Any.Properties.html#5059" class="Function">swap-invol</a> <a id="5193" class="Symbol">(</a><a id="5194" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="5199" class="Symbol">(</a><a id="5200" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="5205" href="Data.List.Relation.Unary.Any.Properties.html#5205" class="Bound">px</a><a id="5207" class="Symbol">))</a> <a id="5212" class="Symbol">=</a> <a id="5214" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="5219" href="Data.List.Relation.Unary.Any.Properties.html#5059" class="Function">swap-invol</a> <a id="5230" class="Symbol">(</a><a id="5231" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="5236" class="Symbol">(</a><a id="5237" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="5243" href="Data.List.Relation.Unary.Any.Properties.html#5243" class="Bound">pys</a><a id="5246" class="Symbol">))</a> <a id="5249" class="Symbol">=</a>
<a id="5253" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="5260" class="Symbol">(</a><a id="5261" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="5269" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a><a id="5274" class="Symbol">)</a> <a id="5276" class="Symbol">(</a><a id="5277" href="Data.List.Relation.Unary.Any.Properties.html#5059" class="Function">swap-invol</a> <a id="5288" class="Symbol">(</a><a id="5289" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="5294" href="Data.List.Relation.Unary.Any.Properties.html#5243" class="Bound">pys</a><a id="5297" class="Symbol">))</a>
<a id="5300" href="Data.List.Relation.Unary.Any.Properties.html#5059" class="Function">swap-invol</a> <a id="5311" class="Symbol">(</a><a id="5312" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="5318" href="Data.List.Relation.Unary.Any.Properties.html#5318" class="Bound">pxys</a><a id="5322" class="Symbol">)</a> <a id="5330" class="Symbol">=</a>
<a id="5334" href="Relation.Binary.PropositionalEquality.Core.html#1729" class="Function">P.trans</a> <a id="5342" class="Symbol">(</a><a id="5343" href="Data.List.Relation.Unary.Any.Properties.html#4805" class="Function">swap-there</a> <a id="5354" class="Symbol">(</a><a id="5355" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="5360" href="Data.List.Relation.Unary.Any.Properties.html#5318" class="Bound">pxys</a><a id="5364" class="Symbol">))</a> <a id="5367" class="Symbol">(</a><a id="5368" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="5375" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="5381" class="Symbol">(</a><a id="5382" href="Data.List.Relation.Unary.Any.Properties.html#5059" class="Function">swap-invol</a> <a id="5393" href="Data.List.Relation.Unary.Any.Properties.html#5318" class="Bound">pxys</a><a id="5397" class="Symbol">))</a>
<a id="swap↔"></a><a id="5401" href="Data.List.Relation.Unary.Any.Properties.html#5401" class="Function">swap↔</a> <a id="5407" class="Symbol">:</a> <a id="5409" class="Symbol">∀</a> <a id="5411" class="Symbol">{</a><a id="5412" href="Data.List.Relation.Unary.Any.Properties.html#5412" class="Bound">P</a> <a id="5414" class="Symbol">:</a> <a id="5416" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="5418" class="Symbol">→</a> <a id="5420" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="5422" class="Symbol">→</a> <a id="5424" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="5428" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="5429" class="Symbol">}</a> <a id="5431" class="Symbol">→</a>
<a id="5440" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="5444" class="Symbol">(λ</a> <a id="5447" href="Data.List.Relation.Unary.Any.Properties.html#5447" class="Bound">x</a> <a id="5449" class="Symbol">→</a> <a id="5451" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="5455" class="Symbol">(</a><a id="5456" href="Data.List.Relation.Unary.Any.Properties.html#5412" class="Bound">P</a> <a id="5458" href="Data.List.Relation.Unary.Any.Properties.html#5447" class="Bound">x</a><a id="5459" class="Symbol">)</a> <a id="5461" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="5463" class="Symbol">)</a> <a id="5465" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="5468" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="5470" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="5474" class="Symbol">(λ</a> <a id="5477" href="Data.List.Relation.Unary.Any.Properties.html#5477" class="Bound">y</a> <a id="5479" class="Symbol">→</a> <a id="5481" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="5485" class="Symbol">(</a><a id="5486" href="Function.Base.html#1554" class="Function">flip</a> <a id="5491" href="Data.List.Relation.Unary.Any.Properties.html#5412" class="Bound">P</a> <a id="5493" href="Data.List.Relation.Unary.Any.Properties.html#5477" class="Bound">y</a><a id="5494" class="Symbol">)</a> <a id="5496" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="5498" class="Symbol">)</a> <a id="5500" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a>
<a id="5503" href="Data.List.Relation.Unary.Any.Properties.html#5401" class="Function">swap↔</a> <a id="5509" class="Symbol">=</a> <a id="5511" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="5519" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="5524" href="Data.List.Relation.Unary.Any.Properties.html#4620" class="Function">swap</a> <a id="5529" href="Data.List.Relation.Unary.Any.Properties.html#5059" class="Function">swap-invol</a> <a id="5540" href="Data.List.Relation.Unary.Any.Properties.html#5059" class="Function">swap-invol</a>
<a id="5552" class="Comment">------------------------------------------------------------------------</a>
<a id="5625" class="Comment">-- Lemmas relating Any to ⊥</a>
<a id="⊥↔Any⊥"></a><a id="5654" href="Data.List.Relation.Unary.Any.Properties.html#5654" class="Function">⊥↔Any⊥</a> <a id="5661" class="Symbol">:</a> <a id="5663" href="Data.Empty.html#526" class="Datatype">⊥</a> <a id="5665" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="5667" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="5671" class="Symbol">(</a><a id="5672" href="Function.Base.html#636" class="Function">const</a> <a id="5678" href="Data.Empty.html#526" class="Datatype">⊥</a><a id="5679" class="Symbol">)</a> <a id="5681" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="5684" href="Data.List.Relation.Unary.Any.Properties.html#5654" class="Function">⊥↔Any⊥</a> <a id="5691" class="Symbol">=</a> <a id="5693" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="5701" class="Symbol">(λ())</a> <a id="5707" class="Symbol">(λ</a> <a id="5710" href="Data.List.Relation.Unary.Any.Properties.html#5710" class="Bound">p</a> <a id="5712" class="Symbol">→</a> <a id="5714" href="Data.List.Relation.Unary.Any.Properties.html#5753" class="Function">from</a> <a id="5719" href="Data.List.Relation.Unary.Any.Properties.html#5710" class="Bound">p</a><a id="5720" class="Symbol">)</a> <a id="5722" class="Symbol">(λ())</a> <a id="5728" class="Symbol">(λ</a> <a id="5731" href="Data.List.Relation.Unary.Any.Properties.html#5731" class="Bound">p</a> <a id="5733" class="Symbol">→</a> <a id="5735" href="Data.List.Relation.Unary.Any.Properties.html#5753" class="Function">from</a> <a id="5740" href="Data.List.Relation.Unary.Any.Properties.html#5731" class="Bound">p</a><a id="5741" class="Symbol">)</a>
<a id="5745" class="Keyword">where</a>
<a id="5753" href="Data.List.Relation.Unary.Any.Properties.html#5753" class="Function">from</a> <a id="5758" class="Symbol">:</a> <a id="5760" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="5764" class="Symbol">(</a><a id="5765" href="Function.Base.html#636" class="Function">const</a> <a id="5771" href="Data.Empty.html#526" class="Datatype">⊥</a><a id="5772" class="Symbol">)</a> <a id="5774" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="5777" class="Symbol">→</a> <a id="5779" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a>
<a id="5783" href="Data.List.Relation.Unary.Any.Properties.html#5753" class="Function">from</a> <a id="5788" class="Symbol">(</a><a id="5789" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="5795" href="Data.List.Relation.Unary.Any.Properties.html#5795" class="Bound">p</a><a id="5796" class="Symbol">)</a> <a id="5798" class="Symbol">=</a> <a id="5800" href="Data.List.Relation.Unary.Any.Properties.html#5753" class="Function">from</a> <a id="5805" href="Data.List.Relation.Unary.Any.Properties.html#5795" class="Bound">p</a>
<a id="⊥↔Any[]"></a><a id="5808" href="Data.List.Relation.Unary.Any.Properties.html#5808" class="Function">⊥↔Any[]</a> <a id="5816" class="Symbol">:</a> <a id="5818" href="Data.Empty.html#526" class="Datatype">⊥</a> <a id="5820" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="5822" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="5826" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="5828" class="InductiveConstructor">[]</a>
<a id="5831" href="Data.List.Relation.Unary.Any.Properties.html#5808" class="Function">⊥↔Any[]</a> <a id="5839" class="Symbol">=</a> <a id="5841" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="5849" class="Symbol">(λ())</a> <a id="5855" class="Symbol">(λ())</a> <a id="5861" class="Symbol">(λ())</a> <a id="5867" class="Symbol">(λ())</a>
<a id="5874" class="Comment">------------------------------------------------------------------------</a>
<a id="5947" class="Comment">-- Lemmas relating Any to ⊤</a>
<a id="5976" class="Comment">-- These introduction and elimination rules are not inverses, though.</a>
<a id="any⁺"></a><a id="6047" href="Data.List.Relation.Unary.Any.Properties.html#6047" class="Function">any⁺</a> <a id="6052" class="Symbol">:</a> <a id="6054" class="Symbol">∀</a> <a id="6056" class="Symbol">(</a><a id="6057" href="Data.List.Relation.Unary.Any.Properties.html#6057" class="Bound">p</a> <a id="6059" class="Symbol">:</a> <a id="6061" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="6063" class="Symbol">→</a> <a id="6065" href="Agda.Builtin.Bool.html#163" class="Datatype">Bool</a><a id="6069" class="Symbol">)</a> <a id="6071" class="Symbol">→</a> <a id="6073" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6077" class="Symbol">(</a><a id="6078" href="Data.Bool.Base.html#1451" class="Function">T</a> <a id="6080" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="6082" href="Data.List.Relation.Unary.Any.Properties.html#6057" class="Bound">p</a><a id="6083" class="Symbol">)</a> <a id="6085" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="6088" class="Symbol">→</a> <a id="6090" href="Data.Bool.Base.html#1451" class="Function">T</a> <a id="6092" class="Symbol">(</a><a id="6093" href="Data.List.Base.html#4677" class="Function">any</a> <a id="6097" href="Data.List.Relation.Unary.Any.Properties.html#6057" class="Bound">p</a> <a id="6099" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="6101" class="Symbol">)</a>
<a id="6103" href="Data.List.Relation.Unary.Any.Properties.html#6047" class="Function">any⁺</a> <a id="6108" href="Data.List.Relation.Unary.Any.Properties.html#6108" class="Bound">p</a> <a id="6110" class="Symbol">(</a><a id="6111" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="6117" href="Data.List.Relation.Unary.Any.Properties.html#6117" class="Bound">px</a><a id="6119" class="Symbol">)</a> <a id="6130" class="Symbol">=</a> <a id="6132" href="Function.Equivalence.html#1000" class="Field">Equivalence.from</a> <a id="6149" href="Data.Bool.Properties.html#15215" class="Function">T-∨</a> <a id="6153" href="Function.Equality.html#1064" class="Field Operator">⟨$⟩</a> <a id="6157" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="6162" href="Data.List.Relation.Unary.Any.Properties.html#6117" class="Bound">px</a>
<a id="6165" href="Data.List.Relation.Unary.Any.Properties.html#6047" class="Function">any⁺</a> <a id="6170" href="Data.List.Relation.Unary.Any.Properties.html#6170" class="Bound">p</a> <a id="6172" class="Symbol">(</a><a id="6173" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="6179" class="Symbol">{</a><a id="6180" class="Argument">x</a> <a id="6182" class="Symbol">=</a> <a id="6184" href="Data.List.Relation.Unary.Any.Properties.html#6184" class="Bound">x</a><a id="6185" class="Symbol">}</a> <a id="6187" href="Data.List.Relation.Unary.Any.Properties.html#6187" class="Bound">pxs</a><a id="6190" class="Symbol">)</a> <a id="6192" class="Keyword">with</a> <a id="6197" href="Data.List.Relation.Unary.Any.Properties.html#6170" class="Bound">p</a> <a id="6199" href="Data.List.Relation.Unary.Any.Properties.html#6184" class="Bound">x</a>
<a id="6201" class="Symbol">...</a> <a id="6205" class="Symbol">|</a> <a id="6207" href="Agda.Builtin.Bool.html#188" class="InductiveConstructor">true</a> <a id="6213" class="Symbol">=</a> <a id="6215" class="Symbol">_</a>
<a id="6217" class="Symbol">...</a> <a id="6221" class="Symbol">|</a> <a id="6223" href="Agda.Builtin.Bool.html#182" class="InductiveConstructor">false</a> <a id="6229" class="Symbol">=</a> <a id="6231" href="Data.List.Relation.Unary.Any.Properties.html#6047" class="Function">any⁺</a> <a id="6236" class="Bound">p</a> <a id="6238" class="Bound">pxs</a>
<a id="any⁻"></a><a id="6243" href="Data.List.Relation.Unary.Any.Properties.html#6243" class="Function">any⁻</a> <a id="6248" class="Symbol">:</a> <a id="6250" class="Symbol">∀</a> <a id="6252" class="Symbol">(</a><a id="6253" href="Data.List.Relation.Unary.Any.Properties.html#6253" class="Bound">p</a> <a id="6255" class="Symbol">:</a> <a id="6257" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="6259" class="Symbol">→</a> <a id="6261" href="Agda.Builtin.Bool.html#163" class="Datatype">Bool</a><a id="6265" class="Symbol">)</a> <a id="6267" href="Data.List.Relation.Unary.Any.Properties.html#6267" class="Bound">xs</a> <a id="6270" class="Symbol">→</a> <a id="6272" href="Data.Bool.Base.html#1451" class="Function">T</a> <a id="6274" class="Symbol">(</a><a id="6275" href="Data.List.Base.html#4677" class="Function">any</a> <a id="6279" href="Data.List.Relation.Unary.Any.Properties.html#6253" class="Bound">p</a> <a id="6281" href="Data.List.Relation.Unary.Any.Properties.html#6267" class="Bound">xs</a><a id="6283" class="Symbol">)</a> <a id="6285" class="Symbol">→</a> <a id="6287" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6291" class="Symbol">(</a><a id="6292" href="Data.Bool.Base.html#1451" class="Function">T</a> <a id="6294" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="6296" href="Data.List.Relation.Unary.Any.Properties.html#6253" class="Bound">p</a><a id="6297" class="Symbol">)</a> <a id="6299" href="Data.List.Relation.Unary.Any.Properties.html#6267" class="Bound">xs</a>
<a id="6302" href="Data.List.Relation.Unary.Any.Properties.html#6243" class="Function">any⁻</a> <a id="6307" href="Data.List.Relation.Unary.Any.Properties.html#6307" class="Bound">p</a> <a id="6309" class="Symbol">(</a><a id="6310" href="Data.List.Relation.Unary.Any.Properties.html#6310" class="Bound">x</a> <a id="6312" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="6314" href="Data.List.Relation.Unary.Any.Properties.html#6314" class="Bound">xs</a><a id="6316" class="Symbol">)</a> <a id="6318" href="Data.List.Relation.Unary.Any.Properties.html#6318" class="Bound">px∷xs</a> <a id="6324" class="Keyword">with</a> <a id="6329" href="Data.List.Relation.Unary.Any.Properties.html#6307" class="Bound">p</a> <a id="6331" href="Data.List.Relation.Unary.Any.Properties.html#6310" class="Bound">x</a> <a id="6333" class="Symbol">|</a> <a id="6335" href="Relation.Binary.PropositionalEquality.html#2382" class="Function">inspect</a> <a id="6343" href="Data.List.Relation.Unary.Any.Properties.html#6307" class="Bound">p</a> <a id="6345" href="Data.List.Relation.Unary.Any.Properties.html#6310" class="Bound">x</a>
<a id="6347" class="Symbol">...</a> <a id="6351" class="Symbol">|</a> <a id="6353" href="Agda.Builtin.Bool.html#188" class="InductiveConstructor">true</a> <a id="6359" class="Symbol">|</a> <a id="6361" href="Relation.Binary.PropositionalEquality.html#2356" class="InductiveConstructor Operator">P.[</a> <a id="6365" href="Data.List.Relation.Unary.Any.Properties.html#6365" class="Bound">eq</a> <a id="6368" href="Relation.Binary.PropositionalEquality.html#2356" class="InductiveConstructor Operator">]</a> <a id="6370" class="Symbol">=</a> <a id="6372" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="6377" class="Symbol">(</a><a id="6378" href="Function.Equivalence.html#1000" class="Field">Equivalence.from</a> <a id="6395" href="Data.Bool.Properties.html#14733" class="Function">T-≡</a> <a id="6399" href="Function.Equality.html#1064" class="Field Operator">⟨$⟩</a> <a id="6403" href="Data.List.Relation.Unary.Any.Properties.html#6365" class="Bound">eq</a><a id="6405" class="Symbol">)</a>
<a id="6407" class="Symbol">...</a> <a id="6411" class="Symbol">|</a> <a id="6413" href="Agda.Builtin.Bool.html#182" class="InductiveConstructor">false</a> <a id="6419" class="Symbol">|</a> <a id="6421" class="Symbol">_</a> <a id="6430" class="Symbol">=</a> <a id="6432" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="6438" class="Symbol">(</a><a id="6439" href="Data.List.Relation.Unary.Any.Properties.html#6243" class="Function">any⁻</a> <a id="6444" class="Bound">p</a> <a id="6446" class="Bound">xs</a> <a id="6449" class="Bound">px∷xs</a><a id="6454" class="Symbol">)</a>
<a id="any⇔"></a><a id="6457" href="Data.List.Relation.Unary.Any.Properties.html#6457" class="Function">any⇔</a> <a id="6462" class="Symbol">:</a> <a id="6464" class="Symbol">∀</a> <a id="6466" class="Symbol">{</a><a id="6467" href="Data.List.Relation.Unary.Any.Properties.html#6467" class="Bound">p</a> <a id="6469" class="Symbol">:</a> <a id="6471" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="6473" class="Symbol">→</a> <a id="6475" href="Agda.Builtin.Bool.html#163" class="Datatype">Bool</a><a id="6479" class="Symbol">}</a> <a id="6481" class="Symbol">→</a> <a id="6483" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6487" class="Symbol">(</a><a id="6488" href="Data.Bool.Base.html#1451" class="Function">T</a> <a id="6490" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="6492" href="Data.List.Relation.Unary.Any.Properties.html#6467" class="Bound">p</a><a id="6493" class="Symbol">)</a> <a id="6495" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="6498" href="Function.Equivalence.html#1204" class="Function Operator">⇔</a> <a id="6500" href="Data.Bool.Base.html#1451" class="Function">T</a> <a id="6502" class="Symbol">(</a><a id="6503" href="Data.List.Base.html#4677" class="Function">any</a> <a id="6507" href="Data.List.Relation.Unary.Any.Properties.html#6467" class="Bound">p</a> <a id="6509" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="6511" class="Symbol">)</a>
<a id="6513" href="Data.List.Relation.Unary.Any.Properties.html#6457" class="Function">any⇔</a> <a id="6518" class="Symbol">=</a> <a id="6520" href="Function.Equivalence.html#1297" class="Function">equivalence</a> <a id="6532" class="Symbol">(</a><a id="6533" href="Data.List.Relation.Unary.Any.Properties.html#6047" class="Function">any⁺</a> <a id="6538" class="Symbol">_)</a> <a id="6541" class="Symbol">(</a><a id="6542" href="Data.List.Relation.Unary.Any.Properties.html#6243" class="Function">any⁻</a> <a id="6547" class="Symbol">_</a> <a id="6549" class="Symbol">_)</a>
<a id="6553" class="Comment">------------------------------------------------------------------------</a>
<a id="6626" class="Comment">-- Sums commute with Any</a>
<a id="Any-⊎⁺"></a><a id="6652" href="Data.List.Relation.Unary.Any.Properties.html#6652" class="Function">Any-⊎⁺</a> <a id="6659" class="Symbol">:</a> <a id="6661" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6665" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="6667" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="6670" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="6672" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6676" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="6678" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="6681" class="Symbol">→</a> <a id="6683" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6687" class="Symbol">(λ</a> <a id="6690" href="Data.List.Relation.Unary.Any.Properties.html#6690" class="Bound">x</a> <a id="6692" class="Symbol">→</a> <a id="6694" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="6696" href="Data.List.Relation.Unary.Any.Properties.html#6690" class="Bound">x</a> <a id="6698" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="6700" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="6702" href="Data.List.Relation.Unary.Any.Properties.html#6690" class="Bound">x</a><a id="6703" class="Symbol">)</a> <a id="6705" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="6708" href="Data.List.Relation.Unary.Any.Properties.html#6652" class="Function">Any-⊎⁺</a> <a id="6715" class="Symbol">=</a> <a id="6717" href="Data.Sum.Base.html#1089" class="Function Operator">[</a> <a id="6719" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="6727" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="6732" href="Data.Sum.Base.html#1089" class="Function Operator">,</a> <a id="6734" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="6742" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="6747" href="Data.Sum.Base.html#1089" class="Function Operator">]′</a>
<a id="Any-⊎⁻"></a><a id="6751" href="Data.List.Relation.Unary.Any.Properties.html#6751" class="Function">Any-⊎⁻</a> <a id="6758" class="Symbol">:</a> <a id="6760" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6764" class="Symbol">(λ</a> <a id="6767" href="Data.List.Relation.Unary.Any.Properties.html#6767" class="Bound">x</a> <a id="6769" class="Symbol">→</a> <a id="6771" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="6773" href="Data.List.Relation.Unary.Any.Properties.html#6767" class="Bound">x</a> <a id="6775" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="6777" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="6779" href="Data.List.Relation.Unary.Any.Properties.html#6767" class="Bound">x</a><a id="6780" class="Symbol">)</a> <a id="6782" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="6785" class="Symbol">→</a> <a id="6787" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6791" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="6793" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="6796" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="6798" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6802" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="6804" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="6807" href="Data.List.Relation.Unary.Any.Properties.html#6751" class="Function">Any-⊎⁻</a> <a id="6814" class="Symbol">(</a><a id="6815" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="6820" class="Symbol">(</a><a id="6821" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="6826" href="Data.List.Relation.Unary.Any.Properties.html#6826" class="Bound">p</a><a id="6827" class="Symbol">))</a> <a id="6830" class="Symbol">=</a> <a id="6832" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="6837" class="Symbol">(</a><a id="6838" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="6843" href="Data.List.Relation.Unary.Any.Properties.html#6826" class="Bound">p</a><a id="6844" class="Symbol">)</a>
<a id="6846" href="Data.List.Relation.Unary.Any.Properties.html#6751" class="Function">Any-⊎⁻</a> <a id="6853" class="Symbol">(</a><a id="6854" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="6859" class="Symbol">(</a><a id="6860" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="6865" href="Data.List.Relation.Unary.Any.Properties.html#6865" class="Bound">q</a><a id="6866" class="Symbol">))</a> <a id="6869" class="Symbol">=</a> <a id="6871" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="6876" class="Symbol">(</a><a id="6877" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="6882" href="Data.List.Relation.Unary.Any.Properties.html#6865" class="Bound">q</a><a id="6883" class="Symbol">)</a>
<a id="6885" href="Data.List.Relation.Unary.Any.Properties.html#6751" class="Function">Any-⊎⁻</a> <a id="6892" class="Symbol">(</a><a id="6893" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="6899" href="Data.List.Relation.Unary.Any.Properties.html#6899" class="Bound">p</a><a id="6900" class="Symbol">)</a> <a id="6908" class="Symbol">=</a> <a id="6910" href="Data.Sum.Base.html#1362" class="Function">Sum.map</a> <a id="6918" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="6924" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="6930" class="Symbol">(</a><a id="6931" href="Data.List.Relation.Unary.Any.Properties.html#6751" class="Function">Any-⊎⁻</a> <a id="6938" href="Data.List.Relation.Unary.Any.Properties.html#6899" class="Bound">p</a><a id="6939" class="Symbol">)</a>
<a id="⊎↔"></a><a id="6942" href="Data.List.Relation.Unary.Any.Properties.html#6942" class="Function">⊎↔</a> <a id="6945" class="Symbol">:</a> <a id="6947" class="Symbol">(</a><a id="6948" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6952" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="6954" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="6957" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="6959" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6963" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="6965" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="6967" class="Symbol">)</a> <a id="6969" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="6971" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="6975" class="Symbol">(λ</a> <a id="6978" href="Data.List.Relation.Unary.Any.Properties.html#6978" class="Bound">x</a> <a id="6980" class="Symbol">→</a> <a id="6982" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="6984" href="Data.List.Relation.Unary.Any.Properties.html#6978" class="Bound">x</a> <a id="6986" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="6988" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="6990" href="Data.List.Relation.Unary.Any.Properties.html#6978" class="Bound">x</a><a id="6991" class="Symbol">)</a> <a id="6993" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="6996" href="Data.List.Relation.Unary.Any.Properties.html#6942" class="Function">⊎↔</a> <a id="6999" class="Symbol">{</a><a id="7000" class="Argument">P</a> <a id="7002" class="Symbol">=</a> <a id="7004" href="Data.List.Relation.Unary.Any.Properties.html#7004" class="Bound">P</a><a id="7005" class="Symbol">}</a> <a id="7007" class="Symbol">{</a><a id="7008" class="Argument">Q</a> <a id="7010" class="Symbol">=</a> <a id="7012" href="Data.List.Relation.Unary.Any.Properties.html#7012" class="Bound">Q</a><a id="7013" class="Symbol">}</a> <a id="7015" class="Symbol">=</a> <a id="7017" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="7025" href="Data.List.Relation.Unary.Any.Properties.html#6652" class="Function">Any-⊎⁺</a> <a id="7032" href="Data.List.Relation.Unary.Any.Properties.html#6751" class="Function">Any-⊎⁻</a> <a id="7039" href="Data.List.Relation.Unary.Any.Properties.html#7065" class="Function">from∘to</a> <a id="7047" href="Data.List.Relation.Unary.Any.Properties.html#7314" class="Function">to∘from</a>
<a id="7057" class="Keyword">where</a>
<a id="7065" href="Data.List.Relation.Unary.Any.Properties.html#7065" class="Function">from∘to</a> <a id="7073" class="Symbol">:</a> <a id="7075" class="Symbol">(</a><a id="7076" href="Data.List.Relation.Unary.Any.Properties.html#7076" class="Bound">p</a> <a id="7078" class="Symbol">:</a> <a id="7080" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7084" href="Data.List.Relation.Unary.Any.Properties.html#7004" class="Bound">P</a> <a id="7086" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="7089" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="7091" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7095" href="Data.List.Relation.Unary.Any.Properties.html#7012" class="Bound">Q</a> <a id="7097" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="7099" class="Symbol">)</a> <a id="7101" class="Symbol">→</a> <a id="7103" href="Data.List.Relation.Unary.Any.Properties.html#6751" class="Function">Any-⊎⁻</a> <a id="7110" class="Symbol">(</a><a id="7111" href="Data.List.Relation.Unary.Any.Properties.html#6652" class="Function">Any-⊎⁺</a> <a id="7118" href="Data.List.Relation.Unary.Any.Properties.html#7076" class="Bound">p</a><a id="7119" class="Symbol">)</a> <a id="7121" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="7123" href="Data.List.Relation.Unary.Any.Properties.html#7076" class="Bound">p</a>
<a id="7127" href="Data.List.Relation.Unary.Any.Properties.html#7065" class="Function">from∘to</a> <a id="7135" class="Symbol">(</a><a id="7136" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="7141" class="Symbol">(</a><a id="7142" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="7148" href="Data.List.Relation.Unary.Any.Properties.html#7148" class="Bound">p</a><a id="7149" class="Symbol">))</a> <a id="7152" class="Symbol">=</a> <a id="7154" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="7161" href="Data.List.Relation.Unary.Any.Properties.html#7065" class="Function">from∘to</a> <a id="7169" class="Symbol">(</a><a id="7170" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="7175" class="Symbol">(</a><a id="7176" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="7182" href="Data.List.Relation.Unary.Any.Properties.html#7182" class="Bound">p</a><a id="7183" class="Symbol">))</a> <a id="7186" class="Keyword">rewrite</a> <a id="7194" href="Data.List.Relation.Unary.Any.Properties.html#7065" class="Function">from∘to</a> <a id="7202" class="Symbol">(</a><a id="7203" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="7208" href="Data.List.Relation.Unary.Any.Properties.html#7182" class="Bound">p</a><a id="7209" class="Symbol">)</a> <a id="7211" class="Symbol">=</a> <a id="7213" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="7220" href="Data.List.Relation.Unary.Any.Properties.html#7065" class="Function">from∘to</a> <a id="7228" class="Symbol">(</a><a id="7229" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="7234" class="Symbol">(</a><a id="7235" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="7241" href="Data.List.Relation.Unary.Any.Properties.html#7241" class="Bound">q</a><a id="7242" class="Symbol">))</a> <a id="7245" class="Symbol">=</a> <a id="7247" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="7254" href="Data.List.Relation.Unary.Any.Properties.html#7065" class="Function">from∘to</a> <a id="7262" class="Symbol">(</a><a id="7263" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="7268" class="Symbol">(</a><a id="7269" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="7275" href="Data.List.Relation.Unary.Any.Properties.html#7275" class="Bound">q</a><a id="7276" class="Symbol">))</a> <a id="7279" class="Keyword">rewrite</a> <a id="7287" href="Data.List.Relation.Unary.Any.Properties.html#7065" class="Function">from∘to</a> <a id="7295" class="Symbol">(</a><a id="7296" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="7301" href="Data.List.Relation.Unary.Any.Properties.html#7275" class="Bound">q</a><a id="7302" class="Symbol">)</a> <a id="7304" class="Symbol">=</a> <a id="7306" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="7314" href="Data.List.Relation.Unary.Any.Properties.html#7314" class="Function">to∘from</a> <a id="7322" class="Symbol">:</a> <a id="7324" class="Symbol">(</a><a id="7325" href="Data.List.Relation.Unary.Any.Properties.html#7325" class="Bound">p</a> <a id="7327" class="Symbol">:</a> <a id="7329" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7333" class="Symbol">(λ</a> <a id="7336" href="Data.List.Relation.Unary.Any.Properties.html#7336" class="Bound">x</a> <a id="7338" class="Symbol">→</a> <a id="7340" href="Data.List.Relation.Unary.Any.Properties.html#7004" class="Bound">P</a> <a id="7342" href="Data.List.Relation.Unary.Any.Properties.html#7336" class="Bound">x</a> <a id="7344" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="7346" href="Data.List.Relation.Unary.Any.Properties.html#7012" class="Bound">Q</a> <a id="7348" href="Data.List.Relation.Unary.Any.Properties.html#7336" class="Bound">x</a><a id="7349" class="Symbol">)</a> <a id="7351" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="7353" class="Symbol">)</a> <a id="7355" class="Symbol">→</a> <a id="7357" href="Data.List.Relation.Unary.Any.Properties.html#6652" class="Function">Any-⊎⁺</a> <a id="7364" class="Symbol">(</a><a id="7365" href="Data.List.Relation.Unary.Any.Properties.html#6751" class="Function">Any-⊎⁻</a> <a id="7372" href="Data.List.Relation.Unary.Any.Properties.html#7325" class="Bound">p</a><a id="7373" class="Symbol">)</a> <a id="7375" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="7377" href="Data.List.Relation.Unary.Any.Properties.html#7325" class="Bound">p</a>
<a id="7381" href="Data.List.Relation.Unary.Any.Properties.html#7314" class="Function">to∘from</a> <a id="7389" class="Symbol">(</a><a id="7390" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="7395" class="Symbol">(</a><a id="7396" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="7401" href="Data.List.Relation.Unary.Any.Properties.html#7401" class="Bound">p</a><a id="7402" class="Symbol">))</a> <a id="7405" class="Symbol">=</a> <a id="7407" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="7414" href="Data.List.Relation.Unary.Any.Properties.html#7314" class="Function">to∘from</a> <a id="7422" class="Symbol">(</a><a id="7423" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="7428" class="Symbol">(</a><a id="7429" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="7434" href="Data.List.Relation.Unary.Any.Properties.html#7434" class="Bound">q</a><a id="7435" class="Symbol">))</a> <a id="7438" class="Symbol">=</a> <a id="7440" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="7447" href="Data.List.Relation.Unary.Any.Properties.html#7314" class="Function">to∘from</a> <a id="7455" class="Symbol">(</a><a id="7456" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="7462" href="Data.List.Relation.Unary.Any.Properties.html#7462" class="Bound">p</a><a id="7463" class="Symbol">)</a> <a id="7465" class="Keyword">with</a> <a id="7470" href="Data.List.Relation.Unary.Any.Properties.html#6751" class="Function">Any-⊎⁻</a> <a id="7477" href="Data.List.Relation.Unary.Any.Properties.html#7462" class="Bound">p</a> <a id="7479" class="Symbol">|</a> <a id="7481" href="Data.List.Relation.Unary.Any.Properties.html#7314" class="Function">to∘from</a> <a id="7489" href="Data.List.Relation.Unary.Any.Properties.html#7462" class="Bound">p</a>
<a id="7493" href="Data.List.Relation.Unary.Any.Properties.html#7314" class="Function">to∘from</a> <a id="7501" class="Symbol">(</a><a id="7502" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="7508" class="DottedPattern Symbol">.(</a><a id="7510" href="Data.List.Relation.Unary.Any.html#1643" class="DottedPattern Function">Any.map</a> <a id="7518" href="Data.Sum.Base.html#784" class="DottedPattern InductiveConstructor">inj₁</a> <a id="7523" href="Data.List.Relation.Unary.Any.Properties.html#7534" class="DottedPattern Bound">p</a><a id="7524" class="DottedPattern Symbol">)</a><a id="7525" class="Symbol">)</a> <a id="7527" class="Symbol">|</a> <a id="7529" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="7534" href="Data.List.Relation.Unary.Any.Properties.html#7534" class="Bound">p</a> <a id="7536" class="Symbol">|</a> <a id="7538" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a> <a id="7543" class="Symbol">=</a> <a id="7545" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="7552" href="Data.List.Relation.Unary.Any.Properties.html#7314" class="Function">to∘from</a> <a id="7560" class="Symbol">(</a><a id="7561" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="7567" class="DottedPattern Symbol">.(</a><a id="7569" href="Data.List.Relation.Unary.Any.html#1643" class="DottedPattern Function">Any.map</a> <a id="7577" href="Data.Sum.Base.html#809" class="DottedPattern InductiveConstructor">inj₂</a> <a id="7582" href="Data.List.Relation.Unary.Any.Properties.html#7593" class="DottedPattern Bound">q</a><a id="7583" class="DottedPattern Symbol">)</a><a id="7584" class="Symbol">)</a> <a id="7586" class="Symbol">|</a> <a id="7588" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="7593" href="Data.List.Relation.Unary.Any.Properties.html#7593" class="Bound">q</a> <a id="7595" class="Symbol">|</a> <a id="7597" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a> <a id="7602" class="Symbol">=</a> <a id="7604" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="7610" class="Comment">------------------------------------------------------------------------</a>
<a id="7683" class="Comment">-- Products "commute" with Any.</a>
<a id="Any-×⁺"></a><a id="7716" href="Data.List.Relation.Unary.Any.Properties.html#7716" class="Function">Any-×⁺</a> <a id="7723" class="Symbol">:</a> <a id="7725" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7729" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="7731" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="7734" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="7736" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7740" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="7742" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a> <a id="7745" class="Symbol">→</a> <a id="7747" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7751" class="Symbol">(λ</a> <a id="7754" href="Data.List.Relation.Unary.Any.Properties.html#7754" class="Bound">x</a> <a id="7756" class="Symbol">→</a> <a id="7758" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7762" class="Symbol">(λ</a> <a id="7765" href="Data.List.Relation.Unary.Any.Properties.html#7765" class="Bound">y</a> <a id="7767" class="Symbol">→</a> <a id="7769" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="7771" href="Data.List.Relation.Unary.Any.Properties.html#7754" class="Bound">x</a> <a id="7773" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="7775" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="7777" href="Data.List.Relation.Unary.Any.Properties.html#7765" class="Bound">y</a><a id="7778" class="Symbol">)</a> <a id="7780" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="7782" class="Symbol">)</a> <a id="7784" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="7787" href="Data.List.Relation.Unary.Any.Properties.html#7716" class="Function">Any-×⁺</a> <a id="7794" class="Symbol">(</a><a id="7795" href="Data.List.Relation.Unary.Any.Properties.html#7795" class="Bound">p</a> <a id="7797" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="7799" href="Data.List.Relation.Unary.Any.Properties.html#7799" class="Bound">q</a><a id="7800" class="Symbol">)</a> <a id="7802" class="Symbol">=</a> <a id="7804" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="7812" class="Symbol">(λ</a> <a id="7815" href="Data.List.Relation.Unary.Any.Properties.html#7815" class="Bound">p</a> <a id="7817" class="Symbol">→</a> <a id="7819" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="7827" class="Symbol">(λ</a> <a id="7830" href="Data.List.Relation.Unary.Any.Properties.html#7830" class="Bound">q</a> <a id="7832" class="Symbol">→</a> <a id="7834" class="Symbol">(</a><a id="7835" href="Data.List.Relation.Unary.Any.Properties.html#7815" class="Bound">p</a> <a id="7837" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="7839" href="Data.List.Relation.Unary.Any.Properties.html#7830" class="Bound">q</a><a id="7840" class="Symbol">))</a> <a id="7843" href="Data.List.Relation.Unary.Any.Properties.html#7799" class="Bound">q</a><a id="7844" class="Symbol">)</a> <a id="7846" href="Data.List.Relation.Unary.Any.Properties.html#7795" class="Bound">p</a>
<a id="Any-×⁻"></a><a id="7849" href="Data.List.Relation.Unary.Any.Properties.html#7849" class="Function">Any-×⁻</a> <a id="7856" class="Symbol">:</a> <a id="7858" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7862" class="Symbol">(λ</a> <a id="7865" href="Data.List.Relation.Unary.Any.Properties.html#7865" class="Bound">x</a> <a id="7867" class="Symbol">→</a> <a id="7869" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7873" class="Symbol">(λ</a> <a id="7876" href="Data.List.Relation.Unary.Any.Properties.html#7876" class="Bound">y</a> <a id="7878" class="Symbol">→</a> <a id="7880" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="7882" href="Data.List.Relation.Unary.Any.Properties.html#7865" class="Bound">x</a> <a id="7884" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="7886" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="7888" href="Data.List.Relation.Unary.Any.Properties.html#7876" class="Bound">y</a><a id="7889" class="Symbol">)</a> <a id="7891" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="7893" class="Symbol">)</a> <a id="7895" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="7898" class="Symbol">→</a>
<a id="7909" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7913" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="7915" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="7918" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="7920" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="7924" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="7926" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a>
<a id="7929" href="Data.List.Relation.Unary.Any.Properties.html#7849" class="Function">Any-×⁻</a> <a id="7936" href="Data.List.Relation.Unary.Any.Properties.html#7936" class="Bound">pq</a> <a id="7939" class="Keyword">with</a> <a id="7944" href="Data.Product.html#2675" class="Function">Prod.map₂</a> <a id="7954" class="Symbol">(</a><a id="7955" href="Data.Product.html#2675" class="Function">Prod.map₂</a> <a id="7965" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a><a id="7969" class="Symbol">)</a> <a id="7971" class="Symbol">(</a><a id="7972" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="7977" href="Data.List.Relation.Unary.Any.Properties.html#7936" class="Bound">pq</a><a id="7979" class="Symbol">)</a>
<a id="7981" class="Symbol">...</a> <a id="7985" class="Symbol">|</a> <a id="7987" class="Symbol">(</a><a id="7988" href="Data.List.Relation.Unary.Any.Properties.html#7988" class="Bound">x</a> <a id="7990" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="7992" href="Data.List.Relation.Unary.Any.Properties.html#7992" class="Bound">x∈xs</a> <a id="7997" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="7999" href="Data.List.Relation.Unary.Any.Properties.html#7999" class="Bound">y</a> <a id="8001" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8003" href="Data.List.Relation.Unary.Any.Properties.html#8003" class="Bound">y∈ys</a> <a id="8008" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8010" href="Data.List.Relation.Unary.Any.Properties.html#8010" class="Bound">p</a> <a id="8012" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8014" href="Data.List.Relation.Unary.Any.Properties.html#8014" class="Bound">q</a><a id="8015" class="Symbol">)</a> <a id="8017" class="Symbol">=</a> <a id="8019" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="8024" href="Data.List.Relation.Unary.Any.Properties.html#7992" class="Bound">x∈xs</a> <a id="8029" href="Data.List.Relation.Unary.Any.Properties.html#8010" class="Bound">p</a> <a id="8031" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8033" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="8038" href="Data.List.Relation.Unary.Any.Properties.html#8003" class="Bound">y∈ys</a> <a id="8043" href="Data.List.Relation.Unary.Any.Properties.html#8014" class="Bound">q</a>
<a id="×↔"></a><a id="8046" href="Data.List.Relation.Unary.Any.Properties.html#8046" class="Function">×↔</a> <a id="8049" class="Symbol">:</a> <a id="8051" class="Symbol">∀</a> <a id="8053" class="Symbol">{</a><a id="8054" href="Data.List.Relation.Unary.Any.Properties.html#8054" class="Bound">xs</a> <a id="8057" href="Data.List.Relation.Unary.Any.Properties.html#8057" class="Bound">ys</a><a id="8059" class="Symbol">}</a> <a id="8061" class="Symbol">→</a>
<a id="8068" class="Symbol">(</a><a id="8069" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="8073" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="8075" href="Data.List.Relation.Unary.Any.Properties.html#8054" class="Bound">xs</a> <a id="8078" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="8080" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="8084" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="8086" href="Data.List.Relation.Unary.Any.Properties.html#8057" class="Bound">ys</a><a id="8088" class="Symbol">)</a> <a id="8090" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="8092" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="8096" class="Symbol">(λ</a> <a id="8099" href="Data.List.Relation.Unary.Any.Properties.html#8099" class="Bound">x</a> <a id="8101" class="Symbol">→</a> <a id="8103" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="8107" class="Symbol">(λ</a> <a id="8110" href="Data.List.Relation.Unary.Any.Properties.html#8110" class="Bound">y</a> <a id="8112" class="Symbol">→</a> <a id="8114" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="8116" href="Data.List.Relation.Unary.Any.Properties.html#8099" class="Bound">x</a> <a id="8118" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="8120" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="8122" href="Data.List.Relation.Unary.Any.Properties.html#8110" class="Bound">y</a><a id="8123" class="Symbol">)</a> <a id="8125" href="Data.List.Relation.Unary.Any.Properties.html#8057" class="Bound">ys</a><a id="8127" class="Symbol">)</a> <a id="8129" href="Data.List.Relation.Unary.Any.Properties.html#8054" class="Bound">xs</a>
<a id="8132" href="Data.List.Relation.Unary.Any.Properties.html#8046" class="Function">×↔</a> <a id="8135" class="Symbol">{</a><a id="8136" class="Argument">P</a> <a id="8138" class="Symbol">=</a> <a id="8140" href="Data.List.Relation.Unary.Any.Properties.html#8140" class="Bound">P</a><a id="8141" class="Symbol">}</a> <a id="8143" class="Symbol">{</a><a id="8144" class="Argument">Q</a> <a id="8146" class="Symbol">=</a> <a id="8148" href="Data.List.Relation.Unary.Any.Properties.html#8148" class="Bound">Q</a><a id="8149" class="Symbol">}</a> <a id="8151" class="Symbol">{</a><a id="8152" href="Data.List.Relation.Unary.Any.Properties.html#8152" class="Bound">xs</a><a id="8154" class="Symbol">}</a> <a id="8156" class="Symbol">{</a><a id="8157" href="Data.List.Relation.Unary.Any.Properties.html#8157" class="Bound">ys</a><a id="8159" class="Symbol">}</a> <a id="8161" class="Symbol">=</a> <a id="8163" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="8171" href="Data.List.Relation.Unary.Any.Properties.html#7716" class="Function">Any-×⁺</a> <a id="8178" href="Data.List.Relation.Unary.Any.Properties.html#7849" class="Function">Any-×⁻</a> <a id="8185" href="Data.List.Relation.Unary.Any.Properties.html#8233" class="Function">from∘to</a> <a id="8193" href="Data.List.Relation.Unary.Any.Properties.html#9190" class="Function">to∘from</a>
<a id="8203" class="Keyword">where</a>
<a id="8211" class="Keyword">open</a> <a id="8216" href="Relation.Binary.PropositionalEquality.Core.html#2708" class="Module">P.≡-Reasoning</a>
<a id="8233" href="Data.List.Relation.Unary.Any.Properties.html#8233" class="Function">from∘to</a> <a id="8241" class="Symbol">:</a> <a id="8243" class="Symbol">∀</a> <a id="8245" href="Data.List.Relation.Unary.Any.Properties.html#8245" class="Bound">pq</a> <a id="8248" class="Symbol">→</a> <a id="8250" href="Data.List.Relation.Unary.Any.Properties.html#7849" class="Function">Any-×⁻</a> <a id="8257" class="Symbol">(</a><a id="8258" href="Data.List.Relation.Unary.Any.Properties.html#7716" class="Function">Any-×⁺</a> <a id="8265" href="Data.List.Relation.Unary.Any.Properties.html#8245" class="Bound">pq</a><a id="8267" class="Symbol">)</a> <a id="8269" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="8271" href="Data.List.Relation.Unary.Any.Properties.html#8245" class="Bound">pq</a>
<a id="8276" href="Data.List.Relation.Unary.Any.Properties.html#8233" class="Function">from∘to</a> <a id="8284" class="Symbol">(</a><a id="8285" href="Data.List.Relation.Unary.Any.Properties.html#8285" class="Bound">p</a> <a id="8287" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8289" href="Data.List.Relation.Unary.Any.Properties.html#8289" class="Bound">q</a><a id="8290" class="Symbol">)</a> <a id="8292" class="Symbol">=</a>
<a id="8299" href="Data.List.Relation.Unary.Any.Properties.html#7849" class="Function">Any-×⁻</a> <a id="8306" class="Symbol">(</a><a id="8307" href="Data.List.Relation.Unary.Any.Properties.html#7716" class="Function">Any-×⁺</a> <a id="8314" class="Symbol">(</a><a id="8315" href="Data.List.Relation.Unary.Any.Properties.html#8285" class="Bound">p</a> <a id="8317" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8319" href="Data.List.Relation.Unary.Any.Properties.html#8289" class="Bound">q</a><a id="8320" class="Symbol">))</a>
<a id="8330" href="Relation.Binary.PropositionalEquality.Core.html#2864" class="Function Operator">≡⟨⟩</a>
<a id="8339" class="Symbol">(</a><a id="8340" class="Keyword">let</a> <a id="8344" class="Symbol">(</a><a id="8345" href="Data.List.Relation.Unary.Any.Properties.html#8345" class="Bound">x</a> <a id="8347" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8349" href="Data.List.Relation.Unary.Any.Properties.html#8349" class="Bound">x∈xs</a> <a id="8354" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8356" href="Data.List.Relation.Unary.Any.Properties.html#8356" class="Bound">pq</a><a id="8358" class="Symbol">)</a> <a id="8363" class="Symbol">=</a> <a id="8365" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="8370" class="Symbol">(</a><a id="8371" href="Data.List.Relation.Unary.Any.Properties.html#7716" class="Function">Any-×⁺</a> <a id="8378" class="Symbol">(</a><a id="8379" href="Data.List.Relation.Unary.Any.Properties.html#8285" class="Bound">p</a> <a id="8381" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8383" href="Data.List.Relation.Unary.Any.Properties.html#8289" class="Bound">q</a><a id="8384" class="Symbol">))</a>
<a id="8396" class="Symbol">(</a><a id="8397" href="Data.List.Relation.Unary.Any.Properties.html#8397" class="Bound">y</a> <a id="8399" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8401" href="Data.List.Relation.Unary.Any.Properties.html#8401" class="Bound">y∈ys</a> <a id="8406" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8408" href="Data.List.Relation.Unary.Any.Properties.html#8408" class="Bound">p</a> <a id="8410" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8412" href="Data.List.Relation.Unary.Any.Properties.html#8412" class="Bound">q</a><a id="8413" class="Symbol">)</a> <a id="8415" class="Symbol">=</a> <a id="8417" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="8422" href="Data.List.Relation.Unary.Any.Properties.html#8356" class="Bound">pq</a>
<a id="8430" class="Keyword">in</a> <a id="8434" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="8439" href="Data.List.Relation.Unary.Any.Properties.html#8349" class="Bound">x∈xs</a> <a id="8444" href="Data.List.Relation.Unary.Any.Properties.html#8408" class="Bound">p</a> <a id="8446" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8448" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="8453" href="Data.List.Relation.Unary.Any.Properties.html#8401" class="Bound">y∈ys</a> <a id="8458" href="Data.List.Relation.Unary.Any.Properties.html#8412" class="Bound">q</a><a id="8459" class="Symbol">)</a>
<a id="8467" href="Relation.Binary.PropositionalEquality.Core.html#2923" class="Function">≡⟨</a> <a id="8470" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="8477" class="Symbol">(λ</a> <a id="8480" href="Data.List.Relation.Unary.Any.Properties.html#8480" class="Bound">•</a> <a id="8482" class="Symbol">→</a> <a id="8484" class="Keyword">let</a> <a id="8488" class="Symbol">(</a><a id="8489" href="Data.List.Relation.Unary.Any.Properties.html#8489" class="Bound">x</a> <a id="8491" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8493" href="Data.List.Relation.Unary.Any.Properties.html#8493" class="Bound">x∈xs</a> <a id="8498" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8500" href="Data.List.Relation.Unary.Any.Properties.html#8500" class="Bound">pq</a><a id="8502" class="Symbol">)</a> <a id="8507" class="Symbol">=</a> <a id="8509" href="Data.List.Relation.Unary.Any.Properties.html#8480" class="Bound">•</a>
<a id="8537" class="Symbol">(</a><a id="8538" href="Data.List.Relation.Unary.Any.Properties.html#8538" class="Bound">y</a> <a id="8540" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8542" href="Data.List.Relation.Unary.Any.Properties.html#8542" class="Bound">y∈ys</a> <a id="8547" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8549" href="Data.List.Relation.Unary.Any.Properties.html#8549" class="Bound">p</a> <a id="8551" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8553" href="Data.List.Relation.Unary.Any.Properties.html#8553" class="Bound">q</a><a id="8554" class="Symbol">)</a> <a id="8556" class="Symbol">=</a> <a id="8558" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="8563" href="Data.List.Relation.Unary.Any.Properties.html#8500" class="Bound">pq</a>
<a id="8588" class="Keyword">in</a> <a id="8592" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="8597" href="Data.List.Relation.Unary.Any.Properties.html#8493" class="Bound">x∈xs</a> <a id="8602" href="Data.List.Relation.Unary.Any.Properties.html#8549" class="Bound">p</a> <a id="8604" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8606" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="8611" href="Data.List.Relation.Unary.Any.Properties.html#8542" class="Bound">y∈ys</a> <a id="8616" href="Data.List.Relation.Unary.Any.Properties.html#8553" class="Bound">q</a><a id="8617" class="Symbol">)</a>
<a id="8634" class="Symbol">(</a><a id="8635" href="Data.List.Membership.Propositional.Properties.Core.html#1439" class="Function">find∘map</a> <a id="8644" href="Data.List.Relation.Unary.Any.Properties.html#8285" class="Bound">p</a> <a id="8646" class="Symbol">(λ</a> <a id="8649" href="Data.List.Relation.Unary.Any.Properties.html#8649" class="Bound">p</a> <a id="8651" class="Symbol">→</a> <a id="8653" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="8661" class="Symbol">(</a><a id="8662" href="Data.List.Relation.Unary.Any.Properties.html#8649" class="Bound">p</a> <a id="8664" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,_</a><a id="8666" class="Symbol">)</a> <a id="8668" href="Data.List.Relation.Unary.Any.Properties.html#8289" class="Bound">q</a><a id="8669" class="Symbol">))</a> <a id="8672" href="Relation.Binary.PropositionalEquality.Core.html#2923" class="Function">⟩</a>
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<a id="8721" class="Symbol">(</a><a id="8722" href="Data.List.Relation.Unary.Any.Properties.html#8722" class="Bound">y</a> <a id="8724" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8726" href="Data.List.Relation.Unary.Any.Properties.html#8726" class="Bound">y∈ys</a> <a id="8731" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8733" href="Data.List.Relation.Unary.Any.Properties.html#8733" class="Bound">p</a> <a id="8735" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8737" href="Data.List.Relation.Unary.Any.Properties.html#8737" class="Bound">q</a><a id="8738" class="Symbol">)</a> <a id="8740" class="Symbol">=</a> <a id="8742" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="8747" class="Symbol">(</a><a id="8748" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="8756" class="Symbol">(</a><a id="8757" href="Data.List.Relation.Unary.Any.Properties.html#8696" class="Bound">p</a> <a id="8759" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,_</a><a id="8761" class="Symbol">)</a> <a id="8763" href="Data.List.Relation.Unary.Any.Properties.html#8289" class="Bound">q</a><a id="8764" class="Symbol">)</a>
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<a id="8808" href="Relation.Binary.PropositionalEquality.Core.html#2923" class="Function">≡⟨</a> <a id="8811" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="8818" class="Symbol">(λ</a> <a id="8821" href="Data.List.Relation.Unary.Any.Properties.html#8821" class="Bound">•</a> <a id="8823" class="Symbol">→</a> <a id="8825" class="Keyword">let</a> <a id="8829" class="Symbol">(</a><a id="8830" href="Data.List.Relation.Unary.Any.Properties.html#8830" class="Bound">x</a> <a id="8832" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8834" href="Data.List.Relation.Unary.Any.Properties.html#8834" class="Bound">x∈xs</a> <a id="8839" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8841" href="Data.List.Relation.Unary.Any.Properties.html#8841" class="Bound">p</a><a id="8842" class="Symbol">)</a> <a id="8848" class="Symbol">=</a> <a id="8850" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="8855" href="Data.List.Relation.Unary.Any.Properties.html#8285" class="Bound">p</a>
<a id="8883" class="Symbol">(</a><a id="8884" href="Data.List.Relation.Unary.Any.Properties.html#8884" class="Bound">y</a> <a id="8886" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8888" href="Data.List.Relation.Unary.Any.Properties.html#8888" class="Bound">y∈ys</a> <a id="8893" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8895" href="Data.List.Relation.Unary.Any.Properties.html#8895" class="Bound">p</a> <a id="8897" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8899" href="Data.List.Relation.Unary.Any.Properties.html#8899" class="Bound">q</a><a id="8900" class="Symbol">)</a> <a id="8902" class="Symbol">=</a> <a id="8904" href="Data.List.Relation.Unary.Any.Properties.html#8821" class="Bound">•</a>
<a id="8928" class="Keyword">in</a> <a id="8932" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="8937" href="Data.List.Relation.Unary.Any.Properties.html#8834" class="Bound">x∈xs</a> <a id="8942" href="Data.List.Relation.Unary.Any.Properties.html#8895" class="Bound">p</a> <a id="8944" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="8946" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="8951" href="Data.List.Relation.Unary.Any.Properties.html#8888" class="Bound">y∈ys</a> <a id="8956" href="Data.List.Relation.Unary.Any.Properties.html#8899" class="Bound">q</a><a id="8957" class="Symbol">)</a>
<a id="8974" class="Symbol">(</a><a id="8975" href="Data.List.Membership.Propositional.Properties.Core.html#1439" class="Function">find∘map</a> <a id="8984" href="Data.List.Relation.Unary.Any.Properties.html#8289" class="Bound">q</a> <a id="8986" class="Symbol">(</a><a id="8987" href="Agda.Builtin.Sigma.html#264" class="Field">proj₂</a> <a id="8993" class="Symbol">(</a><a id="8994" href="Agda.Builtin.Sigma.html#264" class="Field">proj₂</a> <a id="9000" class="Symbol">(</a><a id="9001" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="9006" href="Data.List.Relation.Unary.Any.Properties.html#8285" class="Bound">p</a><a id="9007" class="Symbol">))</a> <a id="9010" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,_</a><a id="9012" class="Symbol">))</a> <a id="9015" href="Relation.Binary.PropositionalEquality.Core.html#2923" class="Function">⟩</a>
<a id="9022" class="Symbol">(</a><a id="9023" class="Keyword">let</a> <a id="9027" class="Symbol">(</a><a id="9028" href="Data.List.Relation.Unary.Any.Properties.html#9028" class="Bound">x</a> <a id="9030" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9032" href="Data.List.Relation.Unary.Any.Properties.html#9032" class="Bound">x∈xs</a> <a id="9037" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9039" href="Data.List.Relation.Unary.Any.Properties.html#9039" class="Bound">p</a><a id="9040" class="Symbol">)</a> <a id="9042" class="Symbol">=</a> <a id="9044" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="9049" href="Data.List.Relation.Unary.Any.Properties.html#8285" class="Bound">p</a>
<a id="9060" class="Symbol">(</a><a id="9061" href="Data.List.Relation.Unary.Any.Properties.html#9061" class="Bound">y</a> <a id="9063" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9065" href="Data.List.Relation.Unary.Any.Properties.html#9065" class="Bound">y∈ys</a> <a id="9070" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9072" href="Data.List.Relation.Unary.Any.Properties.html#9072" class="Bound">q</a><a id="9073" class="Symbol">)</a> <a id="9075" class="Symbol">=</a> <a id="9077" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="9082" href="Data.List.Relation.Unary.Any.Properties.html#8289" class="Bound">q</a>
<a id="9089" class="Keyword">in</a> <a id="9093" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="9098" href="Data.List.Relation.Unary.Any.Properties.html#9032" class="Bound">x∈xs</a> <a id="9103" href="Data.List.Relation.Unary.Any.Properties.html#9039" class="Bound">p</a> <a id="9105" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9107" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="9112" href="Data.List.Relation.Unary.Any.Properties.html#9065" class="Bound">y∈ys</a> <a id="9117" href="Data.List.Relation.Unary.Any.Properties.html#9072" class="Bound">q</a><a id="9118" class="Symbol">)</a>
<a id="9126" href="Relation.Binary.PropositionalEquality.Core.html#2923" class="Function">≡⟨</a> <a id="9129" href="Relation.Binary.PropositionalEquality.Core.html#1367" class="Function">P.cong₂</a> <a id="9137" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">_,_</a> <a id="9141" class="Symbol">(</a><a id="9142" href="Data.List.Membership.Propositional.Properties.Core.html#2129" class="Function">lose∘find</a> <a id="9152" href="Data.List.Relation.Unary.Any.Properties.html#8285" class="Bound">p</a><a id="9153" class="Symbol">)</a> <a id="9155" class="Symbol">(</a><a id="9156" href="Data.List.Membership.Propositional.Properties.Core.html#2129" class="Function">lose∘find</a> <a id="9166" href="Data.List.Relation.Unary.Any.Properties.html#8289" class="Bound">q</a><a id="9167" class="Symbol">)</a> <a id="9169" href="Relation.Binary.PropositionalEquality.Core.html#2923" class="Function">⟩</a>
<a id="9176" class="Symbol">(</a><a id="9177" href="Data.List.Relation.Unary.Any.Properties.html#8285" class="Bound">p</a> <a id="9179" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9181" href="Data.List.Relation.Unary.Any.Properties.html#8289" class="Bound">q</a><a id="9182" class="Symbol">)</a> <a id="9184" href="Relation.Binary.PropositionalEquality.Core.html#3105" class="Function Operator">∎</a>
<a id="9190" href="Data.List.Relation.Unary.Any.Properties.html#9190" class="Function">to∘from</a> <a id="9198" class="Symbol">:</a> <a id="9200" class="Symbol">∀</a> <a id="9202" href="Data.List.Relation.Unary.Any.Properties.html#9202" class="Bound">pq</a> <a id="9205" class="Symbol">→</a> <a id="9207" href="Data.List.Relation.Unary.Any.Properties.html#7716" class="Function">Any-×⁺</a> <a id="9214" class="Symbol">{</a><a id="9215" class="Argument">xs</a> <a id="9218" class="Symbol">=</a> <a id="9220" href="Data.List.Relation.Unary.Any.Properties.html#8152" class="Bound">xs</a><a id="9222" class="Symbol">}</a> <a id="9224" class="Symbol">(</a><a id="9225" href="Data.List.Relation.Unary.Any.Properties.html#7849" class="Function">Any-×⁻</a> <a id="9232" href="Data.List.Relation.Unary.Any.Properties.html#9202" class="Bound">pq</a><a id="9234" class="Symbol">)</a> <a id="9236" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="9238" href="Data.List.Relation.Unary.Any.Properties.html#9202" class="Bound">pq</a>
<a id="9243" href="Data.List.Relation.Unary.Any.Properties.html#9190" class="Function">to∘from</a> <a id="9251" href="Data.List.Relation.Unary.Any.Properties.html#9251" class="Bound">pq</a>
<a id="9258" class="Keyword">with</a> <a id="9263" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="9268" href="Data.List.Relation.Unary.Any.Properties.html#9251" class="Bound">pq</a>
<a id="9277" class="Symbol">|</a> <a id="9279" class="Symbol">(λ</a> <a id="9282" class="Symbol">(</a><a id="9283" href="Data.List.Relation.Unary.Any.Properties.html#9283" class="Bound">f</a> <a id="9285" class="Symbol">:</a> <a id="9287" class="Symbol">(</a><a id="9288" href="Agda.Builtin.Sigma.html#252" class="Field">proj₁</a> <a id="9294" class="Symbol">(</a><a id="9295" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="9300" href="Data.List.Relation.Unary.Any.Properties.html#9251" class="Bound">pq</a><a id="9302" class="Symbol">)</a> <a id="9304" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡_</a><a id="9306" class="Symbol">)</a> <a id="9308" href="Data.List.Relation.Unary.Any.Properties.html#2121" class="Function Operator">⋐</a> <a id="9310" class="Symbol">_)</a> <a id="9313" class="Symbol">→</a> <a id="9315" href="Data.List.Membership.Propositional.Properties.Core.html#1140" class="Function">map∘find</a> <a id="9324" href="Data.List.Relation.Unary.Any.Properties.html#9251" class="Bound">pq</a> <a id="9327" class="Symbol">{</a><a id="9328" href="Data.List.Relation.Unary.Any.Properties.html#9283" class="Bound">f</a><a id="9329" class="Symbol">})</a>
<a id="9334" class="Symbol">...</a> <a id="9338" class="Symbol">|</a> <a id="9340" class="Symbol">(</a><a id="9341" href="Data.List.Relation.Unary.Any.Properties.html#9341" class="Bound">x</a> <a id="9343" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9345" href="Data.List.Relation.Unary.Any.Properties.html#9345" class="Bound">x∈xs</a> <a id="9350" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9352" href="Data.List.Relation.Unary.Any.Properties.html#9352" class="Bound">pq′</a><a id="9355" class="Symbol">)</a> <a id="9357" class="Symbol">|</a> <a id="9359" href="Data.List.Relation.Unary.Any.Properties.html#9359" class="Bound">lem₁</a>
<a id="9368" class="Keyword">with</a> <a id="9373" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="9378" href="Data.List.Relation.Unary.Any.Properties.html#9352" class="Bound">pq′</a>
<a id="9388" class="Symbol">|</a> <a id="9390" class="Symbol">(λ</a> <a id="9393" class="Symbol">(</a><a id="9394" href="Data.List.Relation.Unary.Any.Properties.html#9394" class="Bound">f</a> <a id="9396" class="Symbol">:</a> <a id="9398" class="Symbol">(</a><a id="9399" href="Agda.Builtin.Sigma.html#252" class="Field">proj₁</a> <a id="9405" class="Symbol">(</a><a id="9406" href="Data.List.Membership.Setoid.html#1445" class="Function">find</a> <a id="9411" href="Data.List.Relation.Unary.Any.Properties.html#9352" class="Bound">pq′</a><a id="9414" class="Symbol">)</a> <a id="9416" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡_</a><a id="9418" class="Symbol">)</a> <a id="9420" href="Data.List.Relation.Unary.Any.Properties.html#2121" class="Function Operator">⋐</a> <a id="9422" class="Symbol">_)</a> <a id="9425" class="Symbol">→</a> <a id="9427" href="Data.List.Membership.Propositional.Properties.Core.html#1140" class="Function">map∘find</a> <a id="9436" href="Data.List.Relation.Unary.Any.Properties.html#9352" class="Bound">pq′</a> <a id="9440" class="Symbol">{</a><a id="9441" href="Data.List.Relation.Unary.Any.Properties.html#9394" class="Bound">f</a><a id="9442" class="Symbol">})</a>
<a id="9447" class="Symbol">...</a> <a id="9451" class="Symbol">|</a> <a id="9453" class="Symbol">(</a><a id="9454" href="Data.List.Relation.Unary.Any.Properties.html#9454" class="Bound">y</a> <a id="9456" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9458" href="Data.List.Relation.Unary.Any.Properties.html#9458" class="Bound">y∈ys</a> <a id="9463" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9465" href="Data.List.Relation.Unary.Any.Properties.html#9465" class="Bound">p</a> <a id="9467" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9469" href="Data.List.Relation.Unary.Any.Properties.html#9469" class="Bound">q</a><a id="9470" class="Symbol">)</a> <a id="9472" class="Symbol">|</a> <a id="9474" href="Data.List.Relation.Unary.Any.Properties.html#9474" class="Bound">lem₂</a>
<a id="9483" class="Keyword">rewrite</a> <a id="9491" href="Relation.Binary.PropositionalEquality.Core.html#1684" class="Function">P.sym</a> <a id="9497" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="9499" href="Data.List.Relation.Unary.Any.Properties.html#3936" class="Function">map-∘</a> <a id="9505" class="Symbol">{</a><a id="9506" class="Argument">R</a> <a id="9508" class="Symbol">=</a> <a id="9510" class="Symbol">λ</a> <a id="9512" href="Data.List.Relation.Unary.Any.Properties.html#9512" class="Bound">x</a> <a id="9514" class="Symbol">→</a> <a id="9516" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="9520" class="Symbol">(λ</a> <a id="9523" href="Data.List.Relation.Unary.Any.Properties.html#9523" class="Bound">y</a> <a id="9525" class="Symbol">→</a> <a id="9527" href="Data.List.Relation.Unary.Any.Properties.html#8140" class="Bound">P</a> <a id="9529" href="Data.List.Relation.Unary.Any.Properties.html#9512" class="Bound">x</a> <a id="9531" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="9533" href="Data.List.Relation.Unary.Any.Properties.html#8148" class="Bound">Q</a> <a id="9535" href="Data.List.Relation.Unary.Any.Properties.html#9523" class="Bound">y</a><a id="9536" class="Symbol">)</a> <a id="9538" href="Data.List.Relation.Unary.Any.Properties.html#8157" class="Bound">ys</a><a id="9540" class="Symbol">}</a>
<a id="9568" class="Symbol">(λ</a> <a id="9571" href="Data.List.Relation.Unary.Any.Properties.html#9571" class="Bound">p</a> <a id="9573" class="Symbol">→</a> <a id="9575" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="9583" class="Symbol">(λ</a> <a id="9586" href="Data.List.Relation.Unary.Any.Properties.html#9586" class="Bound">q</a> <a id="9588" class="Symbol">→</a> <a id="9590" href="Data.List.Relation.Unary.Any.Properties.html#9571" class="Bound">p</a> <a id="9592" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9594" href="Data.List.Relation.Unary.Any.Properties.html#9586" class="Bound">q</a><a id="9595" class="Symbol">)</a> <a id="9597" class="Symbol">(</a><a id="9598" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="9603" href="Data.List.Relation.Unary.Any.Properties.html#9458" class="Bound">y∈ys</a> <a id="9608" href="Data.List.Relation.Unary.Any.Properties.html#9469" class="Bound">q</a><a id="9609" class="Symbol">))</a>
<a id="9638" class="Symbol">(λ</a> <a id="9641" href="Data.List.Relation.Unary.Any.Properties.html#9641" class="Bound">y</a> <a id="9643" class="Symbol">→</a> <a id="9645" href="Relation.Binary.PropositionalEquality.Core.html#1780" class="Function">P.subst</a> <a id="9653" href="Data.List.Relation.Unary.Any.Properties.html#8140" class="Bound">P</a> <a id="9655" href="Data.List.Relation.Unary.Any.Properties.html#9641" class="Bound">y</a> <a id="9657" href="Data.List.Relation.Unary.Any.Properties.html#9465" class="Bound">p</a><a id="9658" class="Symbol">)</a>
<a id="9686" class="Bound">x∈xs</a>
<a id="9703" class="Symbol">=</a> <a id="9705" class="Bound">lem₁</a> <a id="9710" class="Symbol">_</a> <a id="9712" href="Data.List.Relation.Unary.Any.Properties.html#9733" class="Function">helper</a>
<a id="9723" class="Keyword">where</a>
<a id="9733" href="Data.List.Relation.Unary.Any.Properties.html#9733" class="Function">helper</a> <a id="9740" class="Symbol">:</a> <a id="9742" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="9750" class="Symbol">(λ</a> <a id="9753" href="Data.List.Relation.Unary.Any.Properties.html#9753" class="Bound">q</a> <a id="9755" class="Symbol">→</a> <a id="9757" href="Data.List.Relation.Unary.Any.Properties.html#9465" class="Bound">p</a> <a id="9759" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9761" href="Data.List.Relation.Unary.Any.Properties.html#9753" class="Bound">q</a><a id="9762" class="Symbol">)</a> <a id="9764" class="Symbol">(</a><a id="9765" href="Data.List.Membership.Propositional.html#1052" class="Function">lose</a> <a id="9770" href="Data.List.Relation.Unary.Any.Properties.html#9458" class="Bound">y∈ys</a> <a id="9775" href="Data.List.Relation.Unary.Any.Properties.html#9469" class="Bound">q</a><a id="9776" class="Symbol">)</a> <a id="9778" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="9780" class="Bound">pq′</a>
<a id="9788" href="Data.List.Relation.Unary.Any.Properties.html#9733" class="Function">helper</a> <a id="9795" class="Keyword">rewrite</a> <a id="9803" href="Relation.Binary.PropositionalEquality.Core.html#1684" class="Function">P.sym</a> <a id="9809" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="9811" href="Data.List.Relation.Unary.Any.Properties.html#3936" class="Function">map-∘</a> <a id="9817" class="Symbol">(λ</a> <a id="9820" href="Data.List.Relation.Unary.Any.Properties.html#9820" class="Bound">q</a> <a id="9822" class="Symbol">→</a> <a id="9824" href="Data.List.Relation.Unary.Any.Properties.html#9465" class="Bound">p</a> <a id="9826" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="9828" href="Data.List.Relation.Unary.Any.Properties.html#9820" class="Bound">q</a><a id="9829" class="Symbol">)</a>
<a id="9864" class="Symbol">(λ</a> <a id="9867" href="Data.List.Relation.Unary.Any.Properties.html#9867" class="Bound">y</a> <a id="9869" class="Symbol">→</a> <a id="9871" href="Relation.Binary.PropositionalEquality.Core.html#1780" class="Function">P.subst</a> <a id="9879" href="Data.List.Relation.Unary.Any.Properties.html#8148" class="Bound">Q</a> <a id="9881" href="Data.List.Relation.Unary.Any.Properties.html#9867" class="Bound">y</a> <a id="9883" href="Data.List.Relation.Unary.Any.Properties.html#9469" class="Bound">q</a><a id="9884" class="Symbol">)</a>
<a id="9919" href="Data.List.Relation.Unary.Any.Properties.html#9458" class="Bound">y∈ys</a>
<a id="9935" class="Symbol">=</a> <a id="9937" href="Data.List.Relation.Unary.Any.Properties.html#9474" class="Bound">lem₂</a> <a id="9942" class="Symbol">_</a> <a id="9944" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="9950" class="Comment">------------------------------------------------------------------------</a>
<a id="10023" class="Comment">-- Half-applied product commutes with Any.</a>
<a id="10067" class="Keyword">module</a> <a id="10074" href="Data.List.Relation.Unary.Any.Properties.html#10074" class="Module">_</a> <a id="10076" class="Symbol">{</a><a id="10077" href="Data.List.Relation.Unary.Any.Properties.html#10077" class="Bound Operator">_~_</a> <a id="10081" class="Symbol">:</a> <a id="10083" href="Relation.Binary.Core.html#766" class="Function">REL</a> <a id="10087" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="10089" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="10091" href="Data.List.Relation.Unary.Any.Properties.html#2382" class="Generalizable">r</a><a id="10092" class="Symbol">}</a> <a id="10094" class="Keyword">where</a>
<a id="10103" href="Data.List.Relation.Unary.Any.Properties.html#10103" class="Function">Any-Σ⁺ʳ</a> <a id="10111" class="Symbol">:</a> <a id="10113" class="Symbol">(</a><a id="10114" href="Data.Product.html#1369" class="Function">∃</a> <a id="10116" class="Symbol">λ</a> <a id="10118" href="Data.List.Relation.Unary.Any.Properties.html#10118" class="Bound">x</a> <a id="10120" class="Symbol">→</a> <a id="10122" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="10126" class="Symbol">(</a><a id="10127" href="Data.List.Relation.Unary.Any.Properties.html#10077" class="Bound Operator">_~</a> <a id="10130" href="Data.List.Relation.Unary.Any.Properties.html#10118" class="Bound">x</a><a id="10131" class="Symbol">)</a> <a id="10133" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="10135" class="Symbol">)</a> <a id="10137" class="Symbol">→</a> <a id="10139" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="10143" class="Symbol">(</a><a id="10144" href="Data.Product.html#1369" class="Function">∃</a> <a id="10146" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="10148" href="Data.List.Relation.Unary.Any.Properties.html#10077" class="Bound Operator">_~_</a><a id="10151" class="Symbol">)</a> <a id="10153" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="10158" href="Data.List.Relation.Unary.Any.Properties.html#10103" class="Function">Any-Σ⁺ʳ</a> <a id="10166" class="Symbol">(</a><a id="10167" href="Data.List.Relation.Unary.Any.Properties.html#10167" class="Bound">b</a> <a id="10169" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="10171" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="10176" href="Data.List.Relation.Unary.Any.Properties.html#10176" class="Bound">px</a><a id="10178" class="Symbol">)</a> <a id="10180" class="Symbol">=</a> <a id="10182" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="10187" class="Symbol">(</a><a id="10188" href="Data.List.Relation.Unary.Any.Properties.html#10167" class="Bound">b</a> <a id="10190" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="10192" href="Data.List.Relation.Unary.Any.Properties.html#10176" class="Bound">px</a><a id="10194" class="Symbol">)</a>
<a id="10198" href="Data.List.Relation.Unary.Any.Properties.html#10103" class="Function">Any-Σ⁺ʳ</a> <a id="10206" class="Symbol">(</a><a id="10207" href="Data.List.Relation.Unary.Any.Properties.html#10207" class="Bound">b</a> <a id="10209" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="10211" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="10217" href="Data.List.Relation.Unary.Any.Properties.html#10217" class="Bound">pxs</a><a id="10220" class="Symbol">)</a> <a id="10222" class="Symbol">=</a> <a id="10224" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="10230" class="Symbol">(</a><a id="10231" href="Data.List.Relation.Unary.Any.Properties.html#10103" class="Function">Any-Σ⁺ʳ</a> <a id="10239" class="Symbol">(</a><a id="10240" href="Data.List.Relation.Unary.Any.Properties.html#10207" class="Bound">b</a> <a id="10242" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="10244" href="Data.List.Relation.Unary.Any.Properties.html#10217" class="Bound">pxs</a><a id="10247" class="Symbol">))</a>
<a id="10253" href="Data.List.Relation.Unary.Any.Properties.html#10253" class="Function">Any-Σ⁻ʳ</a> <a id="10261" class="Symbol">:</a> <a id="10263" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="10267" class="Symbol">(</a><a id="10268" href="Data.Product.html#1369" class="Function">∃</a> <a id="10270" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="10272" href="Data.List.Relation.Unary.Any.Properties.html#10077" class="Bound Operator">_~_</a><a id="10275" class="Symbol">)</a> <a id="10277" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="10280" class="Symbol">→</a> <a id="10282" href="Data.Product.html#1369" class="Function">∃</a> <a id="10284" class="Symbol">λ</a> <a id="10286" href="Data.List.Relation.Unary.Any.Properties.html#10286" class="Bound">x</a> <a id="10288" class="Symbol">→</a> <a id="10290" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="10294" class="Symbol">(</a><a id="10295" href="Data.List.Relation.Unary.Any.Properties.html#10077" class="Bound Operator">_~</a> <a id="10298" href="Data.List.Relation.Unary.Any.Properties.html#10286" class="Bound">x</a><a id="10299" class="Symbol">)</a> <a id="10301" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="10306" href="Data.List.Relation.Unary.Any.Properties.html#10253" class="Function">Any-Σ⁻ʳ</a> <a id="10314" class="Symbol">(</a><a id="10315" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="10320" class="Symbol">(</a><a id="10321" href="Data.List.Relation.Unary.Any.Properties.html#10321" class="Bound">b</a> <a id="10323" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="10325" href="Data.List.Relation.Unary.Any.Properties.html#10325" class="Bound">x</a><a id="10326" class="Symbol">))</a> <a id="10329" class="Symbol">=</a> <a id="10331" href="Data.List.Relation.Unary.Any.Properties.html#10321" class="Bound">b</a> <a id="10333" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="10335" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="10340" href="Data.List.Relation.Unary.Any.Properties.html#10325" class="Bound">x</a>
<a id="10344" href="Data.List.Relation.Unary.Any.Properties.html#10253" class="Function">Any-Σ⁻ʳ</a> <a id="10352" class="Symbol">(</a><a id="10353" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="10359" href="Data.List.Relation.Unary.Any.Properties.html#10359" class="Bound">xs</a><a id="10361" class="Symbol">)</a> <a id="10363" class="Symbol">=</a> <a id="10365" href="Data.Product.html#2675" class="Function">Prod.map₂</a> <a id="10375" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="10381" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="10383" href="Data.List.Relation.Unary.Any.Properties.html#10253" class="Function">Any-Σ⁻ʳ</a> <a id="10391" href="Data.List.Relation.Unary.Any.Properties.html#10359" class="Bound">xs</a>
<a id="10395" class="Comment">------------------------------------------------------------------------</a>
<a id="10468" class="Comment">-- Invertible introduction (⁺) and elimination (⁻) rules for various</a>
<a id="10537" class="Comment">-- list functions</a>
<a id="10555" class="Comment">------------------------------------------------------------------------</a>
<a id="10629" class="Comment">------------------------------------------------------------------------</a>
<a id="10702" class="Comment">-- singleton</a>
<a id="singleton⁺"></a><a id="10716" href="Data.List.Relation.Unary.Any.Properties.html#10716" class="Function">singleton⁺</a> <a id="10727" class="Symbol">:</a> <a id="10729" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="10731" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="10733" class="Symbol">→</a> <a id="10735" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="10739" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="10741" href="Data.List.Base.html#5025" class="Function Operator">[</a> <a id="10743" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="10745" href="Data.List.Base.html#5025" class="Function Operator">]</a>
<a id="10747" href="Data.List.Relation.Unary.Any.Properties.html#10716" class="Function">singleton⁺</a> <a id="10758" href="Data.List.Relation.Unary.Any.Properties.html#10758" class="Bound">Px</a> <a id="10761" class="Symbol">=</a> <a id="10763" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="10768" href="Data.List.Relation.Unary.Any.Properties.html#10758" class="Bound">Px</a>
<a id="singleton⁻"></a><a id="10772" href="Data.List.Relation.Unary.Any.Properties.html#10772" class="Function">singleton⁻</a> <a id="10783" class="Symbol">:</a> <a id="10785" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="10789" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="10791" href="Data.List.Base.html#5025" class="Function Operator">[</a> <a id="10793" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="10795" href="Data.List.Base.html#5025" class="Function Operator">]</a> <a id="10797" class="Symbol">→</a> <a id="10799" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="10801" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a>
<a id="10803" href="Data.List.Relation.Unary.Any.Properties.html#10772" class="Function">singleton⁻</a> <a id="10814" class="Symbol">(</a><a id="10815" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="10820" href="Data.List.Relation.Unary.Any.Properties.html#10820" class="Bound">Px</a><a id="10822" class="Symbol">)</a> <a id="10824" class="Symbol">=</a> <a id="10826" href="Data.List.Relation.Unary.Any.Properties.html#10820" class="Bound">Px</a>
<a id="10830" class="Comment">------------------------------------------------------------------------</a>
<a id="10903" class="Comment">-- map</a>
<a id="10911" class="Keyword">module</a> <a id="10918" href="Data.List.Relation.Unary.Any.Properties.html#10918" class="Module">_</a> <a id="10920" class="Symbol">{</a><a id="10921" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a> <a id="10923" class="Symbol">:</a> <a id="10925" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="10927" class="Symbol">→</a> <a id="10929" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a><a id="10930" class="Symbol">}</a> <a id="10932" class="Keyword">where</a>
<a id="10941" href="Data.List.Relation.Unary.Any.Properties.html#10941" class="Function">map⁺</a> <a id="10946" class="Symbol">:</a> <a id="10948" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="10952" class="Symbol">(</a><a id="10953" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="10955" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="10957" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a><a id="10958" class="Symbol">)</a> <a id="10960" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="10963" class="Symbol">→</a> <a id="10965" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="10969" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="10971" class="Symbol">(</a><a id="10972" href="Data.List.Base.html#1544" class="Function">List.map</a> <a id="10981" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a> <a id="10983" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="10985" class="Symbol">)</a>
<a id="10989" href="Data.List.Relation.Unary.Any.Properties.html#10941" class="Function">map⁺</a> <a id="10994" class="Symbol">(</a><a id="10995" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="11000" href="Data.List.Relation.Unary.Any.Properties.html#11000" class="Bound">p</a><a id="11001" class="Symbol">)</a> <a id="11004" class="Symbol">=</a> <a id="11006" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="11011" href="Data.List.Relation.Unary.Any.Properties.html#11000" class="Bound">p</a>
<a id="11015" href="Data.List.Relation.Unary.Any.Properties.html#10941" class="Function">map⁺</a> <a id="11020" class="Symbol">(</a><a id="11021" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="11027" href="Data.List.Relation.Unary.Any.Properties.html#11027" class="Bound">p</a><a id="11028" class="Symbol">)</a> <a id="11030" class="Symbol">=</a> <a id="11032" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="11038" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="11040" href="Data.List.Relation.Unary.Any.Properties.html#10941" class="Function">map⁺</a> <a id="11045" href="Data.List.Relation.Unary.Any.Properties.html#11027" class="Bound">p</a>
<a id="11050" href="Data.List.Relation.Unary.Any.Properties.html#11050" class="Function">map⁻</a> <a id="11055" class="Symbol">:</a> <a id="11057" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11061" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="11063" class="Symbol">(</a><a id="11064" href="Data.List.Base.html#1544" class="Function">List.map</a> <a id="11073" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a> <a id="11075" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="11077" class="Symbol">)</a> <a id="11079" class="Symbol">→</a> <a id="11081" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11085" class="Symbol">(</a><a id="11086" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="11088" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="11090" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a><a id="11091" class="Symbol">)</a> <a id="11093" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="11098" href="Data.List.Relation.Unary.Any.Properties.html#11050" class="Function">map⁻</a> <a id="11103" class="Symbol">{</a><a id="11104" class="Argument">xs</a> <a id="11107" class="Symbol">=</a> <a id="11109" href="Data.List.Relation.Unary.Any.Properties.html#11109" class="Bound">x</a> <a id="11111" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="11113" href="Data.List.Relation.Unary.Any.Properties.html#11113" class="Bound">xs</a><a id="11115" class="Symbol">}</a> <a id="11117" class="Symbol">(</a><a id="11118" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="11123" href="Data.List.Relation.Unary.Any.Properties.html#11123" class="Bound">p</a><a id="11124" class="Symbol">)</a> <a id="11127" class="Symbol">=</a> <a id="11129" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="11134" href="Data.List.Relation.Unary.Any.Properties.html#11123" class="Bound">p</a>
<a id="11138" href="Data.List.Relation.Unary.Any.Properties.html#11050" class="Function">map⁻</a> <a id="11143" class="Symbol">{</a><a id="11144" class="Argument">xs</a> <a id="11147" class="Symbol">=</a> <a id="11149" href="Data.List.Relation.Unary.Any.Properties.html#11149" class="Bound">x</a> <a id="11151" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="11153" href="Data.List.Relation.Unary.Any.Properties.html#11153" class="Bound">xs</a><a id="11155" class="Symbol">}</a> <a id="11157" class="Symbol">(</a><a id="11158" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="11164" href="Data.List.Relation.Unary.Any.Properties.html#11164" class="Bound">p</a><a id="11165" class="Symbol">)</a> <a id="11167" class="Symbol">=</a> <a id="11169" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="11175" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="11177" href="Data.List.Relation.Unary.Any.Properties.html#11050" class="Function">map⁻</a> <a id="11182" href="Data.List.Relation.Unary.Any.Properties.html#11164" class="Bound">p</a>
<a id="11187" href="Data.List.Relation.Unary.Any.Properties.html#11187" class="Function">map⁺∘map⁻</a> <a id="11197" class="Symbol">:</a> <a id="11199" class="Symbol">(</a><a id="11200" href="Data.List.Relation.Unary.Any.Properties.html#11200" class="Bound">p</a> <a id="11202" class="Symbol">:</a> <a id="11204" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11208" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="11210" class="Symbol">(</a><a id="11211" href="Data.List.Base.html#1544" class="Function">List.map</a> <a id="11220" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a> <a id="11222" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="11224" class="Symbol">))</a> <a id="11227" class="Symbol">→</a> <a id="11229" href="Data.List.Relation.Unary.Any.Properties.html#10941" class="Function">map⁺</a> <a id="11234" class="Symbol">(</a><a id="11235" href="Data.List.Relation.Unary.Any.Properties.html#11050" class="Function">map⁻</a> <a id="11240" href="Data.List.Relation.Unary.Any.Properties.html#11200" class="Bound">p</a><a id="11241" class="Symbol">)</a> <a id="11243" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="11245" href="Data.List.Relation.Unary.Any.Properties.html#11200" class="Bound">p</a>
<a id="11249" href="Data.List.Relation.Unary.Any.Properties.html#11187" class="Function">map⁺∘map⁻</a> <a id="11259" class="Symbol">{</a><a id="11260" class="Argument">xs</a> <a id="11263" class="Symbol">=</a> <a id="11265" href="Data.List.Relation.Unary.Any.Properties.html#11265" class="Bound">x</a> <a id="11267" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="11269" href="Data.List.Relation.Unary.Any.Properties.html#11269" class="Bound">xs</a><a id="11271" class="Symbol">}</a> <a id="11273" class="Symbol">(</a><a id="11274" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="11280" href="Data.List.Relation.Unary.Any.Properties.html#11280" class="Bound">p</a><a id="11281" class="Symbol">)</a> <a id="11283" class="Symbol">=</a> <a id="11285" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="11292" href="Data.List.Relation.Unary.Any.Properties.html#11187" class="Function">map⁺∘map⁻</a> <a id="11302" class="Symbol">{</a><a id="11303" class="Argument">xs</a> <a id="11306" class="Symbol">=</a> <a id="11308" href="Data.List.Relation.Unary.Any.Properties.html#11308" class="Bound">x</a> <a id="11310" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="11312" href="Data.List.Relation.Unary.Any.Properties.html#11312" class="Bound">xs</a><a id="11314" class="Symbol">}</a> <a id="11316" class="Symbol">(</a><a id="11317" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="11323" href="Data.List.Relation.Unary.Any.Properties.html#11323" class="Bound">p</a><a id="11324" class="Symbol">)</a> <a id="11326" class="Symbol">=</a> <a id="11328" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="11335" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="11341" class="Symbol">(</a><a id="11342" href="Data.List.Relation.Unary.Any.Properties.html#11187" class="Function">map⁺∘map⁻</a> <a id="11352" href="Data.List.Relation.Unary.Any.Properties.html#11323" class="Bound">p</a><a id="11353" class="Symbol">)</a>
<a id="11358" href="Data.List.Relation.Unary.Any.Properties.html#11358" class="Function">map⁻∘map⁺</a> <a id="11368" class="Symbol">:</a> <a id="11370" class="Symbol">∀</a> <a id="11372" class="Symbol">(</a><a id="11373" href="Data.List.Relation.Unary.Any.Properties.html#11373" class="Bound">P</a> <a id="11375" class="Symbol">:</a> <a id="11377" href="Relation.Unary.html#1101" class="Function">Pred</a> <a id="11382" href="Data.List.Relation.Unary.Any.Properties.html#10929" class="Bound">B</a> <a id="11384" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a><a id="11385" class="Symbol">)</a> <a id="11387" class="Symbol">→</a>
<a id="11403" class="Symbol">(</a><a id="11404" href="Data.List.Relation.Unary.Any.Properties.html#11404" class="Bound">p</a> <a id="11406" class="Symbol">:</a> <a id="11408" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11412" class="Symbol">(</a><a id="11413" href="Data.List.Relation.Unary.Any.Properties.html#11373" class="Bound">P</a> <a id="11415" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="11417" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a><a id="11418" class="Symbol">)</a> <a id="11420" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="11422" class="Symbol">)</a> <a id="11424" class="Symbol">→</a> <a id="11426" href="Data.List.Relation.Unary.Any.Properties.html#11050" class="Function">map⁻</a> <a id="11431" class="Symbol">{</a><a id="11432" class="Argument">P</a> <a id="11434" class="Symbol">=</a> <a id="11436" href="Data.List.Relation.Unary.Any.Properties.html#11373" class="Bound">P</a><a id="11437" class="Symbol">}</a> <a id="11439" class="Symbol">(</a><a id="11440" href="Data.List.Relation.Unary.Any.Properties.html#10941" class="Function">map⁺</a> <a id="11445" href="Data.List.Relation.Unary.Any.Properties.html#11404" class="Bound">p</a><a id="11446" class="Symbol">)</a> <a id="11448" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="11450" href="Data.List.Relation.Unary.Any.Properties.html#11404" class="Bound">p</a>
<a id="11454" href="Data.List.Relation.Unary.Any.Properties.html#11358" class="Function">map⁻∘map⁺</a> <a id="11464" href="Data.List.Relation.Unary.Any.Properties.html#11464" class="Bound">P</a> <a id="11466" class="Symbol">(</a><a id="11467" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="11473" href="Data.List.Relation.Unary.Any.Properties.html#11473" class="Bound">p</a><a id="11474" class="Symbol">)</a> <a id="11476" class="Symbol">=</a> <a id="11478" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="11485" href="Data.List.Relation.Unary.Any.Properties.html#11358" class="Function">map⁻∘map⁺</a> <a id="11495" href="Data.List.Relation.Unary.Any.Properties.html#11495" class="Bound">P</a> <a id="11497" class="Symbol">(</a><a id="11498" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="11504" href="Data.List.Relation.Unary.Any.Properties.html#11504" class="Bound">p</a><a id="11505" class="Symbol">)</a> <a id="11507" class="Symbol">=</a> <a id="11509" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="11516" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="11522" class="Symbol">(</a><a id="11523" href="Data.List.Relation.Unary.Any.Properties.html#11358" class="Function">map⁻∘map⁺</a> <a id="11533" href="Data.List.Relation.Unary.Any.Properties.html#11495" class="Bound">P</a> <a id="11535" href="Data.List.Relation.Unary.Any.Properties.html#11504" class="Bound">p</a><a id="11536" class="Symbol">)</a>
<a id="11541" href="Data.List.Relation.Unary.Any.Properties.html#11541" class="Function">map↔</a> <a id="11546" class="Symbol">:</a> <a id="11548" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11552" class="Symbol">(</a><a id="11553" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="11555" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="11557" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a><a id="11558" class="Symbol">)</a> <a id="11560" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="11563" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="11565" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11569" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="11571" class="Symbol">(</a><a id="11572" href="Data.List.Base.html#1544" class="Function">List.map</a> <a id="11581" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a> <a id="11583" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="11585" class="Symbol">)</a>
<a id="11589" href="Data.List.Relation.Unary.Any.Properties.html#11541" class="Function">map↔</a> <a id="11594" class="Symbol">=</a> <a id="11596" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="11604" href="Data.List.Relation.Unary.Any.Properties.html#10941" class="Function">map⁺</a> <a id="11609" href="Data.List.Relation.Unary.Any.Properties.html#11050" class="Function">map⁻</a> <a id="11614" class="Symbol">(</a><a id="11615" href="Data.List.Relation.Unary.Any.Properties.html#11358" class="Function">map⁻∘map⁺</a> <a id="11625" class="Symbol">_)</a> <a id="11628" href="Data.List.Relation.Unary.Any.Properties.html#11187" class="Function">map⁺∘map⁻</a>
<a id="11641" href="Data.List.Relation.Unary.Any.Properties.html#11641" class="Function">gmap</a> <a id="11646" class="Symbol">:</a> <a id="11648" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="11650" href="Data.List.Relation.Unary.Any.Properties.html#2121" class="Function Operator">⋐</a> <a id="11652" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="11654" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="11656" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a> <a id="11658" class="Symbol">→</a> <a id="11660" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11664" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="11666" href="Data.List.Relation.Unary.Any.Properties.html#2121" class="Function Operator">⋐</a> <a id="11668" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11672" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="11674" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="11676" href="Data.List.Base.html#1544" class="Function">map</a> <a id="11680" href="Data.List.Relation.Unary.Any.Properties.html#10921" class="Bound">f</a>
<a id="11684" href="Data.List.Relation.Unary.Any.Properties.html#11641" class="Function">gmap</a> <a id="11689" href="Data.List.Relation.Unary.Any.Properties.html#11689" class="Bound">g</a> <a id="11691" class="Symbol">=</a> <a id="11693" href="Data.List.Relation.Unary.Any.Properties.html#10941" class="Function">map⁺</a> <a id="11698" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="11700" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="11708" href="Data.List.Relation.Unary.Any.Properties.html#11689" class="Bound">g</a>
<a id="11711" class="Comment">------------------------------------------------------------------------</a>
<a id="11784" class="Comment">-- mapMaybe</a>
<a id="11797" class="Keyword">module</a> <a id="11804" href="Data.List.Relation.Unary.Any.Properties.html#11804" class="Module">_</a> <a id="11806" class="Symbol">(</a><a id="11807" href="Data.List.Relation.Unary.Any.Properties.html#11807" class="Bound">f</a> <a id="11809" class="Symbol">:</a> <a id="11811" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="11813" class="Symbol">→</a> <a id="11815" href="Agda.Builtin.Maybe.html#136" class="Datatype">Maybe</a> <a id="11821" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a><a id="11822" class="Symbol">)</a> <a id="11824" class="Keyword">where</a>
<a id="11833" href="Data.List.Relation.Unary.Any.Properties.html#11833" class="Function">mapMaybe⁺</a> <a id="11843" class="Symbol">:</a> <a id="11845" class="Symbol">∀</a> <a id="11847" href="Data.List.Relation.Unary.Any.Properties.html#11847" class="Bound">xs</a> <a id="11850" class="Symbol">→</a> <a id="11852" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11856" class="Symbol">(</a><a id="11857" href="Data.Maybe.Relation.Unary.Any.html#830" class="Datatype">MAny.Any</a> <a id="11866" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a><a id="11867" class="Symbol">)</a> <a id="11869" class="Symbol">(</a><a id="11870" href="Data.List.Base.html#1544" class="Function">map</a> <a id="11874" href="Data.List.Relation.Unary.Any.Properties.html#11807" class="Bound">f</a> <a id="11876" href="Data.List.Relation.Unary.Any.Properties.html#11847" class="Bound">xs</a><a id="11878" class="Symbol">)</a> <a id="11880" class="Symbol">→</a> <a id="11882" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="11886" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="11888" class="Symbol">(</a><a id="11889" href="Data.List.Base.html#1629" class="Function">mapMaybe</a> <a id="11898" href="Data.List.Relation.Unary.Any.Properties.html#11807" class="Bound">f</a> <a id="11900" href="Data.List.Relation.Unary.Any.Properties.html#11847" class="Bound">xs</a><a id="11902" class="Symbol">)</a>
<a id="11906" href="Data.List.Relation.Unary.Any.Properties.html#11833" class="Function">mapMaybe⁺</a> <a id="11916" class="Symbol">(</a><a id="11917" href="Data.List.Relation.Unary.Any.Properties.html#11917" class="Bound">x</a> <a id="11919" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="11921" href="Data.List.Relation.Unary.Any.Properties.html#11921" class="Bound">xs</a><a id="11923" class="Symbol">)</a> <a id="11925" href="Data.List.Relation.Unary.Any.Properties.html#11925" class="Bound">ps</a> <a id="11928" class="Keyword">with</a> <a id="11933" href="Data.List.Relation.Unary.Any.Properties.html#11807" class="Bound">f</a> <a id="11935" href="Data.List.Relation.Unary.Any.Properties.html#11917" class="Bound">x</a> <a id="11937" class="Symbol">|</a> <a id="11939" href="Data.List.Relation.Unary.Any.Properties.html#11925" class="Bound">ps</a>
<a id="11944" class="Symbol">...</a> <a id="11948" class="Symbol">|</a> <a id="11950" href="Agda.Builtin.Maybe.html#195" class="InductiveConstructor">nothing</a> <a id="11958" class="Symbol">|</a> <a id="11960" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="11966" href="Data.List.Relation.Unary.Any.Properties.html#11966" class="Bound">pxs</a> <a id="11975" class="Symbol">=</a> <a id="11977" href="Data.List.Relation.Unary.Any.Properties.html#11833" class="Function">mapMaybe⁺</a> <a id="11987" class="Bound">xs</a> <a id="11990" href="Data.List.Relation.Unary.Any.Properties.html#11966" class="Bound">pxs</a>
<a id="11996" class="Symbol">...</a> <a id="12000" class="Symbol">|</a> <a id="12002" href="Agda.Builtin.Maybe.html#174" class="InductiveConstructor">just</a> <a id="12007" class="Symbol">_</a> <a id="12010" class="Symbol">|</a> <a id="12012" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="12017" class="Symbol">(</a><a id="12018" href="Data.Maybe.Relation.Unary.Any.html#900" class="InductiveConstructor">just</a> <a id="12023" href="Data.List.Relation.Unary.Any.Properties.html#12023" class="Bound">py</a><a id="12025" class="Symbol">)</a> <a id="12027" class="Symbol">=</a> <a id="12029" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="12034" href="Data.List.Relation.Unary.Any.Properties.html#12023" class="Bound">py</a>
<a id="12039" class="Symbol">...</a> <a id="12043" class="Symbol">|</a> <a id="12045" href="Agda.Builtin.Maybe.html#174" class="InductiveConstructor">just</a> <a id="12050" class="Symbol">_</a> <a id="12053" class="Symbol">|</a> <a id="12055" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12061" href="Data.List.Relation.Unary.Any.Properties.html#12061" class="Bound">pxs</a> <a id="12070" class="Symbol">=</a> <a id="12072" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12078" class="Symbol">(</a><a id="12079" href="Data.List.Relation.Unary.Any.Properties.html#11833" class="Function">mapMaybe⁺</a> <a id="12089" class="Bound">xs</a> <a id="12092" href="Data.List.Relation.Unary.Any.Properties.html#12061" class="Bound">pxs</a><a id="12095" class="Symbol">)</a>
<a id="12098" class="Comment">------------------------------------------------------------------------</a>
<a id="12171" class="Comment">-- _++_</a>
<a id="12180" class="Keyword">module</a> <a id="12187" href="Data.List.Relation.Unary.Any.Properties.html#12187" class="Module">_</a> <a id="12189" class="Symbol">{</a><a id="12190" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12192" class="Symbol">:</a> <a id="12194" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="12196" class="Symbol">→</a> <a id="12198" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="12202" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a><a id="12203" class="Symbol">}</a> <a id="12205" class="Keyword">where</a>
<a id="12214" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="12219" class="Symbol">:</a> <a id="12221" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12225" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12227" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="12230" class="Symbol">→</a> <a id="12232" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12236" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12238" class="Symbol">(</a><a id="12239" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="12242" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="12245" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="12247" class="Symbol">)</a>
<a id="12251" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="12256" class="Symbol">(</a><a id="12257" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="12262" href="Data.List.Relation.Unary.Any.Properties.html#12262" class="Bound">p</a><a id="12263" class="Symbol">)</a> <a id="12266" class="Symbol">=</a> <a id="12268" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="12273" href="Data.List.Relation.Unary.Any.Properties.html#12262" class="Bound">p</a>
<a id="12277" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="12282" class="Symbol">(</a><a id="12283" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12289" href="Data.List.Relation.Unary.Any.Properties.html#12289" class="Bound">p</a><a id="12290" class="Symbol">)</a> <a id="12292" class="Symbol">=</a> <a id="12294" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12300" class="Symbol">(</a><a id="12301" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="12306" href="Data.List.Relation.Unary.Any.Properties.html#12289" class="Bound">p</a><a id="12307" class="Symbol">)</a>
<a id="12312" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="12317" class="Symbol">:</a> <a id="12319" class="Symbol">∀</a> <a id="12321" href="Data.List.Relation.Unary.Any.Properties.html#12321" class="Bound">xs</a> <a id="12324" class="Symbol">{</a><a id="12325" href="Data.List.Relation.Unary.Any.Properties.html#12325" class="Bound">ys</a><a id="12327" class="Symbol">}</a> <a id="12329" class="Symbol">→</a> <a id="12331" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12335" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12337" href="Data.List.Relation.Unary.Any.Properties.html#12325" class="Bound">ys</a> <a id="12340" class="Symbol">→</a> <a id="12342" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12346" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12348" class="Symbol">(</a><a id="12349" href="Data.List.Relation.Unary.Any.Properties.html#12321" class="Bound">xs</a> <a id="12352" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="12355" href="Data.List.Relation.Unary.Any.Properties.html#12325" class="Bound">ys</a><a id="12357" class="Symbol">)</a>
<a id="12361" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="12366" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="12375" href="Data.List.Relation.Unary.Any.Properties.html#12375" class="Bound">p</a> <a id="12377" class="Symbol">=</a> <a id="12379" href="Data.List.Relation.Unary.Any.Properties.html#12375" class="Bound">p</a>
<a id="12383" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="12388" class="Symbol">(</a><a id="12389" href="Data.List.Relation.Unary.Any.Properties.html#12389" class="Bound">x</a> <a id="12391" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="12393" href="Data.List.Relation.Unary.Any.Properties.html#12393" class="Bound">xs</a><a id="12395" class="Symbol">)</a> <a id="12397" href="Data.List.Relation.Unary.Any.Properties.html#12397" class="Bound">p</a> <a id="12399" class="Symbol">=</a> <a id="12401" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12407" class="Symbol">(</a><a id="12408" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="12413" href="Data.List.Relation.Unary.Any.Properties.html#12393" class="Bound">xs</a> <a id="12416" href="Data.List.Relation.Unary.Any.Properties.html#12397" class="Bound">p</a><a id="12417" class="Symbol">)</a>
<a id="12422" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="12426" class="Symbol">:</a> <a id="12428" class="Symbol">∀</a> <a id="12430" href="Data.List.Relation.Unary.Any.Properties.html#12430" class="Bound">xs</a> <a id="12433" class="Symbol">{</a><a id="12434" href="Data.List.Relation.Unary.Any.Properties.html#12434" class="Bound">ys</a><a id="12436" class="Symbol">}</a> <a id="12438" class="Symbol">→</a> <a id="12440" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12444" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12446" class="Symbol">(</a><a id="12447" href="Data.List.Relation.Unary.Any.Properties.html#12430" class="Bound">xs</a> <a id="12450" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="12453" href="Data.List.Relation.Unary.Any.Properties.html#12434" class="Bound">ys</a><a id="12455" class="Symbol">)</a> <a id="12457" class="Symbol">→</a> <a id="12459" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12463" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12465" href="Data.List.Relation.Unary.Any.Properties.html#12430" class="Bound">xs</a> <a id="12468" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="12470" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12474" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12476" href="Data.List.Relation.Unary.Any.Properties.html#12434" class="Bound">ys</a>
<a id="12481" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="12485" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="12494" href="Data.List.Relation.Unary.Any.Properties.html#12494" class="Bound">p</a> <a id="12504" class="Symbol">=</a> <a id="12506" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="12511" href="Data.List.Relation.Unary.Any.Properties.html#12494" class="Bound">p</a>
<a id="12515" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="12519" class="Symbol">(</a><a id="12520" href="Data.List.Relation.Unary.Any.Properties.html#12520" class="Bound">x</a> <a id="12522" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="12524" href="Data.List.Relation.Unary.Any.Properties.html#12524" class="Bound">xs</a><a id="12526" class="Symbol">)</a> <a id="12528" class="Symbol">(</a><a id="12529" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="12534" href="Data.List.Relation.Unary.Any.Properties.html#12534" class="Bound">p</a><a id="12535" class="Symbol">)</a> <a id="12538" class="Symbol">=</a> <a id="12540" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="12545" class="Symbol">(</a><a id="12546" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="12551" href="Data.List.Relation.Unary.Any.Properties.html#12534" class="Bound">p</a><a id="12552" class="Symbol">)</a>
<a id="12556" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="12560" class="Symbol">(</a><a id="12561" href="Data.List.Relation.Unary.Any.Properties.html#12561" class="Bound">x</a> <a id="12563" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="12565" href="Data.List.Relation.Unary.Any.Properties.html#12565" class="Bound">xs</a><a id="12567" class="Symbol">)</a> <a id="12569" class="Symbol">(</a><a id="12570" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12576" href="Data.List.Relation.Unary.Any.Properties.html#12576" class="Bound">p</a><a id="12577" class="Symbol">)</a> <a id="12579" class="Symbol">=</a> <a id="12581" href="Data.Sum.Base.html#1362" class="Function">Sum.map</a> <a id="12589" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12595" href="Function.Base.html#615" class="Function">id</a> <a id="12598" class="Symbol">(</a><a id="12599" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="12603" href="Data.List.Relation.Unary.Any.Properties.html#12565" class="Bound">xs</a> <a id="12606" href="Data.List.Relation.Unary.Any.Properties.html#12576" class="Bound">p</a><a id="12607" class="Symbol">)</a>
<a id="12612" href="Data.List.Relation.Unary.Any.Properties.html#12612" class="Function">++⁺∘++⁻</a> <a id="12620" class="Symbol">:</a> <a id="12622" class="Symbol">∀</a> <a id="12624" href="Data.List.Relation.Unary.Any.Properties.html#12624" class="Bound">xs</a> <a id="12627" class="Symbol">{</a><a id="12628" href="Data.List.Relation.Unary.Any.Properties.html#12628" class="Bound">ys</a><a id="12630" class="Symbol">}</a> <a id="12632" class="Symbol">(</a><a id="12633" href="Data.List.Relation.Unary.Any.Properties.html#12633" class="Bound">p</a> <a id="12635" class="Symbol">:</a> <a id="12637" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12641" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12643" class="Symbol">(</a><a id="12644" href="Data.List.Relation.Unary.Any.Properties.html#12624" class="Bound">xs</a> <a id="12647" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="12650" href="Data.List.Relation.Unary.Any.Properties.html#12628" class="Bound">ys</a><a id="12652" class="Symbol">))</a> <a id="12655" class="Symbol">→</a> <a id="12657" href="Data.Sum.Base.html#1089" class="Function Operator">[</a> <a id="12659" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="12664" href="Data.Sum.Base.html#1089" class="Function Operator">,</a> <a id="12666" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="12671" href="Data.List.Relation.Unary.Any.Properties.html#12624" class="Bound">xs</a> <a id="12674" href="Data.Sum.Base.html#1089" class="Function Operator">]′</a> <a id="12677" class="Symbol">(</a><a id="12678" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="12682" href="Data.List.Relation.Unary.Any.Properties.html#12624" class="Bound">xs</a> <a id="12685" href="Data.List.Relation.Unary.Any.Properties.html#12633" class="Bound">p</a><a id="12686" class="Symbol">)</a> <a id="12688" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="12690" href="Data.List.Relation.Unary.Any.Properties.html#12633" class="Bound">p</a>
<a id="12694" href="Data.List.Relation.Unary.Any.Properties.html#12612" class="Function">++⁺∘++⁻</a> <a id="12702" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="12711" href="Data.List.Relation.Unary.Any.Properties.html#12711" class="Bound">p</a> <a id="12721" class="Symbol">=</a> <a id="12723" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="12730" href="Data.List.Relation.Unary.Any.Properties.html#12612" class="Function">++⁺∘++⁻</a> <a id="12738" class="Symbol">(</a><a id="12739" href="Data.List.Relation.Unary.Any.Properties.html#12739" class="Bound">x</a> <a id="12741" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="12743" href="Data.List.Relation.Unary.Any.Properties.html#12743" class="Bound">xs</a><a id="12745" class="Symbol">)</a> <a id="12747" class="Symbol">(</a><a id="12748" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="12754" href="Data.List.Relation.Unary.Any.Properties.html#12754" class="Bound">p</a><a id="12755" class="Symbol">)</a> <a id="12757" class="Symbol">=</a> <a id="12759" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="12766" href="Data.List.Relation.Unary.Any.Properties.html#12612" class="Function">++⁺∘++⁻</a> <a id="12774" class="Symbol">(</a><a id="12775" href="Data.List.Relation.Unary.Any.Properties.html#12775" class="Bound">x</a> <a id="12777" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="12779" href="Data.List.Relation.Unary.Any.Properties.html#12779" class="Bound">xs</a><a id="12781" class="Symbol">)</a> <a id="12783" class="Symbol">(</a><a id="12784" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12790" href="Data.List.Relation.Unary.Any.Properties.html#12790" class="Bound">p</a><a id="12791" class="Symbol">)</a> <a id="12793" class="Keyword">with</a> <a id="12798" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="12802" href="Data.List.Relation.Unary.Any.Properties.html#12779" class="Bound">xs</a> <a id="12805" href="Data.List.Relation.Unary.Any.Properties.html#12790" class="Bound">p</a> <a id="12807" class="Symbol">|</a> <a id="12809" href="Data.List.Relation.Unary.Any.Properties.html#12612" class="Function">++⁺∘++⁻</a> <a id="12817" href="Data.List.Relation.Unary.Any.Properties.html#12779" class="Bound">xs</a> <a id="12820" href="Data.List.Relation.Unary.Any.Properties.html#12790" class="Bound">p</a>
<a id="12824" class="Symbol">...</a> <a id="12828" class="Symbol">|</a> <a id="12830" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="12835" href="Data.List.Relation.Unary.Any.Properties.html#12835" class="Bound">p′</a> <a id="12838" class="Symbol">|</a> <a id="12840" href="Data.List.Relation.Unary.Any.Properties.html#12840" class="Bound">ih</a> <a id="12843" class="Symbol">=</a> <a id="12845" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="12852" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12858" href="Data.List.Relation.Unary.Any.Properties.html#12840" class="Bound">ih</a>
<a id="12863" class="Symbol">...</a> <a id="12867" class="Symbol">|</a> <a id="12869" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="12874" href="Data.List.Relation.Unary.Any.Properties.html#12874" class="Bound">p′</a> <a id="12877" class="Symbol">|</a> <a id="12879" href="Data.List.Relation.Unary.Any.Properties.html#12879" class="Bound">ih</a> <a id="12882" class="Symbol">=</a> <a id="12884" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="12891" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="12897" href="Data.List.Relation.Unary.Any.Properties.html#12879" class="Bound">ih</a>
<a id="12903" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="12911" class="Symbol">:</a> <a id="12913" class="Symbol">∀</a> <a id="12915" href="Data.List.Relation.Unary.Any.Properties.html#12915" class="Bound">xs</a> <a id="12918" class="Symbol">{</a><a id="12919" href="Data.List.Relation.Unary.Any.Properties.html#12919" class="Bound">ys</a><a id="12921" class="Symbol">}</a> <a id="12923" class="Symbol">(</a><a id="12924" href="Data.List.Relation.Unary.Any.Properties.html#12924" class="Bound">p</a> <a id="12926" class="Symbol">:</a> <a id="12928" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12932" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12934" href="Data.List.Relation.Unary.Any.Properties.html#12915" class="Bound">xs</a> <a id="12937" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="12939" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="12943" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="12945" href="Data.List.Relation.Unary.Any.Properties.html#12919" class="Bound">ys</a><a id="12947" class="Symbol">)</a> <a id="12949" class="Symbol">→</a>
<a id="12963" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="12967" href="Data.List.Relation.Unary.Any.Properties.html#12915" class="Bound">xs</a> <a id="12970" class="Symbol">(</a><a id="12971" href="Data.Sum.Base.html#1089" class="Function Operator">[</a> <a id="12973" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="12978" href="Data.Sum.Base.html#1089" class="Function Operator">,</a> <a id="12980" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="12985" href="Data.List.Relation.Unary.Any.Properties.html#12915" class="Bound">xs</a> <a id="12988" href="Data.Sum.Base.html#1089" class="Function Operator">]′</a> <a id="12991" href="Data.List.Relation.Unary.Any.Properties.html#12924" class="Bound">p</a><a id="12992" class="Symbol">)</a> <a id="12994" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="12996" href="Data.List.Relation.Unary.Any.Properties.html#12924" class="Bound">p</a>
<a id="13000" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13008" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="13022" class="Symbol">(</a><a id="13023" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="13028" href="Data.List.Relation.Unary.Any.Properties.html#13028" class="Bound">p</a><a id="13029" class="Symbol">)</a> <a id="13039" class="Symbol">=</a> <a id="13041" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="13048" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13056" class="Symbol">(</a><a id="13057" href="Data.List.Relation.Unary.Any.Properties.html#13057" class="Bound">x</a> <a id="13059" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="13061" href="Data.List.Relation.Unary.Any.Properties.html#13061" class="Bound">xs</a><a id="13063" class="Symbol">)</a> <a id="13070" class="Symbol">(</a><a id="13071" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="13076" class="Symbol">(</a><a id="13077" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="13083" href="Data.List.Relation.Unary.Any.Properties.html#13083" class="Bound">p</a><a id="13084" class="Symbol">))</a> <a id="13087" class="Symbol">=</a> <a id="13089" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="13096" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13104" class="Symbol">(</a><a id="13105" href="Data.List.Relation.Unary.Any.Properties.html#13105" class="Bound">x</a> <a id="13107" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="13109" href="Data.List.Relation.Unary.Any.Properties.html#13109" class="Bound">xs</a><a id="13111" class="Symbol">)</a> <a id="13113" class="Symbol">{</a><a id="13114" href="Data.List.Relation.Unary.Any.Properties.html#13114" class="Bound">ys</a><a id="13116" class="Symbol">}</a> <a id="13118" class="Symbol">(</a><a id="13119" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="13124" class="Symbol">(</a><a id="13125" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="13131" href="Data.List.Relation.Unary.Any.Properties.html#13131" class="Bound">p</a><a id="13132" class="Symbol">))</a> <a id="13135" class="Keyword">rewrite</a> <a id="13143" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13151" href="Data.List.Relation.Unary.Any.Properties.html#13109" class="Bound">xs</a> <a id="13154" class="Symbol">{</a><a id="13155" href="Data.List.Relation.Unary.Any.Properties.html#13114" class="Bound">ys</a><a id="13157" class="Symbol">}</a> <a id="13159" class="Symbol">(</a><a id="13160" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="13165" href="Data.List.Relation.Unary.Any.Properties.html#13131" class="Bound">p</a><a id="13166" class="Symbol">)</a> <a id="13168" class="Symbol">=</a> <a id="13170" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="13177" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13185" class="Symbol">(</a><a id="13186" href="Data.List.Relation.Unary.Any.Properties.html#13186" class="Bound">x</a> <a id="13188" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="13190" href="Data.List.Relation.Unary.Any.Properties.html#13190" class="Bound">xs</a><a id="13192" class="Symbol">)</a> <a id="13199" class="Symbol">(</a><a id="13200" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="13205" href="Data.List.Relation.Unary.Any.Properties.html#13205" class="Bound">p</a><a id="13206" class="Symbol">)</a> <a id="13216" class="Keyword">rewrite</a> <a id="13224" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13232" href="Data.List.Relation.Unary.Any.Properties.html#13190" class="Bound">xs</a> <a id="13240" class="Symbol">(</a><a id="13241" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="13246" href="Data.List.Relation.Unary.Any.Properties.html#13205" class="Bound">p</a><a id="13247" class="Symbol">)</a> <a id="13249" class="Symbol">=</a> <a id="13251" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="13259" href="Data.List.Relation.Unary.Any.Properties.html#13259" class="Function">++↔</a> <a id="13263" class="Symbol">:</a> <a id="13265" class="Symbol">∀</a> <a id="13267" class="Symbol">{</a><a id="13268" href="Data.List.Relation.Unary.Any.Properties.html#13268" class="Bound">xs</a> <a id="13271" href="Data.List.Relation.Unary.Any.Properties.html#13271" class="Bound">ys</a><a id="13273" class="Symbol">}</a> <a id="13275" class="Symbol">→</a> <a id="13277" class="Symbol">(</a><a id="13278" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="13282" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="13284" href="Data.List.Relation.Unary.Any.Properties.html#13268" class="Bound">xs</a> <a id="13287" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="13289" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="13293" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="13295" href="Data.List.Relation.Unary.Any.Properties.html#13271" class="Bound">ys</a><a id="13297" class="Symbol">)</a> <a id="13299" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="13301" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="13305" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="13307" class="Symbol">(</a><a id="13308" href="Data.List.Relation.Unary.Any.Properties.html#13268" class="Bound">xs</a> <a id="13311" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="13314" href="Data.List.Relation.Unary.Any.Properties.html#13271" class="Bound">ys</a><a id="13316" class="Symbol">)</a>
<a id="13320" href="Data.List.Relation.Unary.Any.Properties.html#13259" class="Function">++↔</a> <a id="13324" class="Symbol">{</a><a id="13325" class="Argument">xs</a> <a id="13328" class="Symbol">=</a> <a id="13330" href="Data.List.Relation.Unary.Any.Properties.html#13330" class="Bound">xs</a><a id="13332" class="Symbol">}</a> <a id="13334" class="Symbol">=</a> <a id="13336" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="13344" href="Data.Sum.Base.html#1089" class="Function Operator">[</a> <a id="13346" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="13351" href="Data.Sum.Base.html#1089" class="Function Operator">,</a> <a id="13353" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="13358" href="Data.List.Relation.Unary.Any.Properties.html#13330" class="Bound">xs</a> <a id="13361" href="Data.Sum.Base.html#1089" class="Function Operator">]′</a> <a id="13364" class="Symbol">(</a><a id="13365" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="13369" href="Data.List.Relation.Unary.Any.Properties.html#13330" class="Bound">xs</a><a id="13371" class="Symbol">)</a> <a id="13373" class="Symbol">(</a><a id="13374" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13382" href="Data.List.Relation.Unary.Any.Properties.html#13330" class="Bound">xs</a><a id="13384" class="Symbol">)</a> <a id="13386" class="Symbol">(</a><a id="13387" href="Data.List.Relation.Unary.Any.Properties.html#12612" class="Function">++⁺∘++⁻</a> <a id="13395" href="Data.List.Relation.Unary.Any.Properties.html#13330" class="Bound">xs</a><a id="13397" class="Symbol">)</a>
<a id="13402" href="Data.List.Relation.Unary.Any.Properties.html#13402" class="Function">++-comm</a> <a id="13410" class="Symbol">:</a> <a id="13412" class="Symbol">∀</a> <a id="13414" href="Data.List.Relation.Unary.Any.Properties.html#13414" class="Bound">xs</a> <a id="13417" href="Data.List.Relation.Unary.Any.Properties.html#13417" class="Bound">ys</a> <a id="13420" class="Symbol">→</a> <a id="13422" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="13426" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="13428" class="Symbol">(</a><a id="13429" href="Data.List.Relation.Unary.Any.Properties.html#13414" class="Bound">xs</a> <a id="13432" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="13435" href="Data.List.Relation.Unary.Any.Properties.html#13417" class="Bound">ys</a><a id="13437" class="Symbol">)</a> <a id="13439" class="Symbol">→</a> <a id="13441" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="13445" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="13447" class="Symbol">(</a><a id="13448" href="Data.List.Relation.Unary.Any.Properties.html#13417" class="Bound">ys</a> <a id="13451" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="13454" href="Data.List.Relation.Unary.Any.Properties.html#13414" class="Bound">xs</a><a id="13456" class="Symbol">)</a>
<a id="13460" href="Data.List.Relation.Unary.Any.Properties.html#13402" class="Function">++-comm</a> <a id="13468" href="Data.List.Relation.Unary.Any.Properties.html#13468" class="Bound">xs</a> <a id="13471" href="Data.List.Relation.Unary.Any.Properties.html#13471" class="Bound">ys</a> <a id="13474" class="Symbol">=</a> <a id="13476" href="Data.Sum.Base.html#1089" class="Function Operator">[</a> <a id="13478" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="13483" href="Data.List.Relation.Unary.Any.Properties.html#13471" class="Bound">ys</a> <a id="13486" href="Data.Sum.Base.html#1089" class="Function Operator">,</a> <a id="13488" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="13493" href="Data.Sum.Base.html#1089" class="Function Operator">]′</a> <a id="13496" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="13498" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="13502" href="Data.List.Relation.Unary.Any.Properties.html#13468" class="Bound">xs</a>
<a id="13508" href="Data.List.Relation.Unary.Any.Properties.html#13508" class="Function">++-comm∘++-comm</a> <a id="13524" class="Symbol">:</a> <a id="13526" class="Symbol">∀</a> <a id="13528" href="Data.List.Relation.Unary.Any.Properties.html#13528" class="Bound">xs</a> <a id="13531" class="Symbol">{</a><a id="13532" href="Data.List.Relation.Unary.Any.Properties.html#13532" class="Bound">ys</a><a id="13534" class="Symbol">}</a> <a id="13536" class="Symbol">(</a><a id="13537" href="Data.List.Relation.Unary.Any.Properties.html#13537" class="Bound">p</a> <a id="13539" class="Symbol">:</a> <a id="13541" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="13545" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="13547" class="Symbol">(</a><a id="13548" href="Data.List.Relation.Unary.Any.Properties.html#13528" class="Bound">xs</a> <a id="13551" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="13554" href="Data.List.Relation.Unary.Any.Properties.html#13532" class="Bound">ys</a><a id="13556" class="Symbol">))</a> <a id="13559" class="Symbol">→</a>
<a id="13581" href="Data.List.Relation.Unary.Any.Properties.html#13402" class="Function">++-comm</a> <a id="13589" href="Data.List.Relation.Unary.Any.Properties.html#13532" class="Bound">ys</a> <a id="13592" href="Data.List.Relation.Unary.Any.Properties.html#13528" class="Bound">xs</a> <a id="13595" class="Symbol">(</a><a id="13596" href="Data.List.Relation.Unary.Any.Properties.html#13402" class="Function">++-comm</a> <a id="13604" href="Data.List.Relation.Unary.Any.Properties.html#13528" class="Bound">xs</a> <a id="13607" href="Data.List.Relation.Unary.Any.Properties.html#13532" class="Bound">ys</a> <a id="13610" href="Data.List.Relation.Unary.Any.Properties.html#13537" class="Bound">p</a><a id="13611" class="Symbol">)</a> <a id="13613" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="13615" href="Data.List.Relation.Unary.Any.Properties.html#13537" class="Bound">p</a>
<a id="13619" href="Data.List.Relation.Unary.Any.Properties.html#13508" class="Function">++-comm∘++-comm</a> <a id="13635" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="13638" class="Symbol">{</a><a id="13639" href="Data.List.Relation.Unary.Any.Properties.html#13639" class="Bound">ys</a><a id="13641" class="Symbol">}</a> <a id="13643" href="Data.List.Relation.Unary.Any.Properties.html#13643" class="Bound">p</a>
<a id="13649" class="Keyword">rewrite</a> <a id="13657" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13665" href="Data.List.Relation.Unary.Any.Properties.html#13639" class="Bound">ys</a> <a id="13668" class="Symbol">{</a><a id="13669" class="Argument">ys</a> <a id="13672" class="Symbol">=</a> <a id="13674" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a><a id="13676" class="Symbol">}</a> <a id="13678" class="Symbol">(</a><a id="13679" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="13684" href="Data.List.Relation.Unary.Any.Properties.html#13643" class="Bound">p</a><a id="13685" class="Symbol">)</a> <a id="13687" class="Symbol">=</a> <a id="13689" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="13696" href="Data.List.Relation.Unary.Any.Properties.html#13508" class="Function">++-comm∘++-comm</a> <a id="13712" class="Symbol">(</a><a id="13713" href="Data.List.Relation.Unary.Any.Properties.html#13713" class="Bound">x</a> <a id="13715" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="13717" href="Data.List.Relation.Unary.Any.Properties.html#13717" class="Bound">xs</a><a id="13719" class="Symbol">)</a> <a id="13721" class="Symbol">{</a><a id="13722" href="Data.List.Relation.Unary.Any.Properties.html#13722" class="Bound">ys</a><a id="13724" class="Symbol">}</a> <a id="13726" class="Symbol">(</a><a id="13727" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="13732" href="Data.List.Relation.Unary.Any.Properties.html#13732" class="Bound">p</a><a id="13733" class="Symbol">)</a>
<a id="13739" class="Keyword">rewrite</a> <a id="13747" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13755" href="Data.List.Relation.Unary.Any.Properties.html#13722" class="Bound">ys</a> <a id="13758" class="Symbol">{</a><a id="13759" class="Argument">ys</a> <a id="13762" class="Symbol">=</a> <a id="13764" href="Data.List.Relation.Unary.Any.Properties.html#13713" class="Bound">x</a> <a id="13766" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="13768" href="Data.List.Relation.Unary.Any.Properties.html#13717" class="Bound">xs</a><a id="13770" class="Symbol">}</a> <a id="13772" class="Symbol">(</a><a id="13773" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="13778" class="Symbol">(</a><a id="13779" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="13784" href="Data.List.Relation.Unary.Any.Properties.html#13732" class="Bound">p</a><a id="13785" class="Symbol">))</a> <a id="13788" class="Symbol">=</a> <a id="13790" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="13797" href="Data.List.Relation.Unary.Any.Properties.html#13508" class="Function">++-comm∘++-comm</a> <a id="13813" class="Symbol">(</a><a id="13814" href="Data.List.Relation.Unary.Any.Properties.html#13814" class="Bound">x</a> <a id="13816" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="13818" href="Data.List.Relation.Unary.Any.Properties.html#13818" class="Bound">xs</a><a id="13820" class="Symbol">)</a> <a id="13827" class="Symbol">(</a><a id="13828" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="13834" href="Data.List.Relation.Unary.Any.Properties.html#13834" class="Bound">p</a><a id="13835" class="Symbol">)</a> <a id="13837" class="Keyword">with</a> <a id="13842" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="13846" href="Data.List.Relation.Unary.Any.Properties.html#13818" class="Bound">xs</a> <a id="13849" href="Data.List.Relation.Unary.Any.Properties.html#13834" class="Bound">p</a> <a id="13851" class="Symbol">|</a> <a id="13853" href="Data.List.Relation.Unary.Any.Properties.html#13508" class="Function">++-comm∘++-comm</a> <a id="13869" href="Data.List.Relation.Unary.Any.Properties.html#13818" class="Bound">xs</a> <a id="13872" href="Data.List.Relation.Unary.Any.Properties.html#13834" class="Bound">p</a>
<a id="13876" href="Data.List.Relation.Unary.Any.Properties.html#13508" class="Function">++-comm∘++-comm</a> <a id="13892" class="Symbol">(</a><a id="13893" href="Data.List.Relation.Unary.Any.Properties.html#13893" class="Bound">x</a> <a id="13895" class="InductiveConstructor Operator">∷</a> <a id="13897" href="Data.List.Relation.Unary.Any.Properties.html#13897" class="Bound">xs</a><a id="13899" class="Symbol">)</a> <a id="13901" class="Symbol">{</a><a id="13902" href="Data.List.Relation.Unary.Any.Properties.html#13902" class="Bound">ys</a><a id="13904" class="Symbol">}</a> <a id="13906" class="Symbol">(</a><a id="13907" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="13913" class="DottedPattern Symbol">.(</a><a id="13915" href="Data.Sum.Base.html#1089" class="DottedPattern Function Operator">[</a> <a id="13917" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="DottedPattern Function">++⁺ʳ</a> <a id="13922" href="Data.List.Relation.Unary.Any.Properties.html#13897" class="DottedPattern Bound">xs</a> <a id="13925" href="Data.Sum.Base.html#1089" class="DottedPattern Function Operator">,</a> <a id="13927" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="DottedPattern Function">++⁺ˡ</a> <a id="13932" href="Data.Sum.Base.html#1089" class="DottedPattern Function Operator">]′</a> <a id="13935" class="DottedPattern Symbol">(</a><a id="13936" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="DottedPattern Function">++⁻</a> <a id="13940" href="Data.List.Relation.Unary.Any.Properties.html#13902" class="DottedPattern Bound">ys</a> <a id="13943" class="DottedPattern Symbol">(</a><a id="13944" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="DottedPattern Function">++⁺ʳ</a> <a id="13949" href="Data.List.Relation.Unary.Any.Properties.html#13902" class="DottedPattern Bound">ys</a> <a id="13952" href="Data.List.Relation.Unary.Any.Properties.html#13969" class="DottedPattern Bound">p</a><a id="13953" class="DottedPattern Symbol">)))</a><a id="13956" class="Symbol">)</a>
<a id="13962" class="Symbol">|</a> <a id="13964" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="13969" href="Data.List.Relation.Unary.Any.Properties.html#13969" class="Bound">p</a> <a id="13971" class="Symbol">|</a> <a id="13973" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="13982" class="Keyword">rewrite</a> <a id="13990" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="13998" href="Data.List.Relation.Unary.Any.Properties.html#13902" class="Bound">ys</a> <a id="14001" class="Symbol">(</a><a id="14002" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="14023" href="Data.List.Relation.Unary.Any.Properties.html#13969" class="Bound">p</a><a id="14024" class="Symbol">)</a>
<a id="14036" class="Symbol">|</a> <a id="14038" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="14046" href="Data.List.Relation.Unary.Any.Properties.html#13902" class="Bound">ys</a> <a id="14049" class="Symbol">(</a><a id="14050" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="14055" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="14057" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="14063" class="Symbol">{</a><a id="14064" class="Argument">x</a> <a id="14066" class="Symbol">=</a> <a id="14068" href="Data.List.Relation.Unary.Any.Properties.html#13893" class="Bound">x</a><a id="14069" class="Symbol">}</a> <a id="14071" href="Data.List.Relation.Unary.Any.Properties.html#13969" class="Bound">p</a><a id="14072" class="Symbol">)</a> <a id="14074" class="Symbol">=</a> <a id="14076" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="14083" href="Data.List.Relation.Unary.Any.Properties.html#13508" class="Function">++-comm∘++-comm</a> <a id="14099" class="Symbol">(</a><a id="14100" href="Data.List.Relation.Unary.Any.Properties.html#14100" class="Bound">x</a> <a id="14102" class="InductiveConstructor Operator">∷</a> <a id="14104" href="Data.List.Relation.Unary.Any.Properties.html#14104" class="Bound">xs</a><a id="14106" class="Symbol">)</a> <a id="14108" class="Symbol">{</a><a id="14109" href="Data.List.Relation.Unary.Any.Properties.html#14109" class="Bound">ys</a><a id="14111" class="Symbol">}</a> <a id="14113" class="Symbol">(</a><a id="14114" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="14120" class="DottedPattern Symbol">.(</a><a id="14122" href="Data.Sum.Base.html#1089" class="DottedPattern Function Operator">[</a> <a id="14124" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="DottedPattern Function">++⁺ʳ</a> <a id="14129" href="Data.List.Relation.Unary.Any.Properties.html#14104" class="DottedPattern Bound">xs</a> <a id="14132" href="Data.Sum.Base.html#1089" class="DottedPattern Function Operator">,</a> <a id="14134" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="DottedPattern Function">++⁺ˡ</a> <a id="14139" href="Data.Sum.Base.html#1089" class="DottedPattern Function Operator">]′</a> <a id="14142" class="DottedPattern Symbol">(</a><a id="14143" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="DottedPattern Function">++⁻</a> <a id="14147" href="Data.List.Relation.Unary.Any.Properties.html#14109" class="DottedPattern Bound">ys</a> <a id="14150" class="DottedPattern Symbol">(</a><a id="14151" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="DottedPattern Function">++⁺ˡ</a> <a id="14156" href="Data.List.Relation.Unary.Any.Properties.html#14173" class="DottedPattern Bound">p</a><a id="14157" class="DottedPattern Symbol">)))</a><a id="14160" class="Symbol">)</a>
<a id="14166" class="Symbol">|</a> <a id="14168" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="14173" href="Data.List.Relation.Unary.Any.Properties.html#14173" class="Bound">p</a> <a id="14175" class="Symbol">|</a> <a id="14177" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="14186" class="Keyword">rewrite</a> <a id="14194" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="14202" href="Data.List.Relation.Unary.Any.Properties.html#14109" class="Bound">ys</a> <a id="14205" class="Symbol">{</a><a id="14206" class="Argument">ys</a> <a id="14209" class="Symbol">=</a> <a id="14215" href="Data.List.Relation.Unary.Any.Properties.html#14104" class="Bound">xs</a><a id="14217" class="Symbol">}</a> <a id="14219" class="Symbol">(</a><a id="14220" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="14225" href="Data.List.Relation.Unary.Any.Properties.html#14173" class="Bound">p</a><a id="14226" class="Symbol">)</a>
<a id="14238" class="Symbol">|</a> <a id="14240" href="Data.List.Relation.Unary.Any.Properties.html#12903" class="Function">++⁻∘++⁺</a> <a id="14248" href="Data.List.Relation.Unary.Any.Properties.html#14109" class="Bound">ys</a> <a id="14251" class="Symbol">{</a><a id="14252" class="Argument">ys</a> <a id="14255" class="Symbol">=</a> <a id="14257" href="Data.List.Relation.Unary.Any.Properties.html#14100" class="Bound">x</a> <a id="14259" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="14261" href="Data.List.Relation.Unary.Any.Properties.html#14104" class="Bound">xs</a><a id="14263" class="Symbol">}</a> <a id="14265" class="Symbol">(</a><a id="14266" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="14271" href="Data.List.Relation.Unary.Any.Properties.html#14173" class="Bound">p</a><a id="14272" class="Symbol">)</a> <a id="14274" class="Symbol">=</a> <a id="14276" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="14284" href="Data.List.Relation.Unary.Any.Properties.html#14284" class="Function">++↔++</a> <a id="14290" class="Symbol">:</a> <a id="14292" class="Symbol">∀</a> <a id="14294" href="Data.List.Relation.Unary.Any.Properties.html#14294" class="Bound">xs</a> <a id="14297" href="Data.List.Relation.Unary.Any.Properties.html#14297" class="Bound">ys</a> <a id="14300" class="Symbol">→</a> <a id="14302" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="14306" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="14308" class="Symbol">(</a><a id="14309" href="Data.List.Relation.Unary.Any.Properties.html#14294" class="Bound">xs</a> <a id="14312" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="14315" href="Data.List.Relation.Unary.Any.Properties.html#14297" class="Bound">ys</a><a id="14317" class="Symbol">)</a> <a id="14319" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="14321" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="14325" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="14327" class="Symbol">(</a><a id="14328" href="Data.List.Relation.Unary.Any.Properties.html#14297" class="Bound">ys</a> <a id="14331" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="14334" href="Data.List.Relation.Unary.Any.Properties.html#14294" class="Bound">xs</a><a id="14336" class="Symbol">)</a>
<a id="14340" href="Data.List.Relation.Unary.Any.Properties.html#14284" class="Function">++↔++</a> <a id="14346" href="Data.List.Relation.Unary.Any.Properties.html#14346" class="Bound">xs</a> <a id="14349" href="Data.List.Relation.Unary.Any.Properties.html#14349" class="Bound">ys</a> <a id="14352" class="Symbol">=</a> <a id="14354" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="14362" class="Symbol">(</a><a id="14363" href="Data.List.Relation.Unary.Any.Properties.html#13402" class="Function">++-comm</a> <a id="14371" href="Data.List.Relation.Unary.Any.Properties.html#14346" class="Bound">xs</a> <a id="14374" href="Data.List.Relation.Unary.Any.Properties.html#14349" class="Bound">ys</a><a id="14376" class="Symbol">)</a> <a id="14378" class="Symbol">(</a><a id="14379" href="Data.List.Relation.Unary.Any.Properties.html#13402" class="Function">++-comm</a> <a id="14387" href="Data.List.Relation.Unary.Any.Properties.html#14349" class="Bound">ys</a> <a id="14390" href="Data.List.Relation.Unary.Any.Properties.html#14346" class="Bound">xs</a><a id="14392" class="Symbol">)</a>
<a id="14418" class="Symbol">(</a><a id="14419" href="Data.List.Relation.Unary.Any.Properties.html#13508" class="Function">++-comm∘++-comm</a> <a id="14435" href="Data.List.Relation.Unary.Any.Properties.html#14346" class="Bound">xs</a><a id="14437" class="Symbol">)</a> <a id="14439" class="Symbol">(</a><a id="14440" href="Data.List.Relation.Unary.Any.Properties.html#13508" class="Function">++-comm∘++-comm</a> <a id="14456" href="Data.List.Relation.Unary.Any.Properties.html#14349" class="Bound">ys</a><a id="14458" class="Symbol">)</a>
<a id="14463" href="Data.List.Relation.Unary.Any.Properties.html#14463" class="Function">++-insert</a> <a id="14473" class="Symbol">:</a> <a id="14475" class="Symbol">∀</a> <a id="14477" href="Data.List.Relation.Unary.Any.Properties.html#14477" class="Bound">xs</a> <a id="14480" class="Symbol">{</a><a id="14481" href="Data.List.Relation.Unary.Any.Properties.html#14481" class="Bound">ys</a><a id="14483" class="Symbol">}</a> <a id="14485" class="Symbol">→</a> <a id="14487" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="14489" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="14491" class="Symbol">→</a> <a id="14493" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="14497" href="Data.List.Relation.Unary.Any.Properties.html#12190" class="Bound">P</a> <a id="14499" class="Symbol">(</a><a id="14500" href="Data.List.Relation.Unary.Any.Properties.html#14477" class="Bound">xs</a> <a id="14503" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="14506" href="Data.List.Base.html#5025" class="Function Operator">[</a> <a id="14508" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="14510" href="Data.List.Base.html#5025" class="Function Operator">]</a> <a id="14512" href="Data.List.Base.html#1810" class="Function Operator">++</a> <a id="14515" href="Data.List.Relation.Unary.Any.Properties.html#14481" class="Bound">ys</a><a id="14517" class="Symbol">)</a>
<a id="14521" href="Data.List.Relation.Unary.Any.Properties.html#14463" class="Function">++-insert</a> <a id="14531" href="Data.List.Relation.Unary.Any.Properties.html#14531" class="Bound">xs</a> <a id="14534" href="Data.List.Relation.Unary.Any.Properties.html#14534" class="Bound">Px</a> <a id="14537" class="Symbol">=</a> <a id="14539" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="14544" href="Data.List.Relation.Unary.Any.Properties.html#14531" class="Bound">xs</a> <a id="14547" class="Symbol">(</a><a id="14548" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="14553" class="Symbol">(</a><a id="14554" href="Data.List.Relation.Unary.Any.Properties.html#10716" class="Function">singleton⁺</a> <a id="14565" href="Data.List.Relation.Unary.Any.Properties.html#14534" class="Bound">Px</a><a id="14567" class="Symbol">))</a>
<a id="14571" class="Comment">------------------------------------------------------------------------</a>
<a id="14644" class="Comment">-- concat</a>
<a id="14655" class="Keyword">module</a> <a id="14662" href="Data.List.Relation.Unary.Any.Properties.html#14662" class="Module">_</a> <a id="14664" class="Symbol">{</a><a id="14665" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a> <a id="14667" class="Symbol">:</a> <a id="14669" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="14671" class="Symbol">→</a> <a id="14673" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="14677" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a><a id="14678" class="Symbol">}</a> <a id="14680" class="Keyword">where</a>
<a id="14689" href="Data.List.Relation.Unary.Any.Properties.html#14689" class="Function">concat⁺</a> <a id="14697" class="Symbol">:</a> <a id="14699" class="Symbol">∀</a> <a id="14701" class="Symbol">{</a><a id="14702" href="Data.List.Relation.Unary.Any.Properties.html#14702" class="Bound">xss</a><a id="14705" class="Symbol">}</a> <a id="14707" class="Symbol">→</a> <a id="14709" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="14713" class="Symbol">(</a><a id="14714" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="14718" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a><a id="14719" class="Symbol">)</a> <a id="14721" href="Data.List.Relation.Unary.Any.Properties.html#14702" class="Bound">xss</a> <a id="14725" class="Symbol">→</a> <a id="14727" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="14731" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a> <a id="14733" class="Symbol">(</a><a id="14734" href="Data.List.Base.html#4394" class="Function">concat</a> <a id="14741" href="Data.List.Relation.Unary.Any.Properties.html#14702" class="Bound">xss</a><a id="14744" class="Symbol">)</a>
<a id="14748" href="Data.List.Relation.Unary.Any.Properties.html#14689" class="Function">concat⁺</a> <a id="14756" class="Symbol">(</a><a id="14757" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="14762" href="Data.List.Relation.Unary.Any.Properties.html#14762" class="Bound">p</a><a id="14763" class="Symbol">)</a> <a id="14775" class="Symbol">=</a> <a id="14777" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="14782" href="Data.List.Relation.Unary.Any.Properties.html#14762" class="Bound">p</a>
<a id="14786" href="Data.List.Relation.Unary.Any.Properties.html#14689" class="Function">concat⁺</a> <a id="14794" class="Symbol">(</a><a id="14795" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="14801" class="Symbol">{</a><a id="14802" class="Argument">x</a> <a id="14804" class="Symbol">=</a> <a id="14806" href="Data.List.Relation.Unary.Any.Properties.html#14806" class="Bound">xs</a><a id="14808" class="Symbol">}</a> <a id="14810" href="Data.List.Relation.Unary.Any.Properties.html#14810" class="Bound">p</a><a id="14811" class="Symbol">)</a> <a id="14813" class="Symbol">=</a> <a id="14815" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="14820" href="Data.List.Relation.Unary.Any.Properties.html#14806" class="Bound">xs</a> <a id="14823" class="Symbol">(</a><a id="14824" href="Data.List.Relation.Unary.Any.Properties.html#14689" class="Function">concat⁺</a> <a id="14832" href="Data.List.Relation.Unary.Any.Properties.html#14810" class="Bound">p</a><a id="14833" class="Symbol">)</a>
<a id="14838" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="14846" class="Symbol">:</a> <a id="14848" class="Symbol">∀</a> <a id="14850" href="Data.List.Relation.Unary.Any.Properties.html#14850" class="Bound">xss</a> <a id="14854" class="Symbol">→</a> <a id="14856" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="14860" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a> <a id="14862" class="Symbol">(</a><a id="14863" href="Data.List.Base.html#4394" class="Function">concat</a> <a id="14870" href="Data.List.Relation.Unary.Any.Properties.html#14850" class="Bound">xss</a><a id="14873" class="Symbol">)</a> <a id="14875" class="Symbol">→</a> <a id="14877" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="14881" class="Symbol">(</a><a id="14882" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="14886" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a><a id="14887" class="Symbol">)</a> <a id="14889" href="Data.List.Relation.Unary.Any.Properties.html#14850" class="Bound">xss</a>
<a id="14895" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="14903" class="Symbol">(</a><a id="14904" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="14913" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="14915" href="Data.List.Relation.Unary.Any.Properties.html#14915" class="Bound">xss</a><a id="14918" class="Symbol">)</a> <a id="14920" href="Data.List.Relation.Unary.Any.Properties.html#14920" class="Bound">p</a> <a id="14930" class="Symbol">=</a> <a id="14932" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="14938" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="14940" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="14948" href="Data.List.Relation.Unary.Any.Properties.html#14915" class="Bound">xss</a> <a id="14952" href="Data.List.Relation.Unary.Any.Properties.html#14920" class="Bound">p</a>
<a id="14956" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="14964" class="Symbol">((</a><a id="14966" href="Data.List.Relation.Unary.Any.Properties.html#14966" class="Bound">x</a> <a id="14968" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="14970" href="Data.List.Relation.Unary.Any.Properties.html#14970" class="Bound">xs</a><a id="14972" class="Symbol">)</a> <a id="14974" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="14976" href="Data.List.Relation.Unary.Any.Properties.html#14976" class="Bound">xss</a><a id="14979" class="Symbol">)</a> <a id="14981" class="Symbol">(</a><a id="14982" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="14988" href="Data.List.Relation.Unary.Any.Properties.html#14988" class="Bound">p</a><a id="14989" class="Symbol">)</a> <a id="14991" class="Symbol">=</a> <a id="14993" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="14998" class="Symbol">(</a><a id="14999" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="15004" href="Data.List.Relation.Unary.Any.Properties.html#14988" class="Bound">p</a><a id="15005" class="Symbol">)</a>
<a id="15009" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="15017" class="Symbol">((</a><a id="15019" href="Data.List.Relation.Unary.Any.Properties.html#15019" class="Bound">x</a> <a id="15021" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15023" href="Data.List.Relation.Unary.Any.Properties.html#15023" class="Bound">xs</a><a id="15025" class="Symbol">)</a> <a id="15027" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15029" href="Data.List.Relation.Unary.Any.Properties.html#15029" class="Bound">xss</a><a id="15032" class="Symbol">)</a> <a id="15034" class="Symbol">(</a><a id="15035" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="15041" href="Data.List.Relation.Unary.Any.Properties.html#15041" class="Bound">p</a><a id="15042" class="Symbol">)</a> <a id="15044" class="Keyword">with</a> <a id="15049" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="15057" class="Symbol">(</a><a id="15058" href="Data.List.Relation.Unary.Any.Properties.html#15023" class="Bound">xs</a> <a id="15061" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15063" href="Data.List.Relation.Unary.Any.Properties.html#15029" class="Bound">xss</a><a id="15066" class="Symbol">)</a> <a id="15068" href="Data.List.Relation.Unary.Any.Properties.html#15041" class="Bound">p</a>
<a id="15072" class="Symbol">...</a> <a id="15076" class="Symbol">|</a> <a id="15078" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="15084" href="Data.List.Relation.Unary.Any.Properties.html#15084" class="Bound">p′</a> <a id="15087" class="Symbol">=</a> <a id="15089" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="15094" class="Symbol">(</a><a id="15095" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="15101" href="Data.List.Relation.Unary.Any.Properties.html#15084" class="Bound">p′</a><a id="15103" class="Symbol">)</a>
<a id="15107" class="Symbol">...</a> <a id="15111" class="Symbol">|</a> <a id="15113" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="15119" href="Data.List.Relation.Unary.Any.Properties.html#15119" class="Bound">p′</a> <a id="15122" class="Symbol">=</a> <a id="15124" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="15130" href="Data.List.Relation.Unary.Any.Properties.html#15119" class="Bound">p′</a>
<a id="15136" href="Data.List.Relation.Unary.Any.Properties.html#15136" class="Function">concat⁻∘++⁺ˡ</a> <a id="15149" class="Symbol">:</a> <a id="15151" class="Symbol">∀</a> <a id="15153" class="Symbol">{</a><a id="15154" href="Data.List.Relation.Unary.Any.Properties.html#15154" class="Bound">xs</a><a id="15156" class="Symbol">}</a> <a id="15158" href="Data.List.Relation.Unary.Any.Properties.html#15158" class="Bound">xss</a> <a id="15162" class="Symbol">(</a><a id="15163" href="Data.List.Relation.Unary.Any.Properties.html#15163" class="Bound">p</a> <a id="15165" class="Symbol">:</a> <a id="15167" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="15171" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a> <a id="15173" href="Data.List.Relation.Unary.Any.Properties.html#15154" class="Bound">xs</a><a id="15175" class="Symbol">)</a> <a id="15177" class="Symbol">→</a>
<a id="15196" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="15204" class="Symbol">(</a><a id="15205" href="Data.List.Relation.Unary.Any.Properties.html#15154" class="Bound">xs</a> <a id="15208" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15210" href="Data.List.Relation.Unary.Any.Properties.html#15158" class="Bound">xss</a><a id="15213" class="Symbol">)</a> <a id="15215" class="Symbol">(</a><a id="15216" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="15221" href="Data.List.Relation.Unary.Any.Properties.html#15163" class="Bound">p</a><a id="15222" class="Symbol">)</a> <a id="15224" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="15226" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="15231" href="Data.List.Relation.Unary.Any.Properties.html#15163" class="Bound">p</a>
<a id="15235" href="Data.List.Relation.Unary.Any.Properties.html#15136" class="Function">concat⁻∘++⁺ˡ</a> <a id="15248" href="Data.List.Relation.Unary.Any.Properties.html#15248" class="Bound">xss</a> <a id="15252" class="Symbol">(</a><a id="15253" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="15259" href="Data.List.Relation.Unary.Any.Properties.html#15259" class="Bound">p</a><a id="15260" class="Symbol">)</a> <a id="15262" class="Symbol">=</a> <a id="15264" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="15271" href="Data.List.Relation.Unary.Any.Properties.html#15136" class="Function">concat⁻∘++⁺ˡ</a> <a id="15284" href="Data.List.Relation.Unary.Any.Properties.html#15284" class="Bound">xss</a> <a id="15288" class="Symbol">(</a><a id="15289" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="15295" href="Data.List.Relation.Unary.Any.Properties.html#15295" class="Bound">p</a><a id="15296" class="Symbol">)</a> <a id="15298" class="Keyword">rewrite</a> <a id="15306" href="Data.List.Relation.Unary.Any.Properties.html#15136" class="Function">concat⁻∘++⁺ˡ</a> <a id="15319" href="Data.List.Relation.Unary.Any.Properties.html#15284" class="Bound">xss</a> <a id="15323" href="Data.List.Relation.Unary.Any.Properties.html#15295" class="Bound">p</a> <a id="15325" class="Symbol">=</a> <a id="15327" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="15335" href="Data.List.Relation.Unary.Any.Properties.html#15335" class="Function">concat⁻∘++⁺ʳ</a> <a id="15348" class="Symbol">:</a> <a id="15350" class="Symbol">∀</a> <a id="15352" href="Data.List.Relation.Unary.Any.Properties.html#15352" class="Bound">xs</a> <a id="15355" href="Data.List.Relation.Unary.Any.Properties.html#15355" class="Bound">xss</a> <a id="15359" class="Symbol">(</a><a id="15360" href="Data.List.Relation.Unary.Any.Properties.html#15360" class="Bound">p</a> <a id="15362" class="Symbol">:</a> <a id="15364" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="15368" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a> <a id="15370" class="Symbol">(</a><a id="15371" href="Data.List.Base.html#4394" class="Function">concat</a> <a id="15378" href="Data.List.Relation.Unary.Any.Properties.html#15355" class="Bound">xss</a><a id="15381" class="Symbol">))</a> <a id="15384" class="Symbol">→</a>
<a id="15405" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="15413" class="Symbol">(</a><a id="15414" href="Data.List.Relation.Unary.Any.Properties.html#15352" class="Bound">xs</a> <a id="15417" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15419" href="Data.List.Relation.Unary.Any.Properties.html#15355" class="Bound">xss</a><a id="15422" class="Symbol">)</a> <a id="15424" class="Symbol">(</a><a id="15425" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="15430" href="Data.List.Relation.Unary.Any.Properties.html#15352" class="Bound">xs</a> <a id="15433" href="Data.List.Relation.Unary.Any.Properties.html#15360" class="Bound">p</a><a id="15434" class="Symbol">)</a> <a id="15436" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="15438" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="15444" class="Symbol">(</a><a id="15445" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="15453" href="Data.List.Relation.Unary.Any.Properties.html#15355" class="Bound">xss</a> <a id="15457" href="Data.List.Relation.Unary.Any.Properties.html#15360" class="Bound">p</a><a id="15458" class="Symbol">)</a>
<a id="15462" href="Data.List.Relation.Unary.Any.Properties.html#15335" class="Function">concat⁻∘++⁺ʳ</a> <a id="15475" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="15484" href="Data.List.Relation.Unary.Any.Properties.html#15484" class="Bound">xss</a> <a id="15488" href="Data.List.Relation.Unary.Any.Properties.html#15488" class="Bound">p</a> <a id="15490" class="Symbol">=</a> <a id="15492" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="15499" href="Data.List.Relation.Unary.Any.Properties.html#15335" class="Function">concat⁻∘++⁺ʳ</a> <a id="15512" class="Symbol">(</a><a id="15513" href="Data.List.Relation.Unary.Any.Properties.html#15513" class="Bound">x</a> <a id="15515" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15517" href="Data.List.Relation.Unary.Any.Properties.html#15517" class="Bound">xs</a><a id="15519" class="Symbol">)</a> <a id="15521" href="Data.List.Relation.Unary.Any.Properties.html#15521" class="Bound">xss</a> <a id="15525" href="Data.List.Relation.Unary.Any.Properties.html#15525" class="Bound">p</a> <a id="15527" class="Keyword">rewrite</a> <a id="15535" href="Data.List.Relation.Unary.Any.Properties.html#15335" class="Function">concat⁻∘++⁺ʳ</a> <a id="15548" href="Data.List.Relation.Unary.Any.Properties.html#15517" class="Bound">xs</a> <a id="15551" href="Data.List.Relation.Unary.Any.Properties.html#15521" class="Bound">xss</a> <a id="15555" href="Data.List.Relation.Unary.Any.Properties.html#15525" class="Bound">p</a> <a id="15557" class="Symbol">=</a> <a id="15559" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="15567" href="Data.List.Relation.Unary.Any.Properties.html#15567" class="Function">concat⁺∘concat⁻</a> <a id="15583" class="Symbol">:</a> <a id="15585" class="Symbol">∀</a> <a id="15587" href="Data.List.Relation.Unary.Any.Properties.html#15587" class="Bound">xss</a> <a id="15591" class="Symbol">(</a><a id="15592" href="Data.List.Relation.Unary.Any.Properties.html#15592" class="Bound">p</a> <a id="15594" class="Symbol">:</a> <a id="15596" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="15600" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a> <a id="15602" class="Symbol">(</a><a id="15603" href="Data.List.Base.html#4394" class="Function">concat</a> <a id="15610" href="Data.List.Relation.Unary.Any.Properties.html#15587" class="Bound">xss</a><a id="15613" class="Symbol">))</a> <a id="15616" class="Symbol">→</a>
<a id="15640" href="Data.List.Relation.Unary.Any.Properties.html#14689" class="Function">concat⁺</a> <a id="15648" class="Symbol">(</a><a id="15649" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="15657" href="Data.List.Relation.Unary.Any.Properties.html#15587" class="Bound">xss</a> <a id="15661" href="Data.List.Relation.Unary.Any.Properties.html#15592" class="Bound">p</a><a id="15662" class="Symbol">)</a> <a id="15664" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="15666" href="Data.List.Relation.Unary.Any.Properties.html#15592" class="Bound">p</a>
<a id="15670" href="Data.List.Relation.Unary.Any.Properties.html#15567" class="Function">concat⁺∘concat⁻</a> <a id="15686" class="Symbol">(</a><a id="15687" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="15696" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15698" href="Data.List.Relation.Unary.Any.Properties.html#15698" class="Bound">xss</a><a id="15701" class="Symbol">)</a> <a id="15703" href="Data.List.Relation.Unary.Any.Properties.html#15703" class="Bound">p</a> <a id="15713" class="Symbol">=</a> <a id="15715" href="Data.List.Relation.Unary.Any.Properties.html#15567" class="Function">concat⁺∘concat⁻</a> <a id="15731" href="Data.List.Relation.Unary.Any.Properties.html#15698" class="Bound">xss</a> <a id="15735" href="Data.List.Relation.Unary.Any.Properties.html#15703" class="Bound">p</a>
<a id="15739" href="Data.List.Relation.Unary.Any.Properties.html#15567" class="Function">concat⁺∘concat⁻</a> <a id="15755" class="Symbol">((</a><a id="15757" href="Data.List.Relation.Unary.Any.Properties.html#15757" class="Bound">x</a> <a id="15759" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15761" href="Data.List.Relation.Unary.Any.Properties.html#15761" class="Bound">xs</a><a id="15763" class="Symbol">)</a> <a id="15765" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15767" href="Data.List.Relation.Unary.Any.Properties.html#15767" class="Bound">xss</a><a id="15770" class="Symbol">)</a> <a id="15772" class="Symbol">(</a><a id="15773" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="15778" href="Data.List.Relation.Unary.Any.Properties.html#15778" class="Bound">p</a><a id="15779" class="Symbol">)</a> <a id="15782" class="Symbol">=</a> <a id="15784" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="15791" href="Data.List.Relation.Unary.Any.Properties.html#15567" class="Function">concat⁺∘concat⁻</a> <a id="15807" class="Symbol">((</a><a id="15809" href="Data.List.Relation.Unary.Any.Properties.html#15809" class="Bound">x</a> <a id="15811" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15813" href="Data.List.Relation.Unary.Any.Properties.html#15813" class="Bound">xs</a><a id="15815" class="Symbol">)</a> <a id="15817" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15819" href="Data.List.Relation.Unary.Any.Properties.html#15819" class="Bound">xss</a><a id="15822" class="Symbol">)</a> <a id="15824" class="Symbol">(</a><a id="15825" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="15831" href="Data.List.Relation.Unary.Any.Properties.html#15831" class="Bound">p</a><a id="15832" class="Symbol">)</a>
<a id="15838" class="Keyword">with</a> <a id="15843" href="Data.List.Relation.Unary.Any.Properties.html#15831" class="Bound">p</a> <a id="15845" class="Symbol">|</a> <a id="15847" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="15855" class="Symbol">(</a><a id="15856" href="Data.List.Relation.Unary.Any.Properties.html#15813" class="Bound">xs</a> <a id="15859" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15861" href="Data.List.Relation.Unary.Any.Properties.html#15819" class="Bound">xss</a><a id="15864" class="Symbol">)</a> <a id="15866" href="Data.List.Relation.Unary.Any.Properties.html#15831" class="Bound">p</a> <a id="15868" class="Symbol">|</a> <a id="15870" href="Data.List.Relation.Unary.Any.Properties.html#15567" class="Function">concat⁺∘concat⁻</a> <a id="15886" class="Symbol">(</a><a id="15887" href="Data.List.Relation.Unary.Any.Properties.html#15813" class="Bound">xs</a> <a id="15890" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="15892" href="Data.List.Relation.Unary.Any.Properties.html#15819" class="Bound">xss</a><a id="15895" class="Symbol">)</a> <a id="15897" href="Data.List.Relation.Unary.Any.Properties.html#15831" class="Bound">p</a>
<a id="15901" class="Symbol">...</a> <a id="15905" class="Symbol">|</a> <a id="15907" class="DottedPattern Symbol">.(</a><a id="15909" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="DottedPattern Function">++⁺ˡ</a> <a id="15914" href="Data.List.Relation.Unary.Any.Properties.html#15939" class="DottedPattern Bound">p′</a><a id="15916" class="DottedPattern Symbol">)</a> <a id="15931" class="Symbol">|</a> <a id="15933" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="15939" href="Data.List.Relation.Unary.Any.Properties.html#15939" class="Bound">p′</a> <a id="15942" class="Symbol">|</a> <a id="15944" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a> <a id="15949" class="Symbol">=</a> <a id="15951" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="15958" class="Symbol">...</a> <a id="15962" class="Symbol">|</a> <a id="15964" class="DottedPattern Symbol">.(</a><a id="15966" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="DottedPattern Function">++⁺ʳ</a> <a id="15971" class="DottedPattern Bound">xs</a> <a id="15974" class="DottedPattern Symbol">(</a><a id="15975" href="Data.List.Relation.Unary.Any.Properties.html#14689" class="DottedPattern Function">concat⁺</a> <a id="15983" href="Data.List.Relation.Unary.Any.Properties.html#15996" class="DottedPattern Bound">p′</a><a id="15985" class="DottedPattern Symbol">))</a> <a id="15988" class="Symbol">|</a> <a id="15990" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="15996" href="Data.List.Relation.Unary.Any.Properties.html#15996" class="Bound">p′</a> <a id="15999" class="Symbol">|</a> <a id="16001" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a> <a id="16006" class="Symbol">=</a> <a id="16008" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="16016" href="Data.List.Relation.Unary.Any.Properties.html#16016" class="Function">concat⁻∘concat⁺</a> <a id="16032" class="Symbol">:</a> <a id="16034" class="Symbol">∀</a> <a id="16036" class="Symbol">{</a><a id="16037" href="Data.List.Relation.Unary.Any.Properties.html#16037" class="Bound">xss</a><a id="16040" class="Symbol">}</a> <a id="16042" class="Symbol">(</a><a id="16043" href="Data.List.Relation.Unary.Any.Properties.html#16043" class="Bound">p</a> <a id="16045" class="Symbol">:</a> <a id="16047" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="16051" class="Symbol">(</a><a id="16052" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="16056" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a><a id="16057" class="Symbol">)</a> <a id="16059" href="Data.List.Relation.Unary.Any.Properties.html#16037" class="Bound">xss</a><a id="16062" class="Symbol">)</a> <a id="16064" class="Symbol">→</a> <a id="16066" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="16074" href="Data.List.Relation.Unary.Any.Properties.html#16037" class="Bound">xss</a> <a id="16078" class="Symbol">(</a><a id="16079" href="Data.List.Relation.Unary.Any.Properties.html#14689" class="Function">concat⁺</a> <a id="16087" href="Data.List.Relation.Unary.Any.Properties.html#16043" class="Bound">p</a><a id="16088" class="Symbol">)</a> <a id="16090" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="16092" href="Data.List.Relation.Unary.Any.Properties.html#16043" class="Bound">p</a>
<a id="16096" href="Data.List.Relation.Unary.Any.Properties.html#16016" class="Function">concat⁻∘concat⁺</a> <a id="16112" class="Symbol">(</a><a id="16113" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="16139" href="Data.List.Relation.Unary.Any.Properties.html#16139" class="Bound">p</a><a id="16140" class="Symbol">)</a> <a id="16142" class="Symbol">=</a> <a id="16144" href="Data.List.Relation.Unary.Any.Properties.html#15136" class="Function">concat⁻∘++⁺ˡ</a> <a id="16157" class="Symbol">_</a> <a id="16159" href="Data.List.Relation.Unary.Any.Properties.html#16139" class="Bound">p</a>
<a id="16163" href="Data.List.Relation.Unary.Any.Properties.html#16016" class="Function">concat⁻∘concat⁺</a> <a id="16179" class="Symbol">(</a><a id="16180" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="16186" class="Symbol">{</a><a id="16187" class="Argument">x</a> <a id="16189" class="Symbol">=</a> <a id="16191" href="Data.List.Relation.Unary.Any.Properties.html#16191" class="Bound">xs</a><a id="16193" class="Symbol">}</a> <a id="16195" class="Symbol">{</a><a id="16196" class="Argument">xs</a> <a id="16199" class="Symbol">=</a> <a id="16201" href="Data.List.Relation.Unary.Any.Properties.html#16201" class="Bound">xss</a><a id="16204" class="Symbol">}</a> <a id="16206" href="Data.List.Relation.Unary.Any.Properties.html#16206" class="Bound">p</a><a id="16207" class="Symbol">)</a>
<a id="16213" class="Keyword">rewrite</a> <a id="16221" href="Data.List.Relation.Unary.Any.Properties.html#15335" class="Function">concat⁻∘++⁺ʳ</a> <a id="16234" href="Data.List.Relation.Unary.Any.Properties.html#16191" class="Bound">xs</a> <a id="16237" href="Data.List.Relation.Unary.Any.Properties.html#16201" class="Bound">xss</a> <a id="16241" class="Symbol">(</a><a id="16242" href="Data.List.Relation.Unary.Any.Properties.html#14689" class="Function">concat⁺</a> <a id="16250" href="Data.List.Relation.Unary.Any.Properties.html#16206" class="Bound">p</a><a id="16251" class="Symbol">)</a> <a id="16253" class="Symbol">=</a>
<a id="16261" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="16268" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="16274" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="16276" href="Data.List.Relation.Unary.Any.Properties.html#16016" class="Function">concat⁻∘concat⁺</a> <a id="16292" href="Data.List.Relation.Unary.Any.Properties.html#16206" class="Bound">p</a>
<a id="16297" href="Data.List.Relation.Unary.Any.Properties.html#16297" class="Function">concat↔</a> <a id="16305" class="Symbol">:</a> <a id="16307" class="Symbol">∀</a> <a id="16309" class="Symbol">{</a><a id="16310" href="Data.List.Relation.Unary.Any.Properties.html#16310" class="Bound">xss</a><a id="16313" class="Symbol">}</a> <a id="16315" class="Symbol">→</a> <a id="16317" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="16321" class="Symbol">(</a><a id="16322" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="16326" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a><a id="16327" class="Symbol">)</a> <a id="16329" href="Data.List.Relation.Unary.Any.Properties.html#16310" class="Bound">xss</a> <a id="16333" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="16335" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="16339" href="Data.List.Relation.Unary.Any.Properties.html#14665" class="Bound">P</a> <a id="16341" class="Symbol">(</a><a id="16342" href="Data.List.Base.html#4394" class="Function">concat</a> <a id="16349" href="Data.List.Relation.Unary.Any.Properties.html#16310" class="Bound">xss</a><a id="16352" class="Symbol">)</a>
<a id="16356" href="Data.List.Relation.Unary.Any.Properties.html#16297" class="Function">concat↔</a> <a id="16364" class="Symbol">{</a><a id="16365" href="Data.List.Relation.Unary.Any.Properties.html#16365" class="Bound">xss</a><a id="16368" class="Symbol">}</a> <a id="16370" class="Symbol">=</a> <a id="16372" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="16380" href="Data.List.Relation.Unary.Any.Properties.html#14689" class="Function">concat⁺</a> <a id="16388" class="Symbol">(</a><a id="16389" href="Data.List.Relation.Unary.Any.Properties.html#14838" class="Function">concat⁻</a> <a id="16397" href="Data.List.Relation.Unary.Any.Properties.html#16365" class="Bound">xss</a><a id="16400" class="Symbol">)</a> <a id="16402" href="Data.List.Relation.Unary.Any.Properties.html#16016" class="Function">concat⁻∘concat⁺</a> <a id="16418" class="Symbol">(</a><a id="16419" href="Data.List.Relation.Unary.Any.Properties.html#15567" class="Function">concat⁺∘concat⁻</a> <a id="16435" href="Data.List.Relation.Unary.Any.Properties.html#16365" class="Bound">xss</a><a id="16438" class="Symbol">)</a>
<a id="16441" class="Comment">------------------------------------------------------------------------</a>
<a id="16514" class="Comment">-- cartesianProductWith</a>
<a id="16539" class="Keyword">module</a> <a id="16546" href="Data.List.Relation.Unary.Any.Properties.html#16546" class="Module">_</a> <a id="16548" class="Symbol">(</a><a id="16549" href="Data.List.Relation.Unary.Any.Properties.html#16549" class="Bound">f</a> <a id="16551" class="Symbol">:</a> <a id="16553" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="16555" class="Symbol">→</a> <a id="16557" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="16559" class="Symbol">→</a> <a id="16561" href="Data.List.Relation.Unary.Any.Properties.html#2426" class="Generalizable">C</a><a id="16562" class="Symbol">)</a> <a id="16564" class="Keyword">where</a>
<a id="16573" href="Data.List.Relation.Unary.Any.Properties.html#16573" class="Function">cartesianProductWith⁺</a> <a id="16595" class="Symbol">:</a> <a id="16597" class="Symbol">(∀</a> <a id="16600" class="Symbol">{</a><a id="16601" href="Data.List.Relation.Unary.Any.Properties.html#16601" class="Bound">x</a> <a id="16603" href="Data.List.Relation.Unary.Any.Properties.html#16603" class="Bound">y</a><a id="16604" class="Symbol">}</a> <a id="16606" class="Symbol">→</a> <a id="16608" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="16610" href="Data.List.Relation.Unary.Any.Properties.html#16601" class="Bound">x</a> <a id="16612" class="Symbol">→</a> <a id="16614" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="16616" href="Data.List.Relation.Unary.Any.Properties.html#16603" class="Bound">y</a> <a id="16618" class="Symbol">→</a> <a id="16620" href="Data.List.Relation.Unary.Any.Properties.html#2444" class="Generalizable">R</a> <a id="16622" class="Symbol">(</a><a id="16623" href="Data.List.Relation.Unary.Any.Properties.html#16549" class="Bound">f</a> <a id="16625" href="Data.List.Relation.Unary.Any.Properties.html#16601" class="Bound">x</a> <a id="16627" href="Data.List.Relation.Unary.Any.Properties.html#16603" class="Bound">y</a><a id="16628" class="Symbol">))</a> <a id="16631" class="Symbol">→</a>
<a id="16659" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="16663" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="16665" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="16668" class="Symbol">→</a> <a id="16670" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="16674" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="16676" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a> <a id="16679" class="Symbol">→</a>
<a id="16707" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="16711" href="Data.List.Relation.Unary.Any.Properties.html#2444" class="Generalizable">R</a> <a id="16713" class="Symbol">(</a><a id="16714" href="Data.List.Base.html#2208" class="Function">cartesianProductWith</a> <a id="16735" href="Data.List.Relation.Unary.Any.Properties.html#16549" class="Bound">f</a> <a id="16737" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="16740" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="16742" class="Symbol">)</a>
<a id="16746" href="Data.List.Relation.Unary.Any.Properties.html#16573" class="Function">cartesianProductWith⁺</a> <a id="16768" href="Data.List.Relation.Unary.Any.Properties.html#16768" class="Bound">pres</a> <a id="16773" class="Symbol">(</a><a id="16774" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="16780" href="Data.List.Relation.Unary.Any.Properties.html#16780" class="Bound">px</a><a id="16782" class="Symbol">)</a> <a id="16785" href="Data.List.Relation.Unary.Any.Properties.html#16785" class="Bound">qys</a> <a id="16789" class="Symbol">=</a> <a id="16791" href="Data.List.Relation.Unary.Any.Properties.html#12214" class="Function">++⁺ˡ</a> <a id="16796" class="Symbol">(</a><a id="16797" href="Data.List.Relation.Unary.Any.Properties.html#10941" class="Function">map⁺</a> <a id="16802" class="Symbol">(</a><a id="16803" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="16811" class="Symbol">(</a><a id="16812" href="Data.List.Relation.Unary.Any.Properties.html#16768" class="Bound">pres</a> <a id="16817" href="Data.List.Relation.Unary.Any.Properties.html#16780" class="Bound">px</a><a id="16819" class="Symbol">)</a> <a id="16821" href="Data.List.Relation.Unary.Any.Properties.html#16785" class="Bound">qys</a><a id="16824" class="Symbol">))</a>
<a id="16829" href="Data.List.Relation.Unary.Any.Properties.html#16573" class="Function">cartesianProductWith⁺</a> <a id="16851" href="Data.List.Relation.Unary.Any.Properties.html#16851" class="Bound">pres</a> <a id="16856" class="Symbol">(</a><a id="16857" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="16863" href="Data.List.Relation.Unary.Any.Properties.html#16863" class="Bound">qxs</a><a id="16866" class="Symbol">)</a> <a id="16868" href="Data.List.Relation.Unary.Any.Properties.html#16868" class="Bound">qys</a> <a id="16872" class="Symbol">=</a> <a id="16874" href="Data.List.Relation.Unary.Any.Properties.html#12312" class="Function">++⁺ʳ</a> <a id="16879" class="Symbol">_</a> <a id="16881" class="Symbol">(</a><a id="16882" href="Data.List.Relation.Unary.Any.Properties.html#16573" class="Function">cartesianProductWith⁺</a> <a id="16904" href="Data.List.Relation.Unary.Any.Properties.html#16851" class="Bound">pres</a> <a id="16909" href="Data.List.Relation.Unary.Any.Properties.html#16863" class="Bound">qxs</a> <a id="16913" href="Data.List.Relation.Unary.Any.Properties.html#16868" class="Bound">qys</a><a id="16916" class="Symbol">)</a>
<a id="16921" href="Data.List.Relation.Unary.Any.Properties.html#16921" class="Function">cartesianProductWith⁻</a> <a id="16943" class="Symbol">:</a> <a id="16945" class="Symbol">(∀</a> <a id="16948" class="Symbol">{</a><a id="16949" href="Data.List.Relation.Unary.Any.Properties.html#16949" class="Bound">x</a> <a id="16951" href="Data.List.Relation.Unary.Any.Properties.html#16951" class="Bound">y</a><a id="16952" class="Symbol">}</a> <a id="16954" class="Symbol">→</a> <a id="16956" href="Data.List.Relation.Unary.Any.Properties.html#2444" class="Generalizable">R</a> <a id="16958" class="Symbol">(</a><a id="16959" href="Data.List.Relation.Unary.Any.Properties.html#16549" class="Bound">f</a> <a id="16961" href="Data.List.Relation.Unary.Any.Properties.html#16949" class="Bound">x</a> <a id="16963" href="Data.List.Relation.Unary.Any.Properties.html#16951" class="Bound">y</a><a id="16964" class="Symbol">)</a> <a id="16966" class="Symbol">→</a> <a id="16968" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="16970" href="Data.List.Relation.Unary.Any.Properties.html#16949" class="Bound">x</a> <a id="16972" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="16974" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="16976" href="Data.List.Relation.Unary.Any.Properties.html#16951" class="Bound">y</a><a id="16977" class="Symbol">)</a> <a id="16979" class="Symbol">→</a> <a id="16981" class="Symbol">∀</a> <a id="16983" href="Data.List.Relation.Unary.Any.Properties.html#16983" class="Bound">xs</a> <a id="16986" href="Data.List.Relation.Unary.Any.Properties.html#16986" class="Bound">ys</a> <a id="16989" class="Symbol">→</a>
<a id="17017" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="17021" href="Data.List.Relation.Unary.Any.Properties.html#2444" class="Generalizable">R</a> <a id="17023" class="Symbol">(</a><a id="17024" href="Data.List.Base.html#2208" class="Function">cartesianProductWith</a> <a id="17045" href="Data.List.Relation.Unary.Any.Properties.html#16549" class="Bound">f</a> <a id="17047" href="Data.List.Relation.Unary.Any.Properties.html#16983" class="Bound">xs</a> <a id="17050" href="Data.List.Relation.Unary.Any.Properties.html#16986" class="Bound">ys</a><a id="17052" class="Symbol">)</a> <a id="17054" class="Symbol">→</a>
<a id="17082" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="17086" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="17088" href="Data.List.Relation.Unary.Any.Properties.html#16983" class="Bound">xs</a> <a id="17091" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="17093" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="17097" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="17099" href="Data.List.Relation.Unary.Any.Properties.html#16986" class="Bound">ys</a>
<a id="17104" href="Data.List.Relation.Unary.Any.Properties.html#16921" class="Function">cartesianProductWith⁻</a> <a id="17126" href="Data.List.Relation.Unary.Any.Properties.html#17126" class="Bound">resp</a> <a id="17131" class="Symbol">(</a><a id="17132" href="Data.List.Relation.Unary.Any.Properties.html#17132" class="Bound">x</a> <a id="17134" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="17136" href="Data.List.Relation.Unary.Any.Properties.html#17136" class="Bound">xs</a><a id="17138" class="Symbol">)</a> <a id="17140" href="Data.List.Relation.Unary.Any.Properties.html#17140" class="Bound">ys</a> <a id="17143" href="Data.List.Relation.Unary.Any.Properties.html#17143" class="Bound">Rxsys</a> <a id="17149" class="Keyword">with</a> <a id="17154" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="17158" class="Symbol">(</a><a id="17159" href="Data.List.Base.html#1544" class="Function">map</a> <a id="17163" class="Symbol">(</a><a id="17164" href="Data.List.Relation.Unary.Any.Properties.html#16549" class="Bound">f</a> <a id="17166" href="Data.List.Relation.Unary.Any.Properties.html#17132" class="Bound">x</a><a id="17167" class="Symbol">)</a> <a id="17169" href="Data.List.Relation.Unary.Any.Properties.html#17140" class="Bound">ys</a><a id="17171" class="Symbol">)</a> <a id="17173" href="Data.List.Relation.Unary.Any.Properties.html#17143" class="Bound">Rxsys</a>
<a id="17181" href="Data.List.Relation.Unary.Any.Properties.html#16921" class="Function">cartesianProductWith⁻</a> <a id="17203" href="Data.List.Relation.Unary.Any.Properties.html#17203" class="Bound">resp</a> <a id="17208" class="Symbol">(</a><a id="17209" href="Data.List.Relation.Unary.Any.Properties.html#17209" class="Bound">x</a> <a id="17211" class="InductiveConstructor Operator">∷</a> <a id="17213" href="Data.List.Relation.Unary.Any.Properties.html#17213" class="Bound">xs</a><a id="17215" class="Symbol">)</a> <a id="17217" href="Data.List.Relation.Unary.Any.Properties.html#17217" class="Bound">ys</a> <a id="17220" href="Data.List.Relation.Unary.Any.Properties.html#17220" class="Bound">Rxsys</a> <a id="17226" class="Symbol">|</a> <a id="17228" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="17233" href="Data.List.Relation.Unary.Any.Properties.html#17233" class="Bound">Rfxys</a> <a id="17239" class="Keyword">with</a> <a id="17244" href="Data.List.Relation.Unary.Any.Properties.html#11050" class="Function">map⁻</a> <a id="17249" href="Data.List.Relation.Unary.Any.Properties.html#17233" class="Bound">Rfxys</a>
<a id="17257" class="Symbol">...</a> <a id="17261" class="Symbol">|</a> <a id="17263" href="Data.List.Relation.Unary.Any.Properties.html#17263" class="Bound">Rxys</a> <a id="17268" class="Symbol">=</a> <a id="17270" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="17275" class="Symbol">(</a><a id="17276" href="Agda.Builtin.Sigma.html#252" class="Field">proj₁</a> <a id="17282" class="Symbol">(</a><a id="17283" class="Bound">resp</a> <a id="17288" class="Symbol">(</a><a id="17289" href="Agda.Builtin.Sigma.html#264" class="Field">proj₂</a> <a id="17295" class="Symbol">(</a><a id="17296" href="Data.List.Relation.Unary.Any.html#2251" class="Function">Any.satisfied</a> <a id="17310" href="Data.List.Relation.Unary.Any.Properties.html#17263" class="Bound">Rxys</a><a id="17314" class="Symbol">))))</a> <a id="17319" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="17321" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="17329" class="Symbol">(</a><a id="17330" href="Agda.Builtin.Sigma.html#264" class="Field">proj₂</a> <a id="17336" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="17338" class="Bound">resp</a><a id="17342" class="Symbol">)</a> <a id="17344" href="Data.List.Relation.Unary.Any.Properties.html#17263" class="Bound">Rxys</a>
<a id="17351" href="Data.List.Relation.Unary.Any.Properties.html#16921" class="Function">cartesianProductWith⁻</a> <a id="17373" href="Data.List.Relation.Unary.Any.Properties.html#17373" class="Bound">resp</a> <a id="17378" class="Symbol">(</a><a id="17379" href="Data.List.Relation.Unary.Any.Properties.html#17379" class="Bound">x</a> <a id="17381" class="InductiveConstructor Operator">∷</a> <a id="17383" href="Data.List.Relation.Unary.Any.Properties.html#17383" class="Bound">xs</a><a id="17385" class="Symbol">)</a> <a id="17387" href="Data.List.Relation.Unary.Any.Properties.html#17387" class="Bound">ys</a> <a id="17390" href="Data.List.Relation.Unary.Any.Properties.html#17390" class="Bound">Rxsys</a> <a id="17396" class="Symbol">|</a> <a id="17398" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="17403" href="Data.List.Relation.Unary.Any.Properties.html#17403" class="Bound">Rc</a> <a id="17406" class="Keyword">with</a> <a id="17411" href="Data.List.Relation.Unary.Any.Properties.html#16921" class="Function">cartesianProductWith⁻</a> <a id="17433" href="Data.List.Relation.Unary.Any.Properties.html#17373" class="Bound">resp</a> <a id="17438" href="Data.List.Relation.Unary.Any.Properties.html#17383" class="Bound">xs</a> <a id="17441" href="Data.List.Relation.Unary.Any.Properties.html#17387" class="Bound">ys</a> <a id="17444" href="Data.List.Relation.Unary.Any.Properties.html#17403" class="Bound">Rc</a>
<a id="17449" class="Symbol">...</a> <a id="17453" class="Symbol">|</a> <a id="17455" href="Data.List.Relation.Unary.Any.Properties.html#17455" class="Bound">pxs</a> <a id="17459" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="17461" href="Data.List.Relation.Unary.Any.Properties.html#17461" class="Bound">qys</a> <a id="17465" class="Symbol">=</a> <a id="17467" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="17473" href="Data.List.Relation.Unary.Any.Properties.html#17455" class="Bound">pxs</a> <a id="17477" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="17479" href="Data.List.Relation.Unary.Any.Properties.html#17461" class="Bound">qys</a>
<a id="17484" class="Comment">------------------------------------------------------------------------</a>
<a id="17557" class="Comment">-- cartesianProduct</a>
<a id="cartesianProduct⁺"></a><a id="17578" href="Data.List.Relation.Unary.Any.Properties.html#17578" class="Function">cartesianProduct⁺</a> <a id="17596" class="Symbol">:</a> <a id="17598" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="17602" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="17604" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="17607" class="Symbol">→</a> <a id="17609" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="17613" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="17615" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a> <a id="17618" class="Symbol">→</a>
<a id="17640" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="17644" class="Symbol">(</a><a id="17645" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="17647" href="Relation.Unary.html#5466" class="Function Operator">⟨×⟩</a> <a id="17651" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a><a id="17652" class="Symbol">)</a> <a id="17654" class="Symbol">(</a><a id="17655" href="Data.List.Base.html#2393" class="Function">cartesianProduct</a> <a id="17672" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="17675" href="Data.List.Relation.Unary.Any.Properties.html#2476" class="Generalizable">ys</a><a id="17677" class="Symbol">)</a>
<a id="17679" href="Data.List.Relation.Unary.Any.Properties.html#17578" class="Function">cartesianProduct⁺</a> <a id="17697" class="Symbol">=</a> <a id="17699" href="Data.List.Relation.Unary.Any.Properties.html#16573" class="Function">cartesianProductWith⁺</a> <a id="17721" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">_,_</a> <a id="17725" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">_,_</a>
<a id="cartesianProduct⁻"></a><a id="17730" href="Data.List.Relation.Unary.Any.Properties.html#17730" class="Function">cartesianProduct⁻</a> <a id="17748" class="Symbol">:</a> <a id="17750" class="Symbol">∀</a> <a id="17752" href="Data.List.Relation.Unary.Any.Properties.html#17752" class="Bound">xs</a> <a id="17755" href="Data.List.Relation.Unary.Any.Properties.html#17755" class="Bound">ys</a> <a id="17758" class="Symbol">→</a> <a id="17760" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="17764" class="Symbol">(</a><a id="17765" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="17767" href="Relation.Unary.html#5466" class="Function Operator">⟨×⟩</a> <a id="17771" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a><a id="17772" class="Symbol">)</a> <a id="17774" class="Symbol">(</a><a id="17775" href="Data.List.Base.html#2393" class="Function">cartesianProduct</a> <a id="17792" href="Data.List.Relation.Unary.Any.Properties.html#17752" class="Bound">xs</a> <a id="17795" href="Data.List.Relation.Unary.Any.Properties.html#17755" class="Bound">ys</a><a id="17797" class="Symbol">)</a> <a id="17799" class="Symbol">→</a>
<a id="17821" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="17825" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="17827" href="Data.List.Relation.Unary.Any.Properties.html#17752" class="Bound">xs</a> <a id="17830" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="17832" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="17836" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a> <a id="17838" href="Data.List.Relation.Unary.Any.Properties.html#17755" class="Bound">ys</a>
<a id="17841" href="Data.List.Relation.Unary.Any.Properties.html#17730" class="Function">cartesianProduct⁻</a> <a id="17859" class="Symbol">=</a> <a id="17861" href="Data.List.Relation.Unary.Any.Properties.html#16921" class="Function">cartesianProductWith⁻</a> <a id="17883" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">_,_</a> <a id="17887" href="Function.Base.html#615" class="Function">id</a>
<a id="17891" class="Comment">------------------------------------------------------------------------</a>
<a id="17964" class="Comment">-- applyUpTo</a>
<a id="applyUpTo⁺"></a><a id="17978" href="Data.List.Relation.Unary.Any.Properties.html#17978" class="Function">applyUpTo⁺</a> <a id="17989" class="Symbol">:</a> <a id="17991" class="Symbol">∀</a> <a id="17993" href="Data.List.Relation.Unary.Any.Properties.html#17993" class="Bound">f</a> <a id="17995" class="Symbol">{</a><a id="17996" href="Data.List.Relation.Unary.Any.Properties.html#17996" class="Bound">i</a> <a id="17998" href="Data.List.Relation.Unary.Any.Properties.html#17998" class="Bound">n</a><a id="17999" class="Symbol">}</a> <a id="18001" class="Symbol">→</a> <a id="18003" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="18005" class="Symbol">(</a><a id="18006" href="Data.List.Relation.Unary.Any.Properties.html#17993" class="Bound">f</a> <a id="18008" href="Data.List.Relation.Unary.Any.Properties.html#17996" class="Bound">i</a><a id="18009" class="Symbol">)</a> <a id="18011" class="Symbol">→</a> <a id="18013" href="Data.List.Relation.Unary.Any.Properties.html#17996" class="Bound">i</a> <a id="18015" href="Data.Nat.Base.html#1645" class="Function Operator"><</a> <a id="18017" href="Data.List.Relation.Unary.Any.Properties.html#17998" class="Bound">n</a> <a id="18019" class="Symbol">→</a> <a id="18021" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="18025" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="18027" class="Symbol">(</a><a id="18028" href="Data.List.Base.html#5753" class="Function">applyUpTo</a> <a id="18038" href="Data.List.Relation.Unary.Any.Properties.html#17993" class="Bound">f</a> <a id="18040" href="Data.List.Relation.Unary.Any.Properties.html#17998" class="Bound">n</a><a id="18041" class="Symbol">)</a>
<a id="18043" href="Data.List.Relation.Unary.Any.Properties.html#17978" class="Function">applyUpTo⁺</a> <a id="18054" class="Symbol">_</a> <a id="18056" href="Data.List.Relation.Unary.Any.Properties.html#18056" class="Bound">p</a> <a id="18058" class="Symbol">(</a><a id="18059" href="Data.Nat.Base.html#1600" class="InductiveConstructor">s≤s</a> <a id="18063" href="Data.Nat.Base.html#1558" class="InductiveConstructor">z≤n</a><a id="18066" class="Symbol">)</a> <a id="18074" class="Symbol">=</a> <a id="18076" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="18081" href="Data.List.Relation.Unary.Any.Properties.html#18056" class="Bound">p</a>
<a id="18083" href="Data.List.Relation.Unary.Any.Properties.html#17978" class="Function">applyUpTo⁺</a> <a id="18094" href="Data.List.Relation.Unary.Any.Properties.html#18094" class="Bound">f</a> <a id="18096" href="Data.List.Relation.Unary.Any.Properties.html#18096" class="Bound">p</a> <a id="18098" class="Symbol">(</a><a id="18099" href="Data.Nat.Base.html#1600" class="InductiveConstructor">s≤s</a> <a id="18103" class="Symbol">(</a><a id="18104" href="Data.Nat.Base.html#1600" class="InductiveConstructor">s≤s</a> <a id="18108" href="Data.List.Relation.Unary.Any.Properties.html#18108" class="Bound">i<n</a><a id="18111" class="Symbol">))</a> <a id="18114" class="Symbol">=</a>
<a id="18118" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="18124" class="Symbol">(</a><a id="18125" href="Data.List.Relation.Unary.Any.Properties.html#17978" class="Function">applyUpTo⁺</a> <a id="18136" class="Symbol">(</a><a id="18137" href="Data.List.Relation.Unary.Any.Properties.html#18094" class="Bound">f</a> <a id="18139" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="18141" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a><a id="18144" class="Symbol">)</a> <a id="18146" href="Data.List.Relation.Unary.Any.Properties.html#18096" class="Bound">p</a> <a id="18148" class="Symbol">(</a><a id="18149" href="Data.Nat.Base.html#1600" class="InductiveConstructor">s≤s</a> <a id="18153" href="Data.List.Relation.Unary.Any.Properties.html#18108" class="Bound">i<n</a><a id="18156" class="Symbol">))</a>
<a id="applyUpTo⁻"></a><a id="18160" href="Data.List.Relation.Unary.Any.Properties.html#18160" class="Function">applyUpTo⁻</a> <a id="18171" class="Symbol">:</a> <a id="18173" class="Symbol">∀</a> <a id="18175" href="Data.List.Relation.Unary.Any.Properties.html#18175" class="Bound">f</a> <a id="18177" class="Symbol">{</a><a id="18178" href="Data.List.Relation.Unary.Any.Properties.html#18178" class="Bound">n</a><a id="18179" class="Symbol">}</a> <a id="18181" class="Symbol">→</a> <a id="18183" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="18187" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="18189" class="Symbol">(</a><a id="18190" href="Data.List.Base.html#5753" class="Function">applyUpTo</a> <a id="18200" href="Data.List.Relation.Unary.Any.Properties.html#18175" class="Bound">f</a> <a id="18202" href="Data.List.Relation.Unary.Any.Properties.html#18178" class="Bound">n</a><a id="18203" class="Symbol">)</a> <a id="18205" class="Symbol">→</a>
<a id="18220" href="Data.Product.html#1369" class="Function">∃</a> <a id="18222" class="Symbol">λ</a> <a id="18224" href="Data.List.Relation.Unary.Any.Properties.html#18224" class="Bound">i</a> <a id="18226" class="Symbol">→</a> <a id="18228" href="Data.List.Relation.Unary.Any.Properties.html#18224" class="Bound">i</a> <a id="18230" href="Data.Nat.Base.html#1645" class="Function Operator"><</a> <a id="18232" href="Data.List.Relation.Unary.Any.Properties.html#18178" class="Bound">n</a> <a id="18234" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="18236" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="18238" class="Symbol">(</a><a id="18239" href="Data.List.Relation.Unary.Any.Properties.html#18175" class="Bound">f</a> <a id="18241" href="Data.List.Relation.Unary.Any.Properties.html#18224" class="Bound">i</a><a id="18242" class="Symbol">)</a>
<a id="18244" href="Data.List.Relation.Unary.Any.Properties.html#18160" class="Function">applyUpTo⁻</a> <a id="18255" href="Data.List.Relation.Unary.Any.Properties.html#18255" class="Bound">f</a> <a id="18257" class="Symbol">{</a><a id="18258" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a> <a id="18262" href="Data.List.Relation.Unary.Any.Properties.html#18262" class="Bound">n</a><a id="18263" class="Symbol">}</a> <a id="18265" class="Symbol">(</a><a id="18266" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="18271" href="Data.List.Relation.Unary.Any.Properties.html#18271" class="Bound">p</a><a id="18272" class="Symbol">)</a> <a id="18275" class="Symbol">=</a> <a id="18277" href="Agda.Builtin.Nat.html#210" class="InductiveConstructor">zero</a> <a id="18282" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18284" href="Data.Nat.Base.html#1600" class="InductiveConstructor">s≤s</a> <a id="18288" href="Data.Nat.Base.html#1558" class="InductiveConstructor">z≤n</a> <a id="18292" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18294" href="Data.List.Relation.Unary.Any.Properties.html#18271" class="Bound">p</a>
<a id="18296" href="Data.List.Relation.Unary.Any.Properties.html#18160" class="Function">applyUpTo⁻</a> <a id="18307" href="Data.List.Relation.Unary.Any.Properties.html#18307" class="Bound">f</a> <a id="18309" class="Symbol">{</a><a id="18310" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a> <a id="18314" href="Data.List.Relation.Unary.Any.Properties.html#18314" class="Bound">n</a><a id="18315" class="Symbol">}</a> <a id="18317" class="Symbol">(</a><a id="18318" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="18324" href="Data.List.Relation.Unary.Any.Properties.html#18324" class="Bound">p</a><a id="18325" class="Symbol">)</a> <a id="18327" class="Keyword">with</a> <a id="18332" href="Data.List.Relation.Unary.Any.Properties.html#18160" class="Function">applyUpTo⁻</a> <a id="18343" class="Symbol">(</a><a id="18344" href="Data.List.Relation.Unary.Any.Properties.html#18307" class="Bound">f</a> <a id="18346" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="18348" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a><a id="18351" class="Symbol">)</a> <a id="18353" href="Data.List.Relation.Unary.Any.Properties.html#18324" class="Bound">p</a>
<a id="18355" class="Symbol">...</a> <a id="18359" class="Symbol">|</a> <a id="18361" href="Data.List.Relation.Unary.Any.Properties.html#18361" class="Bound">i</a> <a id="18363" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18365" href="Data.List.Relation.Unary.Any.Properties.html#18365" class="Bound">i<n</a> <a id="18369" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18371" href="Data.List.Relation.Unary.Any.Properties.html#18371" class="Bound">q</a> <a id="18373" class="Symbol">=</a> <a id="18375" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a> <a id="18379" href="Data.List.Relation.Unary.Any.Properties.html#18361" class="Bound">i</a> <a id="18381" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18383" href="Data.Nat.Base.html#1600" class="InductiveConstructor">s≤s</a> <a id="18387" href="Data.List.Relation.Unary.Any.Properties.html#18365" class="Bound">i<n</a> <a id="18391" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18393" href="Data.List.Relation.Unary.Any.Properties.html#18371" class="Bound">q</a>
<a id="18396" class="Comment">------------------------------------------------------------------------</a>
<a id="18469" class="Comment">-- applyDownFrom</a>
<a id="18487" class="Keyword">module</a> <a id="18494" href="Data.List.Relation.Unary.Any.Properties.html#18494" class="Module">_</a> <a id="18496" class="Symbol">{</a><a id="18497" href="Data.List.Relation.Unary.Any.Properties.html#18497" class="Bound">P</a> <a id="18499" class="Symbol">:</a> <a id="18501" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="18503" class="Symbol">→</a> <a id="18505" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="18509" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a><a id="18510" class="Symbol">}</a> <a id="18512" class="Keyword">where</a>
<a id="18521" href="Data.List.Relation.Unary.Any.Properties.html#18521" class="Function">applyDownFrom⁺</a> <a id="18536" class="Symbol">:</a> <a id="18538" class="Symbol">∀</a> <a id="18540" href="Data.List.Relation.Unary.Any.Properties.html#18540" class="Bound">f</a> <a id="18542" class="Symbol">{</a><a id="18543" href="Data.List.Relation.Unary.Any.Properties.html#18543" class="Bound">i</a> <a id="18545" href="Data.List.Relation.Unary.Any.Properties.html#18545" class="Bound">n</a><a id="18546" class="Symbol">}</a> <a id="18548" class="Symbol">→</a> <a id="18550" href="Data.List.Relation.Unary.Any.Properties.html#18497" class="Bound">P</a> <a id="18552" class="Symbol">(</a><a id="18553" href="Data.List.Relation.Unary.Any.Properties.html#18540" class="Bound">f</a> <a id="18555" href="Data.List.Relation.Unary.Any.Properties.html#18543" class="Bound">i</a><a id="18556" class="Symbol">)</a> <a id="18558" class="Symbol">→</a> <a id="18560" href="Data.List.Relation.Unary.Any.Properties.html#18543" class="Bound">i</a> <a id="18562" href="Data.Nat.Base.html#1645" class="Function Operator"><</a> <a id="18564" href="Data.List.Relation.Unary.Any.Properties.html#18545" class="Bound">n</a> <a id="18566" class="Symbol">→</a> <a id="18568" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="18572" href="Data.List.Relation.Unary.Any.Properties.html#18497" class="Bound">P</a> <a id="18574" class="Symbol">(</a><a id="18575" href="Data.List.Base.html#5865" class="Function">applyDownFrom</a> <a id="18589" href="Data.List.Relation.Unary.Any.Properties.html#18540" class="Bound">f</a> <a id="18591" href="Data.List.Relation.Unary.Any.Properties.html#18545" class="Bound">n</a><a id="18592" class="Symbol">)</a>
<a id="18596" href="Data.List.Relation.Unary.Any.Properties.html#18521" class="Function">applyDownFrom⁺</a> <a id="18611" href="Data.List.Relation.Unary.Any.Properties.html#18611" class="Bound">f</a> <a id="18613" class="Symbol">{</a><a id="18614" href="Data.List.Relation.Unary.Any.Properties.html#18614" class="Bound">i</a><a id="18615" class="Symbol">}</a> <a id="18617" class="Symbol">{</a><a id="18618" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a> <a id="18622" href="Data.List.Relation.Unary.Any.Properties.html#18622" class="Bound">n</a><a id="18623" class="Symbol">}</a> <a id="18625" href="Data.List.Relation.Unary.Any.Properties.html#18625" class="Bound">p</a> <a id="18627" class="Symbol">(</a><a id="18628" href="Data.Nat.Base.html#1600" class="InductiveConstructor">s≤s</a> <a id="18632" href="Data.List.Relation.Unary.Any.Properties.html#18632" class="Bound">i≤n</a><a id="18635" class="Symbol">)</a> <a id="18637" class="Keyword">with</a> <a id="18642" href="Data.List.Relation.Unary.Any.Properties.html#18614" class="Bound">i</a> <a id="18644" href="Data.Nat.Properties.html#2529" class="Function Operator">≟</a> <a id="18646" href="Data.List.Relation.Unary.Any.Properties.html#18622" class="Bound">n</a>
<a id="18650" class="Symbol">...</a> <a id="18654" class="Symbol">|</a> <a id="18656" href="Relation.Nullary.html#1648" class="InductiveConstructor">yes</a> <a id="18660" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">P.refl</a> <a id="18667" class="Symbol">=</a> <a id="18669" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="18674" class="Bound">p</a>
<a id="18678" class="Symbol">...</a> <a id="18682" class="Symbol">|</a> <a id="18684" href="Relation.Nullary.html#1685" class="InductiveConstructor">no</a> <a id="18688" href="Data.List.Relation.Unary.Any.Properties.html#18688" class="Bound">i≢n</a> <a id="18695" class="Symbol">=</a> <a id="18697" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="18703" class="Symbol">(</a><a id="18704" href="Data.List.Relation.Unary.Any.Properties.html#18521" class="Function">applyDownFrom⁺</a> <a id="18719" class="Bound">f</a> <a id="18721" class="Bound">p</a> <a id="18723" class="Symbol">(</a><a id="18724" href="Data.Nat.Properties.html#8352" class="Function">≤∧≢⇒<</a> <a id="18730" class="Bound">i≤n</a> <a id="18734" href="Data.List.Relation.Unary.Any.Properties.html#18688" class="Bound">i≢n</a><a id="18737" class="Symbol">))</a>
<a id="18743" href="Data.List.Relation.Unary.Any.Properties.html#18743" class="Function">applyDownFrom⁻</a> <a id="18758" class="Symbol">:</a> <a id="18760" class="Symbol">∀</a> <a id="18762" href="Data.List.Relation.Unary.Any.Properties.html#18762" class="Bound">f</a> <a id="18764" class="Symbol">{</a><a id="18765" href="Data.List.Relation.Unary.Any.Properties.html#18765" class="Bound">n</a><a id="18766" class="Symbol">}</a> <a id="18768" class="Symbol">→</a> <a id="18770" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="18774" href="Data.List.Relation.Unary.Any.Properties.html#18497" class="Bound">P</a> <a id="18776" class="Symbol">(</a><a id="18777" href="Data.List.Base.html#5865" class="Function">applyDownFrom</a> <a id="18791" href="Data.List.Relation.Unary.Any.Properties.html#18762" class="Bound">f</a> <a id="18793" href="Data.List.Relation.Unary.Any.Properties.html#18765" class="Bound">n</a><a id="18794" class="Symbol">)</a> <a id="18796" class="Symbol">→</a>
<a id="18817" href="Data.Product.html#1369" class="Function">∃</a> <a id="18819" class="Symbol">λ</a> <a id="18821" href="Data.List.Relation.Unary.Any.Properties.html#18821" class="Bound">i</a> <a id="18823" class="Symbol">→</a> <a id="18825" href="Data.List.Relation.Unary.Any.Properties.html#18821" class="Bound">i</a> <a id="18827" href="Data.Nat.Base.html#1645" class="Function Operator"><</a> <a id="18829" href="Data.List.Relation.Unary.Any.Properties.html#18765" class="Bound">n</a> <a id="18831" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="18833" href="Data.List.Relation.Unary.Any.Properties.html#18497" class="Bound">P</a> <a id="18835" class="Symbol">(</a><a id="18836" href="Data.List.Relation.Unary.Any.Properties.html#18762" class="Bound">f</a> <a id="18838" href="Data.List.Relation.Unary.Any.Properties.html#18821" class="Bound">i</a><a id="18839" class="Symbol">)</a>
<a id="18843" href="Data.List.Relation.Unary.Any.Properties.html#18743" class="Function">applyDownFrom⁻</a> <a id="18858" href="Data.List.Relation.Unary.Any.Properties.html#18858" class="Bound">f</a> <a id="18860" class="Symbol">{</a><a id="18861" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a> <a id="18865" href="Data.List.Relation.Unary.Any.Properties.html#18865" class="Bound">n</a><a id="18866" class="Symbol">}</a> <a id="18868" class="Symbol">(</a><a id="18869" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="18874" href="Data.List.Relation.Unary.Any.Properties.html#18874" class="Bound">p</a><a id="18875" class="Symbol">)</a> <a id="18878" class="Symbol">=</a> <a id="18880" href="Data.List.Relation.Unary.Any.Properties.html#18865" class="Bound">n</a> <a id="18882" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18884" href="Data.Nat.Properties.html#4565" class="Function">≤-refl</a> <a id="18891" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18893" href="Data.List.Relation.Unary.Any.Properties.html#18874" class="Bound">p</a>
<a id="18897" href="Data.List.Relation.Unary.Any.Properties.html#18743" class="Function">applyDownFrom⁻</a> <a id="18912" href="Data.List.Relation.Unary.Any.Properties.html#18912" class="Bound">f</a> <a id="18914" class="Symbol">{</a><a id="18915" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a> <a id="18919" href="Data.List.Relation.Unary.Any.Properties.html#18919" class="Bound">n</a><a id="18920" class="Symbol">}</a> <a id="18922" class="Symbol">(</a><a id="18923" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="18929" href="Data.List.Relation.Unary.Any.Properties.html#18929" class="Bound">p</a><a id="18930" class="Symbol">)</a> <a id="18932" class="Keyword">with</a> <a id="18937" href="Data.List.Relation.Unary.Any.Properties.html#18743" class="Function">applyDownFrom⁻</a> <a id="18952" href="Data.List.Relation.Unary.Any.Properties.html#18912" class="Bound">f</a> <a id="18954" href="Data.List.Relation.Unary.Any.Properties.html#18929" class="Bound">p</a>
<a id="18958" class="Symbol">...</a> <a id="18962" class="Symbol">|</a> <a id="18964" href="Data.List.Relation.Unary.Any.Properties.html#18964" class="Bound">i</a> <a id="18966" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18968" href="Data.List.Relation.Unary.Any.Properties.html#18968" class="Bound">i<n</a> <a id="18972" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18974" href="Data.List.Relation.Unary.Any.Properties.html#18974" class="Bound">pf</a> <a id="18977" class="Symbol">=</a> <a id="18979" href="Data.List.Relation.Unary.Any.Properties.html#18964" class="Bound">i</a> <a id="18981" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18983" href="Data.Nat.Properties.html#7182" class="Function">≤-step</a> <a id="18990" href="Data.List.Relation.Unary.Any.Properties.html#18968" class="Bound">i<n</a> <a id="18994" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="18996" href="Data.List.Relation.Unary.Any.Properties.html#18974" class="Bound">pf</a>
<a id="19000" class="Comment">------------------------------------------------------------------------</a>
<a id="19073" class="Comment">-- tabulate</a>
<a id="tabulate⁺"></a><a id="19086" href="Data.List.Relation.Unary.Any.Properties.html#19086" class="Function">tabulate⁺</a> <a id="19096" class="Symbol">:</a> <a id="19098" class="Symbol">∀</a> <a id="19100" class="Symbol">{</a><a id="19101" href="Data.List.Relation.Unary.Any.Properties.html#19101" class="Bound">n</a><a id="19102" class="Symbol">}</a> <a id="19104" class="Symbol">{</a><a id="19105" href="Data.List.Relation.Unary.Any.Properties.html#19105" class="Bound">f</a> <a id="19107" class="Symbol">:</a> <a id="19109" href="Data.Fin.Base.html#1126" class="Datatype">Fin</a> <a id="19113" href="Data.List.Relation.Unary.Any.Properties.html#19101" class="Bound">n</a> <a id="19115" class="Symbol">→</a> <a id="19117" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="19118" class="Symbol">}</a> <a id="19120" href="Data.List.Relation.Unary.Any.Properties.html#19120" class="Bound">i</a> <a id="19122" class="Symbol">→</a> <a id="19124" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="19126" class="Symbol">(</a><a id="19127" href="Data.List.Relation.Unary.Any.Properties.html#19105" class="Bound">f</a> <a id="19129" href="Data.List.Relation.Unary.Any.Properties.html#19120" class="Bound">i</a><a id="19130" class="Symbol">)</a> <a id="19132" class="Symbol">→</a> <a id="19134" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="19138" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="19140" class="Symbol">(</a><a id="19141" href="Data.List.Base.html#5982" class="Function">tabulate</a> <a id="19150" href="Data.List.Relation.Unary.Any.Properties.html#19105" class="Bound">f</a><a id="19151" class="Symbol">)</a>
<a id="19153" href="Data.List.Relation.Unary.Any.Properties.html#19086" class="Function">tabulate⁺</a> <a id="19163" href="Data.List.Relation.Unary.Any.Properties.html#521" class="InductiveConstructor">fzero</a> <a id="19172" href="Data.List.Relation.Unary.Any.Properties.html#19172" class="Bound">p</a> <a id="19174" class="Symbol">=</a> <a id="19176" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="19181" href="Data.List.Relation.Unary.Any.Properties.html#19172" class="Bound">p</a>
<a id="19183" href="Data.List.Relation.Unary.Any.Properties.html#19086" class="Function">tabulate⁺</a> <a id="19193" class="Symbol">(</a><a id="19194" href="Data.List.Relation.Unary.Any.Properties.html#535" class="InductiveConstructor">fsuc</a> <a id="19199" href="Data.List.Relation.Unary.Any.Properties.html#19199" class="Bound">i</a><a id="19200" class="Symbol">)</a> <a id="19202" href="Data.List.Relation.Unary.Any.Properties.html#19202" class="Bound">p</a> <a id="19204" class="Symbol">=</a> <a id="19206" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="19212" class="Symbol">(</a><a id="19213" href="Data.List.Relation.Unary.Any.Properties.html#19086" class="Function">tabulate⁺</a> <a id="19223" href="Data.List.Relation.Unary.Any.Properties.html#19199" class="Bound">i</a> <a id="19225" href="Data.List.Relation.Unary.Any.Properties.html#19202" class="Bound">p</a><a id="19226" class="Symbol">)</a>
<a id="tabulate⁻"></a><a id="19229" href="Data.List.Relation.Unary.Any.Properties.html#19229" class="Function">tabulate⁻</a> <a id="19239" class="Symbol">:</a> <a id="19241" class="Symbol">∀</a> <a id="19243" class="Symbol">{</a><a id="19244" href="Data.List.Relation.Unary.Any.Properties.html#19244" class="Bound">n</a><a id="19245" class="Symbol">}</a> <a id="19247" class="Symbol">{</a><a id="19248" href="Data.List.Relation.Unary.Any.Properties.html#19248" class="Bound">f</a> <a id="19250" class="Symbol">:</a> <a id="19252" href="Data.Fin.Base.html#1126" class="Datatype">Fin</a> <a id="19256" href="Data.List.Relation.Unary.Any.Properties.html#19244" class="Bound">n</a> <a id="19258" class="Symbol">→</a> <a id="19260" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="19261" class="Symbol">}</a> <a id="19263" class="Symbol">→</a> <a id="19265" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="19269" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="19271" class="Symbol">(</a><a id="19272" href="Data.List.Base.html#5982" class="Function">tabulate</a> <a id="19281" href="Data.List.Relation.Unary.Any.Properties.html#19248" class="Bound">f</a><a id="19282" class="Symbol">)</a> <a id="19284" class="Symbol">→</a> <a id="19286" href="Data.Product.html#1369" class="Function">∃</a> <a id="19288" class="Symbol">λ</a> <a id="19290" href="Data.List.Relation.Unary.Any.Properties.html#19290" class="Bound">i</a> <a id="19292" class="Symbol">→</a> <a id="19294" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="19296" class="Symbol">(</a><a id="19297" href="Data.List.Relation.Unary.Any.Properties.html#19248" class="Bound">f</a> <a id="19299" href="Data.List.Relation.Unary.Any.Properties.html#19290" class="Bound">i</a><a id="19300" class="Symbol">)</a>
<a id="19302" href="Data.List.Relation.Unary.Any.Properties.html#19229" class="Function">tabulate⁻</a> <a id="19312" class="Symbol">{</a><a id="19313" class="Argument">n</a> <a id="19315" class="Symbol">=</a> <a id="19317" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a> <a id="19321" href="Data.List.Relation.Unary.Any.Properties.html#19321" class="Bound">n</a><a id="19322" class="Symbol">}</a> <a id="19324" class="Symbol">(</a><a id="19325" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="19330" href="Data.List.Relation.Unary.Any.Properties.html#19330" class="Bound">p</a><a id="19331" class="Symbol">)</a> <a id="19335" class="Symbol">=</a> <a id="19337" href="Data.List.Relation.Unary.Any.Properties.html#521" class="InductiveConstructor">fzero</a> <a id="19343" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="19345" href="Data.List.Relation.Unary.Any.Properties.html#19330" class="Bound">p</a>
<a id="19347" href="Data.List.Relation.Unary.Any.Properties.html#19229" class="Function">tabulate⁻</a> <a id="19357" class="Symbol">{</a><a id="19358" class="Argument">n</a> <a id="19360" class="Symbol">=</a> <a id="19362" href="Agda.Builtin.Nat.html#223" class="InductiveConstructor">suc</a> <a id="19366" href="Data.List.Relation.Unary.Any.Properties.html#19366" class="Bound">n</a><a id="19367" class="Symbol">}</a> <a id="19369" class="Symbol">(</a><a id="19370" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="19376" href="Data.List.Relation.Unary.Any.Properties.html#19376" class="Bound">p</a><a id="19377" class="Symbol">)</a> <a id="19379" class="Symbol">=</a> <a id="19381" href="Data.Product.html#2486" class="Function">Prod.map</a> <a id="19390" href="Data.List.Relation.Unary.Any.Properties.html#535" class="InductiveConstructor">fsuc</a> <a id="19395" href="Function.Base.html#615" class="Function">id</a> <a id="19398" class="Symbol">(</a><a id="19399" href="Data.List.Relation.Unary.Any.Properties.html#19229" class="Function">tabulate⁻</a> <a id="19409" href="Data.List.Relation.Unary.Any.Properties.html#19376" class="Bound">p</a><a id="19410" class="Symbol">)</a>
<a id="19413" class="Comment">------------------------------------------------------------------------</a>
<a id="19486" class="Comment">-- filter</a>
<a id="19497" class="Keyword">module</a> <a id="19504" href="Data.List.Relation.Unary.Any.Properties.html#19504" class="Module">_</a> <a id="19506" class="Symbol">(</a><a id="19507" href="Data.List.Relation.Unary.Any.Properties.html#19507" class="Bound">Q?</a> <a id="19510" class="Symbol">:</a> <a id="19512" href="Relation.Unary.html#3536" class="Function">U.Decidable</a> <a id="19524" href="Data.List.Relation.Unary.Any.Properties.html#2442" class="Generalizable">Q</a><a id="19525" class="Symbol">)</a> <a id="19527" class="Keyword">where</a>
<a id="19536" href="Data.List.Relation.Unary.Any.Properties.html#19536" class="Function">filter⁺</a> <a id="19544" class="Symbol">:</a> <a id="19546" class="Symbol">(</a><a id="19547" href="Data.List.Relation.Unary.Any.Properties.html#19547" class="Bound">p</a> <a id="19549" class="Symbol">:</a> <a id="19551" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="19555" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="19557" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="19559" class="Symbol">)</a> <a id="19561" class="Symbol">→</a> <a id="19563" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="19567" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="19569" class="Symbol">(</a><a id="19570" href="Data.List.Base.html#8092" class="Function">filter</a> <a id="19577" href="Data.List.Relation.Unary.Any.Properties.html#19507" class="Bound">Q?</a> <a id="19580" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="19582" class="Symbol">)</a> <a id="19584" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="19586" href="Relation.Nullary.html#656" class="Function Operator">¬</a> <a id="19588" href="Data.List.Relation.Unary.Any.Properties.html#19524" class="Bound">Q</a> <a id="19590" class="Symbol">(</a><a id="19591" href="Data.List.Relation.Unary.Any.html#1919" class="Function">Any.lookup</a> <a id="19602" href="Data.List.Relation.Unary.Any.Properties.html#19547" class="Bound">p</a><a id="19603" class="Symbol">)</a>
<a id="19607" href="Data.List.Relation.Unary.Any.Properties.html#19536" class="Function">filter⁺</a> <a id="19615" class="Symbol">{</a><a id="19616" class="Argument">xs</a> <a id="19619" class="Symbol">=</a> <a id="19621" href="Data.List.Relation.Unary.Any.Properties.html#19621" class="Bound">x</a> <a id="19623" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="19625" class="Symbol">_}</a> <a id="19628" class="Symbol">(</a><a id="19629" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="19634" href="Data.List.Relation.Unary.Any.Properties.html#19634" class="Bound">px</a><a id="19636" class="Symbol">)</a> <a id="19638" class="Keyword">with</a> <a id="19643" href="Data.List.Relation.Unary.Any.Properties.html#19507" class="Bound">Q?</a> <a id="19646" href="Data.List.Relation.Unary.Any.Properties.html#19621" class="Bound">x</a>
<a id="19650" class="Symbol">...</a> <a id="19654" class="Symbol">|</a> <a id="19656" href="Agda.Builtin.Bool.html#188" class="InductiveConstructor">true</a> <a id="19662" href="Relation.Nullary.html#1559" class="InductiveConstructor Operator">because</a> <a id="19670" class="Symbol">_</a> <a id="19678" class="Symbol">=</a> <a id="19680" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="19685" class="Symbol">(</a><a id="19686" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="19691" class="Bound">px</a><a id="19693" class="Symbol">)</a>
<a id="19697" class="Symbol">...</a> <a id="19701" class="Symbol">|</a> <a id="19703" href="Agda.Builtin.Bool.html#182" class="InductiveConstructor">false</a> <a id="19709" href="Relation.Nullary.html#1559" class="InductiveConstructor Operator">because</a> <a id="19717" href="Relation.Nullary.html#939" class="InductiveConstructor">ofⁿ</a> <a id="19721" href="Data.List.Relation.Unary.Any.Properties.html#19721" class="Bound">¬Qx</a> <a id="19725" class="Symbol">=</a> <a id="19727" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="19732" href="Data.List.Relation.Unary.Any.Properties.html#19721" class="Bound">¬Qx</a>
<a id="19738" href="Data.List.Relation.Unary.Any.Properties.html#19536" class="Function">filter⁺</a> <a id="19746" class="Symbol">{</a><a id="19747" class="Argument">xs</a> <a id="19750" class="Symbol">=</a> <a id="19752" href="Data.List.Relation.Unary.Any.Properties.html#19752" class="Bound">x</a> <a id="19754" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="19756" class="Symbol">_}</a> <a id="19759" class="Symbol">(</a><a id="19760" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="19766" href="Data.List.Relation.Unary.Any.Properties.html#19766" class="Bound">p</a><a id="19767" class="Symbol">)</a> <a id="19769" class="Keyword">with</a> <a id="19774" href="Relation.Nullary.html#1581" class="Field">does</a> <a id="19779" class="Symbol">(</a><a id="19780" href="Data.List.Relation.Unary.Any.Properties.html#19507" class="Bound">Q?</a> <a id="19783" href="Data.List.Relation.Unary.Any.Properties.html#19752" class="Bound">x</a><a id="19784" class="Symbol">)</a>
<a id="19788" class="Symbol">...</a> <a id="19792" class="Symbol">|</a> <a id="19794" href="Agda.Builtin.Bool.html#188" class="InductiveConstructor">true</a> <a id="19800" class="Symbol">=</a> <a id="19802" href="Data.Sum.Base.html#1440" class="Function">Sum.map₁</a> <a id="19811" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="19817" class="Symbol">(</a><a id="19818" href="Data.List.Relation.Unary.Any.Properties.html#19536" class="Function">filter⁺</a> <a id="19826" class="Bound">p</a><a id="19827" class="Symbol">)</a>
<a id="19831" class="Symbol">...</a> <a id="19835" class="Symbol">|</a> <a id="19837" href="Agda.Builtin.Bool.html#182" class="InductiveConstructor">false</a> <a id="19843" class="Symbol">=</a> <a id="19845" href="Data.List.Relation.Unary.Any.Properties.html#19536" class="Function">filter⁺</a> <a id="19853" class="Bound">p</a>
<a id="19858" href="Data.List.Relation.Unary.Any.Properties.html#19858" class="Function">filter⁻</a> <a id="19866" class="Symbol">:</a> <a id="19868" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="19872" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="19874" class="Symbol">(</a><a id="19875" href="Data.List.Base.html#8092" class="Function">filter</a> <a id="19882" href="Data.List.Relation.Unary.Any.Properties.html#19507" class="Bound">Q?</a> <a id="19885" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="19887" class="Symbol">)</a> <a id="19889" class="Symbol">→</a> <a id="19891" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="19895" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="19897" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="19902" href="Data.List.Relation.Unary.Any.Properties.html#19858" class="Function">filter⁻</a> <a id="19910" class="Symbol">{</a><a id="19911" class="Argument">xs</a> <a id="19914" class="Symbol">=</a> <a id="19916" href="Data.List.Relation.Unary.Any.Properties.html#19916" class="Bound">x</a> <a id="19918" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="19920" href="Data.List.Relation.Unary.Any.Properties.html#19920" class="Bound">xs</a><a id="19922" class="Symbol">}</a> <a id="19924" href="Data.List.Relation.Unary.Any.Properties.html#19924" class="Bound">p</a> <a id="19926" class="Keyword">with</a> <a id="19931" href="Relation.Nullary.html#1581" class="Field">does</a> <a id="19936" class="Symbol">(</a><a id="19937" href="Data.List.Relation.Unary.Any.Properties.html#19507" class="Bound">Q?</a> <a id="19940" href="Data.List.Relation.Unary.Any.Properties.html#19916" class="Bound">x</a><a id="19941" class="Symbol">)</a> <a id="19943" class="Symbol">|</a> <a id="19945" href="Data.List.Relation.Unary.Any.Properties.html#19924" class="Bound">p</a>
<a id="19949" class="Symbol">...</a> <a id="19953" class="Symbol">|</a> <a id="19955" href="Agda.Builtin.Bool.html#188" class="InductiveConstructor">true</a> <a id="19961" class="Symbol">|</a> <a id="19963" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="19968" href="Data.List.Relation.Unary.Any.Properties.html#19968" class="Bound">px</a> <a id="19973" class="Symbol">=</a> <a id="19975" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="19980" href="Data.List.Relation.Unary.Any.Properties.html#19968" class="Bound">px</a>
<a id="19985" class="Symbol">...</a> <a id="19989" class="Symbol">|</a> <a id="19991" href="Agda.Builtin.Bool.html#188" class="InductiveConstructor">true</a> <a id="19997" class="Symbol">|</a> <a id="19999" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="20005" href="Data.List.Relation.Unary.Any.Properties.html#20005" class="Bound">pxs</a> <a id="20009" class="Symbol">=</a> <a id="20011" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="20017" class="Symbol">(</a><a id="20018" href="Data.List.Relation.Unary.Any.Properties.html#19858" class="Function">filter⁻</a> <a id="20026" href="Data.List.Relation.Unary.Any.Properties.html#20005" class="Bound">pxs</a><a id="20029" class="Symbol">)</a>
<a id="20033" class="Symbol">...</a> <a id="20037" class="Symbol">|</a> <a id="20039" href="Agda.Builtin.Bool.html#182" class="InductiveConstructor">false</a> <a id="20045" class="Symbol">|</a> <a id="20047" href="Data.List.Relation.Unary.Any.Properties.html#20047" class="Bound">pxs</a> <a id="20057" class="Symbol">=</a> <a id="20059" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="20065" class="Symbol">(</a><a id="20066" href="Data.List.Relation.Unary.Any.Properties.html#19858" class="Function">filter⁻</a> <a id="20074" href="Data.List.Relation.Unary.Any.Properties.html#20047" class="Bound">pxs</a><a id="20077" class="Symbol">)</a>
<a id="20080" class="Comment">------------------------------------------------------------------------</a>
<a id="20153" class="Comment">-- derun and deduplicate</a>
<a id="20179" class="Keyword">module</a> <a id="20186" href="Data.List.Relation.Unary.Any.Properties.html#20186" class="Module">_</a> <a id="20188" class="Symbol">{</a><a id="20189" href="Data.List.Relation.Unary.Any.Properties.html#20189" class="Bound">R</a> <a id="20191" class="Symbol">:</a> <a id="20193" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="20195" class="Symbol">→</a> <a id="20197" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="20199" class="Symbol">→</a> <a id="20201" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="20205" href="Data.List.Relation.Unary.Any.Properties.html#2382" class="Generalizable">r</a><a id="20206" class="Symbol">}</a> <a id="20208" class="Symbol">(</a><a id="20209" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="20212" class="Symbol">:</a> <a id="20214" href="Relation.Binary.Definitions.html#4575" class="Function">B.Decidable</a> <a id="20226" href="Data.List.Relation.Unary.Any.Properties.html#20189" class="Bound">R</a><a id="20227" class="Symbol">)</a> <a id="20229" class="Keyword">where</a>
<a id="20238" class="Keyword">private</a>
<a id="20250" href="Data.List.Relation.Unary.Any.Properties.html#20250" class="Function">derun⁺-aux</a> <a id="20261" class="Symbol">:</a> <a id="20263" class="Symbol">∀</a> <a id="20265" href="Data.List.Relation.Unary.Any.Properties.html#20265" class="Bound">x</a> <a id="20267" href="Data.List.Relation.Unary.Any.Properties.html#20267" class="Bound">xs</a> <a id="20270" class="Symbol">→</a> <a id="20272" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="20274" href="Relation.Binary.Definitions.html#3593" class="Function Operator">Respects</a> <a id="20283" href="Data.List.Relation.Unary.Any.Properties.html#20189" class="Bound">R</a> <a id="20285" class="Symbol">→</a> <a id="20287" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="20289" href="Data.List.Relation.Unary.Any.Properties.html#20265" class="Bound">x</a> <a id="20291" class="Symbol">→</a> <a id="20293" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="20297" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="20299" class="Symbol">(</a><a id="20300" href="Data.List.Base.html#8805" class="Function">derun</a> <a id="20306" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="20309" class="Symbol">(</a><a id="20310" href="Data.List.Relation.Unary.Any.Properties.html#20265" class="Bound">x</a> <a id="20312" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="20314" href="Data.List.Relation.Unary.Any.Properties.html#20267" class="Bound">xs</a><a id="20316" class="Symbol">))</a>
<a id="20323" href="Data.List.Relation.Unary.Any.Properties.html#20250" class="Function">derun⁺-aux</a> <a id="20334" href="Data.List.Relation.Unary.Any.Properties.html#20334" class="Bound">x</a> <a id="20336" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="20339" href="Data.List.Relation.Unary.Any.Properties.html#20339" class="Bound">resp</a> <a id="20344" href="Data.List.Relation.Unary.Any.Properties.html#20344" class="Bound">Px</a> <a id="20347" class="Symbol">=</a> <a id="20349" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="20354" href="Data.List.Relation.Unary.Any.Properties.html#20344" class="Bound">Px</a>
<a id="20361" href="Data.List.Relation.Unary.Any.Properties.html#20250" class="Function">derun⁺-aux</a> <a id="20372" href="Data.List.Relation.Unary.Any.Properties.html#20372" class="Bound">x</a> <a id="20374" class="Symbol">(</a><a id="20375" href="Data.List.Relation.Unary.Any.Properties.html#20375" class="Bound">y</a> <a id="20377" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="20379" href="Data.List.Relation.Unary.Any.Properties.html#20379" class="Bound">xs</a><a id="20381" class="Symbol">)</a> <a id="20383" href="Data.List.Relation.Unary.Any.Properties.html#20383" class="Bound">resp</a> <a id="20388" href="Data.List.Relation.Unary.Any.Properties.html#20388" class="Bound">Px</a> <a id="20391" class="Keyword">with</a> <a id="20396" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="20399" href="Data.List.Relation.Unary.Any.Properties.html#20372" class="Bound">x</a> <a id="20401" href="Data.List.Relation.Unary.Any.Properties.html#20375" class="Bound">y</a>
<a id="20407" class="Symbol">...</a> <a id="20411" class="Symbol">|</a> <a id="20413" href="Agda.Builtin.Bool.html#188" class="InductiveConstructor">true</a> <a id="20419" href="Relation.Nullary.html#1559" class="InductiveConstructor Operator">because</a> <a id="20427" href="Relation.Nullary.html#902" class="InductiveConstructor">ofʸ</a> <a id="20431" href="Data.List.Relation.Unary.Any.Properties.html#20431" class="Bound">Rxy</a> <a id="20435" class="Symbol">=</a> <a id="20437" href="Data.List.Relation.Unary.Any.Properties.html#20250" class="Function">derun⁺-aux</a> <a id="20448" class="Bound">y</a> <a id="20450" class="Bound">xs</a> <a id="20453" class="Bound">resp</a> <a id="20458" class="Symbol">(</a><a id="20459" class="Bound">resp</a> <a id="20464" href="Data.List.Relation.Unary.Any.Properties.html#20431" class="Bound">Rxy</a> <a id="20468" class="Bound">Px</a><a id="20470" class="Symbol">)</a>
<a id="20476" class="Symbol">...</a> <a id="20480" class="Symbol">|</a> <a id="20482" href="Agda.Builtin.Bool.html#182" class="InductiveConstructor">false</a> <a id="20488" href="Relation.Nullary.html#1559" class="InductiveConstructor Operator">because</a> <a id="20496" class="Symbol">_</a> <a id="20504" class="Symbol">=</a> <a id="20506" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="20511" class="Bound">Px</a>
<a id="20517" href="Data.List.Relation.Unary.Any.Properties.html#20517" class="Function">derun⁺</a> <a id="20524" class="Symbol">:</a> <a id="20526" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="20528" href="Relation.Binary.Definitions.html#3593" class="Function Operator">Respects</a> <a id="20537" href="Data.List.Relation.Unary.Any.Properties.html#20189" class="Bound">R</a> <a id="20539" class="Symbol">→</a> <a id="20541" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="20545" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="20547" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="20550" class="Symbol">→</a> <a id="20552" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="20556" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="20558" class="Symbol">(</a><a id="20559" href="Data.List.Base.html#8805" class="Function">derun</a> <a id="20565" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="20568" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="20570" class="Symbol">)</a>
<a id="20574" href="Data.List.Relation.Unary.Any.Properties.html#20517" class="Function">derun⁺</a> <a id="20581" class="Symbol">{</a><a id="20582" class="Argument">xs</a> <a id="20585" class="Symbol">=</a> <a id="20587" href="Data.List.Relation.Unary.Any.Properties.html#20587" class="Bound">x</a> <a id="20589" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="20591" href="Data.List.Relation.Unary.Any.Properties.html#20591" class="Bound">xs</a><a id="20593" class="Symbol">}</a> <a id="20599" href="Data.List.Relation.Unary.Any.Properties.html#20599" class="Bound">resp</a> <a id="20604" class="Symbol">(</a><a id="20605" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="20610" href="Data.List.Relation.Unary.Any.Properties.html#20610" class="Bound">px</a><a id="20612" class="Symbol">)</a> <a id="20616" class="Symbol">=</a> <a id="20618" href="Data.List.Relation.Unary.Any.Properties.html#20250" class="Function">derun⁺-aux</a> <a id="20629" href="Data.List.Relation.Unary.Any.Properties.html#20587" class="Bound">x</a> <a id="20631" href="Data.List.Relation.Unary.Any.Properties.html#20591" class="Bound">xs</a> <a id="20634" href="Data.List.Relation.Unary.Any.Properties.html#20599" class="Bound">resp</a> <a id="20639" href="Data.List.Relation.Unary.Any.Properties.html#20610" class="Bound">px</a>
<a id="20644" href="Data.List.Relation.Unary.Any.Properties.html#20517" class="Function">derun⁺</a> <a id="20651" class="Symbol">{</a><a id="20652" class="Argument">xs</a> <a id="20655" class="Symbol">=</a> <a id="20657" href="Data.List.Relation.Unary.Any.Properties.html#20657" class="Bound">x</a> <a id="20659" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="20661" href="Data.List.Relation.Unary.Any.Properties.html#20661" class="Bound">y</a> <a id="20663" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="20665" href="Data.List.Relation.Unary.Any.Properties.html#20665" class="Bound">xs</a><a id="20667" class="Symbol">}</a> <a id="20669" href="Data.List.Relation.Unary.Any.Properties.html#20669" class="Bound">resp</a> <a id="20674" class="Symbol">(</a><a id="20675" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="20681" href="Data.List.Relation.Unary.Any.Properties.html#20681" class="Bound">pxs</a><a id="20684" class="Symbol">)</a> <a id="20686" class="Keyword">with</a> <a id="20691" href="Relation.Nullary.html#1581" class="Field">does</a> <a id="20696" class="Symbol">(</a><a id="20697" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="20700" href="Data.List.Relation.Unary.Any.Properties.html#20657" class="Bound">x</a> <a id="20702" href="Data.List.Relation.Unary.Any.Properties.html#20661" class="Bound">y</a><a id="20703" class="Symbol">)</a>
<a id="20707" class="Symbol">...</a> <a id="20711" class="Symbol">|</a> <a id="20713" href="Agda.Builtin.Bool.html#188" class="InductiveConstructor">true</a> <a id="20719" class="Symbol">=</a> <a id="20721" href="Data.List.Relation.Unary.Any.Properties.html#20517" class="Function">derun⁺</a> <a id="20728" class="Bound">resp</a> <a id="20733" class="Bound">pxs</a>
<a id="20739" class="Symbol">...</a> <a id="20743" class="Symbol">|</a> <a id="20745" href="Agda.Builtin.Bool.html#182" class="InductiveConstructor">false</a> <a id="20751" class="Symbol">=</a> <a id="20753" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="20759" class="Symbol">(</a><a id="20760" href="Data.List.Relation.Unary.Any.Properties.html#20517" class="Function">derun⁺</a> <a id="20767" class="Bound">resp</a> <a id="20772" class="Bound">pxs</a><a id="20775" class="Symbol">)</a>
<a id="20780" href="Data.List.Relation.Unary.Any.Properties.html#20780" class="Function">deduplicate⁺</a> <a id="20793" class="Symbol">:</a> <a id="20795" class="Symbol">∀</a> <a id="20797" class="Symbol">{</a><a id="20798" href="Data.List.Relation.Unary.Any.Properties.html#20798" class="Bound">xs</a><a id="20800" class="Symbol">}</a> <a id="20802" class="Symbol">→</a> <a id="20804" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="20806" href="Relation.Binary.Definitions.html#3593" class="Function Operator">Respects</a> <a id="20815" class="Symbol">(</a><a id="20816" href="Function.Base.html#1554" class="Function">flip</a> <a id="20821" href="Data.List.Relation.Unary.Any.Properties.html#20189" class="Bound">R</a><a id="20822" class="Symbol">)</a> <a id="20824" class="Symbol">→</a> <a id="20826" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="20830" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="20832" href="Data.List.Relation.Unary.Any.Properties.html#20798" class="Bound">xs</a> <a id="20835" class="Symbol">→</a> <a id="20837" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="20841" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="20843" class="Symbol">(</a><a id="20844" href="Data.List.Base.html#9017" class="Function">deduplicate</a> <a id="20856" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="20859" href="Data.List.Relation.Unary.Any.Properties.html#20798" class="Bound">xs</a><a id="20861" class="Symbol">)</a>
<a id="20865" href="Data.List.Relation.Unary.Any.Properties.html#20780" class="Function">deduplicate⁺</a> <a id="20878" class="Symbol">{</a><a id="20879" class="Argument">xs</a> <a id="20882" class="Symbol">=</a> <a id="20884" href="Data.List.Relation.Unary.Any.Properties.html#20884" class="Bound">x</a> <a id="20886" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="20888" href="Data.List.Relation.Unary.Any.Properties.html#20888" class="Bound">xs</a><a id="20890" class="Symbol">}</a> <a id="20892" href="Data.List.Relation.Unary.Any.Properties.html#20892" class="Bound">resp</a> <a id="20897" class="Symbol">(</a><a id="20898" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="20903" href="Data.List.Relation.Unary.Any.Properties.html#20903" class="Bound">px</a><a id="20905" class="Symbol">)</a> <a id="20909" class="Symbol">=</a> <a id="20911" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="20916" href="Data.List.Relation.Unary.Any.Properties.html#20903" class="Bound">px</a>
<a id="20921" href="Data.List.Relation.Unary.Any.Properties.html#20780" class="Function">deduplicate⁺</a> <a id="20934" class="Symbol">{</a><a id="20935" class="Argument">xs</a> <a id="20938" class="Symbol">=</a> <a id="20940" href="Data.List.Relation.Unary.Any.Properties.html#20940" class="Bound">x</a> <a id="20942" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="20944" href="Data.List.Relation.Unary.Any.Properties.html#20944" class="Bound">xs</a><a id="20946" class="Symbol">}</a> <a id="20948" href="Data.List.Relation.Unary.Any.Properties.html#20948" class="Bound">resp</a> <a id="20953" class="Symbol">(</a><a id="20954" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="20960" href="Data.List.Relation.Unary.Any.Properties.html#20960" class="Bound">pxs</a><a id="20963" class="Symbol">)</a>
<a id="20969" class="Keyword">with</a> <a id="20974" href="Data.List.Relation.Unary.Any.Properties.html#19536" class="Function">filter⁺</a> <a id="20982" class="Symbol">(</a><a id="20983" href="Relation.Nullary.Negation.Core.html#1355" class="Function">¬?</a> <a id="20986" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="20988" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="20991" href="Data.List.Relation.Unary.Any.Properties.html#20940" class="Bound">x</a><a id="20992" class="Symbol">)</a> <a id="20994" class="Symbol">(</a><a id="20995" href="Data.List.Relation.Unary.Any.Properties.html#20780" class="Function">deduplicate⁺</a> <a id="21008" href="Data.List.Relation.Unary.Any.Properties.html#20948" class="Bound">resp</a> <a id="21013" href="Data.List.Relation.Unary.Any.Properties.html#20960" class="Bound">pxs</a><a id="21016" class="Symbol">)</a>
<a id="21020" class="Symbol">...</a> <a id="21024" class="Symbol">|</a> <a id="21026" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="21031" href="Data.List.Relation.Unary.Any.Properties.html#21031" class="Bound">p</a> <a id="21033" class="Symbol">=</a> <a id="21035" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="21041" href="Data.List.Relation.Unary.Any.Properties.html#21031" class="Bound">p</a>
<a id="21045" class="Symbol">...</a> <a id="21049" class="Symbol">|</a> <a id="21051" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="21056" href="Data.List.Relation.Unary.Any.Properties.html#21056" class="Bound">¬¬q</a> <a id="21060" class="Keyword">with</a> <a id="21065" href="Relation.Nullary.Negation.html#1052" class="Function">decidable-stable</a> <a id="21082" class="Symbol">(</a><a id="21083" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="21086" class="Bound">x</a> <a id="21088" class="Symbol">(</a><a id="21089" href="Data.List.Relation.Unary.Any.html#1919" class="Function">Any.lookup</a> <a id="21100" class="Symbol">(</a><a id="21101" href="Data.List.Relation.Unary.Any.Properties.html#20780" class="Function">deduplicate⁺</a> <a id="21114" class="Bound">resp</a> <a id="21119" class="Bound">pxs</a><a id="21122" class="Symbol">)))</a> <a id="21126" href="Data.List.Relation.Unary.Any.Properties.html#21056" class="Bound">¬¬q</a>
<a id="21132" class="Symbol">...</a> <a id="21137" class="Symbol">|</a> <a id="21139" href="Data.List.Relation.Unary.Any.Properties.html#21139" class="Bound">q</a> <a id="21141" class="Symbol">=</a> <a id="21143" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="21148" class="Symbol">(</a><a id="21149" class="Bound">resp</a> <a id="21154" href="Data.List.Relation.Unary.Any.Properties.html#21139" class="Bound">q</a> <a id="21156" class="Symbol">(</a><a id="21157" href="Data.List.Relation.Unary.Any.Properties.html#4204" class="Function">lookup-result</a> <a id="21171" class="Symbol">(</a><a id="21172" href="Data.List.Relation.Unary.Any.Properties.html#20780" class="Function">deduplicate⁺</a> <a id="21185" class="Bound">resp</a> <a id="21190" class="Bound">pxs</a><a id="21193" class="Symbol">)))</a>
<a id="21200" class="Keyword">private</a>
<a id="21212" href="Data.List.Relation.Unary.Any.Properties.html#21212" class="Function">derun⁻-aux</a> <a id="21223" class="Symbol">:</a> <a id="21225" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="21229" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="21231" class="Symbol">(</a><a id="21232" href="Data.List.Base.html#8805" class="Function">derun</a> <a id="21238" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="21241" class="Symbol">(</a><a id="21242" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="21244" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="21246" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="21248" class="Symbol">))</a> <a id="21251" class="Symbol">→</a> <a id="21253" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="21257" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="21259" class="Symbol">(</a><a id="21260" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="21262" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="21264" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="21266" class="Symbol">)</a>
<a id="21272" href="Data.List.Relation.Unary.Any.Properties.html#21212" class="Function">derun⁻-aux</a> <a id="21283" class="Symbol">{</a><a id="21284" class="Argument">x</a> <a id="21286" class="Symbol">=</a> <a id="21288" href="Data.List.Relation.Unary.Any.Properties.html#21288" class="Bound">x</a><a id="21289" class="Symbol">}</a> <a id="21291" class="Symbol">{</a><a id="21292" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a><a id="21294" class="Symbol">}</a> <a id="21299" class="Symbol">(</a><a id="21300" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="21305" href="Data.List.Relation.Unary.Any.Properties.html#21305" class="Bound">px</a><a id="21307" class="Symbol">)</a> <a id="21309" class="Symbol">=</a> <a id="21311" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="21316" href="Data.List.Relation.Unary.Any.Properties.html#21305" class="Bound">px</a>
<a id="21323" href="Data.List.Relation.Unary.Any.Properties.html#21212" class="Function">derun⁻-aux</a> <a id="21334" class="Symbol">{</a><a id="21335" class="Argument">x</a> <a id="21337" class="Symbol">=</a> <a id="21339" href="Data.List.Relation.Unary.Any.Properties.html#21339" class="Bound">x</a><a id="21340" class="Symbol">}</a> <a id="21342" class="Symbol">{</a><a id="21343" href="Data.List.Relation.Unary.Any.Properties.html#21343" class="Bound">y</a> <a id="21345" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="21347" class="Symbol">_}</a> <a id="21350" href="Data.List.Relation.Unary.Any.Properties.html#21350" class="Bound">p[x∷y∷xs]</a> <a id="21360" class="Keyword">with</a> <a id="21365" href="Relation.Nullary.html#1581" class="Field">does</a> <a id="21370" class="Symbol">(</a><a id="21371" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="21374" href="Data.List.Relation.Unary.Any.Properties.html#21339" class="Bound">x</a> <a id="21376" href="Data.List.Relation.Unary.Any.Properties.html#21343" class="Bound">y</a><a id="21377" class="Symbol">)</a> <a id="21379" class="Symbol">|</a> <a id="21381" href="Data.List.Relation.Unary.Any.Properties.html#21350" class="Bound">p[x∷y∷xs]</a>
<a id="21395" class="Symbol">...</a> <a id="21399" class="Symbol">|</a> <a id="21401" href="Agda.Builtin.Bool.html#188" class="InductiveConstructor">true</a> <a id="21407" class="Symbol">|</a> <a id="21409" href="Data.List.Relation.Unary.Any.Properties.html#21409" class="Bound">p[y∷xs]</a> <a id="21424" class="Symbol">=</a> <a id="21426" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="21432" class="Symbol">(</a><a id="21433" href="Data.List.Relation.Unary.Any.Properties.html#21212" class="Function">derun⁻-aux</a> <a id="21444" href="Data.List.Relation.Unary.Any.Properties.html#21409" class="Bound">p[y∷xs]</a><a id="21451" class="Symbol">)</a>
<a id="21457" class="Symbol">...</a> <a id="21461" class="Symbol">|</a> <a id="21463" href="Agda.Builtin.Bool.html#182" class="InductiveConstructor">false</a> <a id="21469" class="Symbol">|</a> <a id="21471" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="21476" href="Data.List.Relation.Unary.Any.Properties.html#21476" class="Bound">px</a> <a id="21486" class="Symbol">=</a> <a id="21488" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="21493" href="Data.List.Relation.Unary.Any.Properties.html#21476" class="Bound">px</a>
<a id="21500" class="Symbol">...</a> <a id="21504" class="Symbol">|</a> <a id="21506" href="Agda.Builtin.Bool.html#182" class="InductiveConstructor">false</a> <a id="21512" class="Symbol">|</a> <a id="21514" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="21520" href="Data.List.Relation.Unary.Any.Properties.html#21520" class="Bound">p[y∷xs]!</a> <a id="21529" class="Symbol">=</a> <a id="21531" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="21537" class="Symbol">(</a><a id="21538" href="Data.List.Relation.Unary.Any.Properties.html#21212" class="Function">derun⁻-aux</a> <a id="21549" href="Data.List.Relation.Unary.Any.Properties.html#21520" class="Bound">p[y∷xs]!</a><a id="21557" class="Symbol">)</a>
<a id="21562" href="Data.List.Relation.Unary.Any.Properties.html#21562" class="Function">derun⁻</a> <a id="21569" class="Symbol">:</a> <a id="21571" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="21575" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="21577" class="Symbol">(</a><a id="21578" href="Data.List.Base.html#8805" class="Function">derun</a> <a id="21584" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="21587" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="21589" class="Symbol">)</a> <a id="21591" class="Symbol">→</a> <a id="21593" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="21597" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="21599" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="21604" href="Data.List.Relation.Unary.Any.Properties.html#21562" class="Function">derun⁻</a> <a id="21611" class="Symbol">{</a><a id="21612" class="Argument">xs</a> <a id="21615" class="Symbol">=</a> <a id="21617" href="Data.List.Relation.Unary.Any.Properties.html#21617" class="Bound">x</a> <a id="21619" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="21621" href="Data.List.Relation.Unary.Any.Properties.html#21621" class="Bound">xs</a><a id="21623" class="Symbol">}</a> <a id="21625" href="Data.List.Relation.Unary.Any.Properties.html#21625" class="Bound">p[x∷xs]!</a> <a id="21634" class="Symbol">=</a> <a id="21636" href="Data.List.Relation.Unary.Any.Properties.html#21212" class="Function">derun⁻-aux</a> <a id="21647" href="Data.List.Relation.Unary.Any.Properties.html#21625" class="Bound">p[x∷xs]!</a>
<a id="21659" href="Data.List.Relation.Unary.Any.Properties.html#21659" class="Function">deduplicate⁻</a> <a id="21672" class="Symbol">:</a> <a id="21674" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="21678" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="21680" class="Symbol">(</a><a id="21681" href="Data.List.Base.html#9017" class="Function">deduplicate</a> <a id="21693" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="21696" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="21698" class="Symbol">)</a> <a id="21700" class="Symbol">→</a> <a id="21702" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="21706" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="21708" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="21713" href="Data.List.Relation.Unary.Any.Properties.html#21659" class="Function">deduplicate⁻</a> <a id="21726" class="Symbol">{</a><a id="21727" class="Argument">xs</a> <a id="21730" class="Symbol">=</a> <a id="21732" href="Data.List.Relation.Unary.Any.Properties.html#21732" class="Bound">x</a> <a id="21734" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="21736" class="Symbol">_}</a> <a id="21739" class="Symbol">(</a><a id="21740" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="21745" href="Data.List.Relation.Unary.Any.Properties.html#21745" class="Bound">px</a><a id="21747" class="Symbol">)</a> <a id="21752" class="Symbol">=</a> <a id="21754" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="21759" href="Data.List.Relation.Unary.Any.Properties.html#21745" class="Bound">px</a>
<a id="21764" href="Data.List.Relation.Unary.Any.Properties.html#21659" class="Function">deduplicate⁻</a> <a id="21777" class="Symbol">{</a><a id="21778" class="Argument">xs</a> <a id="21781" class="Symbol">=</a> <a id="21783" href="Data.List.Relation.Unary.Any.Properties.html#21783" class="Bound">x</a> <a id="21785" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="21787" class="Symbol">_}</a> <a id="21790" class="Symbol">(</a><a id="21791" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="21797" href="Data.List.Relation.Unary.Any.Properties.html#21797" class="Bound">pxs!</a><a id="21801" class="Symbol">)</a> <a id="21803" class="Symbol">=</a> <a id="21805" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="21811" class="Symbol">(</a><a id="21812" href="Data.List.Relation.Unary.Any.Properties.html#21659" class="Function">deduplicate⁻</a> <a id="21825" class="Symbol">(</a><a id="21826" href="Data.List.Relation.Unary.Any.Properties.html#19858" class="Function">filter⁻</a> <a id="21834" class="Symbol">(</a><a id="21835" href="Relation.Nullary.Negation.Core.html#1355" class="Function">¬?</a> <a id="21838" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="21840" href="Data.List.Relation.Unary.Any.Properties.html#20209" class="Bound">R?</a> <a id="21843" href="Data.List.Relation.Unary.Any.Properties.html#21783" class="Bound">x</a><a id="21844" class="Symbol">)</a> <a id="21846" href="Data.List.Relation.Unary.Any.Properties.html#21797" class="Bound">pxs!</a><a id="21850" class="Symbol">))</a>
<a id="21854" class="Comment">------------------------------------------------------------------------</a>
<a id="21927" class="Comment">-- map-with-∈.</a>
<a id="21943" class="Keyword">module</a> <a id="21950" href="Data.List.Relation.Unary.Any.Properties.html#21950" class="Module">_</a> <a id="21952" class="Symbol">{</a><a id="21953" href="Data.List.Relation.Unary.Any.Properties.html#21953" class="Bound">P</a> <a id="21955" class="Symbol">:</a> <a id="21957" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="21959" class="Symbol">→</a> <a id="21961" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="21965" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a><a id="21966" class="Symbol">}</a> <a id="21968" class="Keyword">where</a>
<a id="21977" href="Data.List.Relation.Unary.Any.Properties.html#21977" class="Function">map-with-∈⁺</a> <a id="21989" class="Symbol">:</a> <a id="21991" class="Symbol">∀</a> <a id="21993" class="Symbol">{</a><a id="21994" href="Data.List.Relation.Unary.Any.Properties.html#21994" class="Bound">xs</a> <a id="21997" class="Symbol">:</a> <a id="21999" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="22004" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="22005" class="Symbol">}</a> <a id="22007" class="Symbol">(</a><a id="22008" href="Data.List.Relation.Unary.Any.Properties.html#22008" class="Bound">f</a> <a id="22010" class="Symbol">:</a> <a id="22012" class="Symbol">∀</a> <a id="22014" class="Symbol">{</a><a id="22015" href="Data.List.Relation.Unary.Any.Properties.html#22015" class="Bound">x</a><a id="22016" class="Symbol">}</a> <a id="22018" class="Symbol">→</a> <a id="22020" href="Data.List.Relation.Unary.Any.Properties.html#22015" class="Bound">x</a> <a id="22022" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="22024" href="Data.List.Relation.Unary.Any.Properties.html#21994" class="Bound">xs</a> <a id="22027" class="Symbol">→</a> <a id="22029" href="Data.List.Relation.Unary.Any.Properties.html#21957" class="Bound">B</a><a id="22030" class="Symbol">)</a> <a id="22032" class="Symbol">→</a>
<a id="22050" class="Symbol">(</a><a id="22051" href="Data.Product.html#1483" class="Function">∃₂</a> <a id="22054" class="Symbol">λ</a> <a id="22056" href="Data.List.Relation.Unary.Any.Properties.html#22056" class="Bound">x</a> <a id="22058" class="Symbol">(</a><a id="22059" href="Data.List.Relation.Unary.Any.Properties.html#22059" class="Bound">x∈xs</a> <a id="22064" class="Symbol">:</a> <a id="22066" href="Data.List.Relation.Unary.Any.Properties.html#22056" class="Bound">x</a> <a id="22068" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="22070" href="Data.List.Relation.Unary.Any.Properties.html#21994" class="Bound">xs</a><a id="22072" class="Symbol">)</a> <a id="22074" class="Symbol">→</a> <a id="22076" href="Data.List.Relation.Unary.Any.Properties.html#21953" class="Bound">P</a> <a id="22078" class="Symbol">(</a><a id="22079" href="Data.List.Relation.Unary.Any.Properties.html#22008" class="Bound">f</a> <a id="22081" href="Data.List.Relation.Unary.Any.Properties.html#22059" class="Bound">x∈xs</a><a id="22085" class="Symbol">))</a> <a id="22088" class="Symbol">→</a>
<a id="22106" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="22110" href="Data.List.Relation.Unary.Any.Properties.html#21953" class="Bound">P</a> <a id="22112" class="Symbol">(</a><a id="22113" href="Data.List.Membership.Setoid.html#1977" class="Function">map-with-∈</a> <a id="22124" href="Data.List.Relation.Unary.Any.Properties.html#21994" class="Bound">xs</a> <a id="22127" href="Data.List.Relation.Unary.Any.Properties.html#22008" class="Bound">f</a><a id="22128" class="Symbol">)</a>
<a id="22132" href="Data.List.Relation.Unary.Any.Properties.html#21977" class="Function">map-with-∈⁺</a> <a id="22144" href="Data.List.Relation.Unary.Any.Properties.html#22144" class="Bound">f</a> <a id="22146" class="Symbol">(_</a> <a id="22149" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="22151" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="22156" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a> <a id="22162" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="22164" href="Data.List.Relation.Unary.Any.Properties.html#22164" class="Bound">p</a><a id="22165" class="Symbol">)</a> <a id="22167" class="Symbol">=</a> <a id="22169" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="22174" href="Data.List.Relation.Unary.Any.Properties.html#22164" class="Bound">p</a>
<a id="22178" href="Data.List.Relation.Unary.Any.Properties.html#21977" class="Function">map-with-∈⁺</a> <a id="22190" href="Data.List.Relation.Unary.Any.Properties.html#22190" class="Bound">f</a> <a id="22192" class="Symbol">(_</a> <a id="22195" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="22197" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="22203" href="Data.List.Relation.Unary.Any.Properties.html#22203" class="Bound">x∈xs</a> <a id="22208" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="22210" href="Data.List.Relation.Unary.Any.Properties.html#22210" class="Bound">p</a><a id="22211" class="Symbol">)</a> <a id="22213" class="Symbol">=</a>
<a id="22219" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="22225" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="22227" href="Data.List.Relation.Unary.Any.Properties.html#21977" class="Function">map-with-∈⁺</a> <a id="22239" class="Symbol">(</a><a id="22240" href="Data.List.Relation.Unary.Any.Properties.html#22190" class="Bound">f</a> <a id="22242" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="22244" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a><a id="22249" class="Symbol">)</a> <a id="22251" class="Symbol">(_</a> <a id="22254" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="22256" href="Data.List.Relation.Unary.Any.Properties.html#22203" class="Bound">x∈xs</a> <a id="22261" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="22263" href="Data.List.Relation.Unary.Any.Properties.html#22210" class="Bound">p</a><a id="22264" class="Symbol">)</a>
<a id="22269" href="Data.List.Relation.Unary.Any.Properties.html#22269" class="Function">map-with-∈⁻</a> <a id="22281" class="Symbol">:</a> <a id="22283" class="Symbol">∀</a> <a id="22285" class="Symbol">(</a><a id="22286" href="Data.List.Relation.Unary.Any.Properties.html#22286" class="Bound">xs</a> <a id="22289" class="Symbol">:</a> <a id="22291" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="22296" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="22297" class="Symbol">)</a> <a id="22299" class="Symbol">(</a><a id="22300" href="Data.List.Relation.Unary.Any.Properties.html#22300" class="Bound">f</a> <a id="22302" class="Symbol">:</a> <a id="22304" class="Symbol">∀</a> <a id="22306" class="Symbol">{</a><a id="22307" href="Data.List.Relation.Unary.Any.Properties.html#22307" class="Bound">x</a><a id="22308" class="Symbol">}</a> <a id="22310" class="Symbol">→</a> <a id="22312" href="Data.List.Relation.Unary.Any.Properties.html#22307" class="Bound">x</a> <a id="22314" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="22316" href="Data.List.Relation.Unary.Any.Properties.html#22286" class="Bound">xs</a> <a id="22319" class="Symbol">→</a> <a id="22321" href="Data.List.Relation.Unary.Any.Properties.html#21957" class="Bound">B</a><a id="22322" class="Symbol">)</a> <a id="22324" class="Symbol">→</a>
<a id="22342" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="22346" href="Data.List.Relation.Unary.Any.Properties.html#21953" class="Bound">P</a> <a id="22348" class="Symbol">(</a><a id="22349" href="Data.List.Membership.Setoid.html#1977" class="Function">map-with-∈</a> <a id="22360" href="Data.List.Relation.Unary.Any.Properties.html#22286" class="Bound">xs</a> <a id="22363" href="Data.List.Relation.Unary.Any.Properties.html#22300" class="Bound">f</a><a id="22364" class="Symbol">)</a> <a id="22366" class="Symbol">→</a>
<a id="22384" href="Data.Product.html#1483" class="Function">∃₂</a> <a id="22387" class="Symbol">λ</a> <a id="22389" href="Data.List.Relation.Unary.Any.Properties.html#22389" class="Bound">x</a> <a id="22391" class="Symbol">(</a><a id="22392" href="Data.List.Relation.Unary.Any.Properties.html#22392" class="Bound">x∈xs</a> <a id="22397" class="Symbol">:</a> <a id="22399" href="Data.List.Relation.Unary.Any.Properties.html#22389" class="Bound">x</a> <a id="22401" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="22403" href="Data.List.Relation.Unary.Any.Properties.html#22286" class="Bound">xs</a><a id="22405" class="Symbol">)</a> <a id="22407" class="Symbol">→</a> <a id="22409" href="Data.List.Relation.Unary.Any.Properties.html#21953" class="Bound">P</a> <a id="22411" class="Symbol">(</a><a id="22412" href="Data.List.Relation.Unary.Any.Properties.html#22300" class="Bound">f</a> <a id="22414" href="Data.List.Relation.Unary.Any.Properties.html#22392" class="Bound">x∈xs</a><a id="22418" class="Symbol">)</a>
<a id="22422" href="Data.List.Relation.Unary.Any.Properties.html#22269" class="Function">map-with-∈⁻</a> <a id="22434" class="Symbol">(</a><a id="22435" href="Data.List.Relation.Unary.Any.Properties.html#22435" class="Bound">y</a> <a id="22437" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="22439" href="Data.List.Relation.Unary.Any.Properties.html#22439" class="Bound">xs</a><a id="22441" class="Symbol">)</a> <a id="22443" href="Data.List.Relation.Unary.Any.Properties.html#22443" class="Bound">f</a> <a id="22445" class="Symbol">(</a><a id="22446" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="22452" href="Data.List.Relation.Unary.Any.Properties.html#22452" class="Bound">p</a><a id="22453" class="Symbol">)</a> <a id="22455" class="Symbol">=</a> <a id="22457" class="Symbol">(</a><a id="22458" href="Data.List.Relation.Unary.Any.Properties.html#22435" class="Bound">y</a> <a id="22460" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="22462" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="22467" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a> <a id="22472" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="22474" href="Data.List.Relation.Unary.Any.Properties.html#22452" class="Bound">p</a><a id="22475" class="Symbol">)</a>
<a id="22479" href="Data.List.Relation.Unary.Any.Properties.html#22269" class="Function">map-with-∈⁻</a> <a id="22491" class="Symbol">(</a><a id="22492" href="Data.List.Relation.Unary.Any.Properties.html#22492" class="Bound">y</a> <a id="22494" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="22496" href="Data.List.Relation.Unary.Any.Properties.html#22496" class="Bound">xs</a><a id="22498" class="Symbol">)</a> <a id="22500" href="Data.List.Relation.Unary.Any.Properties.html#22500" class="Bound">f</a> <a id="22502" class="Symbol">(</a><a id="22503" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="22509" href="Data.List.Relation.Unary.Any.Properties.html#22509" class="Bound">p</a><a id="22510" class="Symbol">)</a> <a id="22512" class="Symbol">=</a>
<a id="22518" href="Data.Product.html#2675" class="Function">Prod.map₂</a> <a id="22528" class="Symbol">(</a><a id="22529" href="Data.Product.html#2486" class="Function">Prod.map</a> <a id="22538" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="22544" href="Function.Base.html#615" class="Function">id</a><a id="22546" class="Symbol">)</a> <a id="22548" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="22550" href="Data.List.Relation.Unary.Any.Properties.html#22269" class="Function">map-with-∈⁻</a> <a id="22562" href="Data.List.Relation.Unary.Any.Properties.html#22496" class="Bound">xs</a> <a id="22565" class="Symbol">(</a><a id="22566" href="Data.List.Relation.Unary.Any.Properties.html#22500" class="Bound">f</a> <a id="22568" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="22570" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a><a id="22575" class="Symbol">)</a> <a id="22577" href="Data.List.Relation.Unary.Any.Properties.html#22509" class="Bound">p</a>
<a id="22582" href="Data.List.Relation.Unary.Any.Properties.html#22582" class="Function">map-with-∈↔</a> <a id="22594" class="Symbol">:</a> <a id="22596" class="Symbol">∀</a> <a id="22598" class="Symbol">{</a><a id="22599" href="Data.List.Relation.Unary.Any.Properties.html#22599" class="Bound">xs</a> <a id="22602" class="Symbol">:</a> <a id="22604" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="22609" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="22610" class="Symbol">}</a> <a id="22612" class="Symbol">{</a><a id="22613" href="Data.List.Relation.Unary.Any.Properties.html#22613" class="Bound">f</a> <a id="22615" class="Symbol">:</a> <a id="22617" class="Symbol">∀</a> <a id="22619" class="Symbol">{</a><a id="22620" href="Data.List.Relation.Unary.Any.Properties.html#22620" class="Bound">x</a><a id="22621" class="Symbol">}</a> <a id="22623" class="Symbol">→</a> <a id="22625" href="Data.List.Relation.Unary.Any.Properties.html#22620" class="Bound">x</a> <a id="22627" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="22629" href="Data.List.Relation.Unary.Any.Properties.html#22599" class="Bound">xs</a> <a id="22632" class="Symbol">→</a> <a id="22634" href="Data.List.Relation.Unary.Any.Properties.html#21957" class="Bound">B</a><a id="22635" class="Symbol">}</a> <a id="22637" class="Symbol">→</a>
<a id="22655" class="Symbol">(</a><a id="22656" href="Data.Product.html#1483" class="Function">∃₂</a> <a id="22659" class="Symbol">λ</a> <a id="22661" href="Data.List.Relation.Unary.Any.Properties.html#22661" class="Bound">x</a> <a id="22663" class="Symbol">(</a><a id="22664" href="Data.List.Relation.Unary.Any.Properties.html#22664" class="Bound">x∈xs</a> <a id="22669" class="Symbol">:</a> <a id="22671" href="Data.List.Relation.Unary.Any.Properties.html#22661" class="Bound">x</a> <a id="22673" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="22675" href="Data.List.Relation.Unary.Any.Properties.html#22599" class="Bound">xs</a><a id="22677" class="Symbol">)</a> <a id="22679" class="Symbol">→</a> <a id="22681" href="Data.List.Relation.Unary.Any.Properties.html#21953" class="Bound">P</a> <a id="22683" class="Symbol">(</a><a id="22684" href="Data.List.Relation.Unary.Any.Properties.html#22613" class="Bound">f</a> <a id="22686" href="Data.List.Relation.Unary.Any.Properties.html#22664" class="Bound">x∈xs</a><a id="22690" class="Symbol">))</a> <a id="22693" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="22695" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="22699" href="Data.List.Relation.Unary.Any.Properties.html#21953" class="Bound">P</a> <a id="22701" class="Symbol">(</a><a id="22702" href="Data.List.Membership.Setoid.html#1977" class="Function">map-with-∈</a> <a id="22713" href="Data.List.Relation.Unary.Any.Properties.html#22599" class="Bound">xs</a> <a id="22716" href="Data.List.Relation.Unary.Any.Properties.html#22613" class="Bound">f</a><a id="22717" class="Symbol">)</a>
<a id="22721" href="Data.List.Relation.Unary.Any.Properties.html#22582" class="Function">map-with-∈↔</a> <a id="22733" class="Symbol">=</a> <a id="22735" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="22743" class="Symbol">(</a><a id="22744" href="Data.List.Relation.Unary.Any.Properties.html#21977" class="Function">map-with-∈⁺</a> <a id="22756" class="Symbol">_)</a> <a id="22759" class="Symbol">(</a><a id="22760" href="Data.List.Relation.Unary.Any.Properties.html#22269" class="Function">map-with-∈⁻</a> <a id="22772" class="Symbol">_</a> <a id="22774" class="Symbol">_)</a> <a id="22777" class="Symbol">(</a><a id="22778" href="Data.List.Relation.Unary.Any.Properties.html#22817" class="Function">from∘to</a> <a id="22786" class="Symbol">_)</a> <a id="22789" class="Symbol">(</a><a id="22790" href="Data.List.Relation.Unary.Any.Properties.html#23117" class="Function">to∘from</a> <a id="22798" class="Symbol">_</a> <a id="22800" class="Symbol">_)</a>
<a id="22807" class="Keyword">where</a>
<a id="22817" href="Data.List.Relation.Unary.Any.Properties.html#22817" class="Function">from∘to</a> <a id="22825" class="Symbol">:</a> <a id="22827" class="Symbol">∀</a> <a id="22829" class="Symbol">{</a><a id="22830" href="Data.List.Relation.Unary.Any.Properties.html#22830" class="Bound">xs</a> <a id="22833" class="Symbol">:</a> <a id="22835" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="22840" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="22841" class="Symbol">}</a> <a id="22843" class="Symbol">(</a><a id="22844" href="Data.List.Relation.Unary.Any.Properties.html#22844" class="Bound">f</a> <a id="22846" class="Symbol">:</a> <a id="22848" class="Symbol">∀</a> <a id="22850" class="Symbol">{</a><a id="22851" href="Data.List.Relation.Unary.Any.Properties.html#22851" class="Bound">x</a><a id="22852" class="Symbol">}</a> <a id="22854" class="Symbol">→</a> <a id="22856" href="Data.List.Relation.Unary.Any.Properties.html#22851" class="Bound">x</a> <a id="22858" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="22860" href="Data.List.Relation.Unary.Any.Properties.html#22830" class="Bound">xs</a> <a id="22863" class="Symbol">→</a> <a id="22865" href="Data.List.Relation.Unary.Any.Properties.html#21957" class="Bound">B</a><a id="22866" class="Symbol">)</a>
<a id="22882" class="Symbol">(</a><a id="22883" href="Data.List.Relation.Unary.Any.Properties.html#22883" class="Bound">p</a> <a id="22885" class="Symbol">:</a> <a id="22887" href="Data.Product.html#1483" class="Function">∃₂</a> <a id="22890" class="Symbol">λ</a> <a id="22892" href="Data.List.Relation.Unary.Any.Properties.html#22892" class="Bound">x</a> <a id="22894" class="Symbol">(</a><a id="22895" href="Data.List.Relation.Unary.Any.Properties.html#22895" class="Bound">x∈xs</a> <a id="22900" class="Symbol">:</a> <a id="22902" href="Data.List.Relation.Unary.Any.Properties.html#22892" class="Bound">x</a> <a id="22904" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="22906" href="Data.List.Relation.Unary.Any.Properties.html#22830" class="Bound">xs</a><a id="22908" class="Symbol">)</a> <a id="22910" class="Symbol">→</a> <a id="22912" href="Data.List.Relation.Unary.Any.Properties.html#21953" class="Bound">P</a> <a id="22914" class="Symbol">(</a><a id="22915" href="Data.List.Relation.Unary.Any.Properties.html#22844" class="Bound">f</a> <a id="22917" href="Data.List.Relation.Unary.Any.Properties.html#22895" class="Bound">x∈xs</a><a id="22921" class="Symbol">))</a> <a id="22924" class="Symbol">→</a>
<a id="22940" href="Data.List.Relation.Unary.Any.Properties.html#22269" class="Function">map-with-∈⁻</a> <a id="22952" href="Data.List.Relation.Unary.Any.Properties.html#22830" class="Bound">xs</a> <a id="22955" href="Data.List.Relation.Unary.Any.Properties.html#22844" class="Bound">f</a> <a id="22957" class="Symbol">(</a><a id="22958" href="Data.List.Relation.Unary.Any.Properties.html#21977" class="Function">map-with-∈⁺</a> <a id="22970" href="Data.List.Relation.Unary.Any.Properties.html#22844" class="Bound">f</a> <a id="22972" href="Data.List.Relation.Unary.Any.Properties.html#22883" class="Bound">p</a><a id="22973" class="Symbol">)</a> <a id="22975" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="22977" href="Data.List.Relation.Unary.Any.Properties.html#22883" class="Bound">p</a>
<a id="22983" href="Data.List.Relation.Unary.Any.Properties.html#22817" class="Function">from∘to</a> <a id="22991" href="Data.List.Relation.Unary.Any.Properties.html#22991" class="Bound">f</a> <a id="22993" class="Symbol">(_</a> <a id="22996" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="22998" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="23003" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a> <a id="23009" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="23011" href="Data.List.Relation.Unary.Any.Properties.html#23011" class="Bound">p</a><a id="23012" class="Symbol">)</a> <a id="23014" class="Symbol">=</a> <a id="23016" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="23025" href="Data.List.Relation.Unary.Any.Properties.html#22817" class="Function">from∘to</a> <a id="23033" href="Data.List.Relation.Unary.Any.Properties.html#23033" class="Bound">f</a> <a id="23035" class="Symbol">(_</a> <a id="23038" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="23040" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="23046" href="Data.List.Relation.Unary.Any.Properties.html#23046" class="Bound">x∈xs</a> <a id="23051" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="23053" href="Data.List.Relation.Unary.Any.Properties.html#23053" class="Bound">p</a><a id="23054" class="Symbol">)</a>
<a id="23062" class="Keyword">rewrite</a> <a id="23070" href="Data.List.Relation.Unary.Any.Properties.html#22817" class="Function">from∘to</a> <a id="23078" class="Symbol">(</a><a id="23079" href="Data.List.Relation.Unary.Any.Properties.html#23033" class="Bound">f</a> <a id="23081" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="23083" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a><a id="23088" class="Symbol">)</a> <a id="23090" class="Symbol">(_</a> <a id="23093" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="23095" href="Data.List.Relation.Unary.Any.Properties.html#23046" class="Bound">x∈xs</a> <a id="23100" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="23102" href="Data.List.Relation.Unary.Any.Properties.html#23053" class="Bound">p</a><a id="23103" class="Symbol">)</a> <a id="23105" class="Symbol">=</a> <a id="23107" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="23117" href="Data.List.Relation.Unary.Any.Properties.html#23117" class="Function">to∘from</a> <a id="23125" class="Symbol">:</a> <a id="23127" class="Symbol">∀</a> <a id="23129" class="Symbol">(</a><a id="23130" href="Data.List.Relation.Unary.Any.Properties.html#23130" class="Bound">xs</a> <a id="23133" class="Symbol">:</a> <a id="23135" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="23140" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="23141" class="Symbol">)</a> <a id="23143" class="Symbol">(</a><a id="23144" href="Data.List.Relation.Unary.Any.Properties.html#23144" class="Bound">f</a> <a id="23146" class="Symbol">:</a> <a id="23148" class="Symbol">∀</a> <a id="23150" class="Symbol">{</a><a id="23151" href="Data.List.Relation.Unary.Any.Properties.html#23151" class="Bound">x</a><a id="23152" class="Symbol">}</a> <a id="23154" class="Symbol">→</a> <a id="23156" href="Data.List.Relation.Unary.Any.Properties.html#23151" class="Bound">x</a> <a id="23158" href="Data.List.Membership.Setoid.html#887" class="Function Operator">∈</a> <a id="23160" href="Data.List.Relation.Unary.Any.Properties.html#23130" class="Bound">xs</a> <a id="23163" class="Symbol">→</a> <a id="23165" href="Data.List.Relation.Unary.Any.Properties.html#21957" class="Bound">B</a><a id="23166" class="Symbol">)</a>
<a id="23182" class="Symbol">(</a><a id="23183" href="Data.List.Relation.Unary.Any.Properties.html#23183" class="Bound">p</a> <a id="23185" class="Symbol">:</a> <a id="23187" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="23191" href="Data.List.Relation.Unary.Any.Properties.html#21953" class="Bound">P</a> <a id="23193" class="Symbol">(</a><a id="23194" href="Data.List.Membership.Setoid.html#1977" class="Function">map-with-∈</a> <a id="23205" href="Data.List.Relation.Unary.Any.Properties.html#23130" class="Bound">xs</a> <a id="23208" href="Data.List.Relation.Unary.Any.Properties.html#23144" class="Bound">f</a><a id="23209" class="Symbol">))</a> <a id="23212" class="Symbol">→</a>
<a id="23228" href="Data.List.Relation.Unary.Any.Properties.html#21977" class="Function">map-with-∈⁺</a> <a id="23240" href="Data.List.Relation.Unary.Any.Properties.html#23144" class="Bound">f</a> <a id="23242" class="Symbol">(</a><a id="23243" href="Data.List.Relation.Unary.Any.Properties.html#22269" class="Function">map-with-∈⁻</a> <a id="23255" href="Data.List.Relation.Unary.Any.Properties.html#23130" class="Bound">xs</a> <a id="23258" href="Data.List.Relation.Unary.Any.Properties.html#23144" class="Bound">f</a> <a id="23260" href="Data.List.Relation.Unary.Any.Properties.html#23183" class="Bound">p</a><a id="23261" class="Symbol">)</a> <a id="23263" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="23265" href="Data.List.Relation.Unary.Any.Properties.html#23183" class="Bound">p</a>
<a id="23271" href="Data.List.Relation.Unary.Any.Properties.html#23117" class="Function">to∘from</a> <a id="23279" class="Symbol">(</a><a id="23280" href="Data.List.Relation.Unary.Any.Properties.html#23280" class="Bound">y</a> <a id="23282" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="23284" href="Data.List.Relation.Unary.Any.Properties.html#23284" class="Bound">xs</a><a id="23286" class="Symbol">)</a> <a id="23288" href="Data.List.Relation.Unary.Any.Properties.html#23288" class="Bound">f</a> <a id="23290" class="Symbol">(</a><a id="23291" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="23297" href="Data.List.Relation.Unary.Any.Properties.html#23297" class="Bound">p</a><a id="23298" class="Symbol">)</a> <a id="23300" class="Symbol">=</a> <a id="23302" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="23311" href="Data.List.Relation.Unary.Any.Properties.html#23117" class="Function">to∘from</a> <a id="23319" class="Symbol">(</a><a id="23320" href="Data.List.Relation.Unary.Any.Properties.html#23320" class="Bound">y</a> <a id="23322" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="23324" href="Data.List.Relation.Unary.Any.Properties.html#23324" class="Bound">xs</a><a id="23326" class="Symbol">)</a> <a id="23328" href="Data.List.Relation.Unary.Any.Properties.html#23328" class="Bound">f</a> <a id="23330" class="Symbol">(</a><a id="23331" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="23337" href="Data.List.Relation.Unary.Any.Properties.html#23337" class="Bound">p</a><a id="23338" class="Symbol">)</a> <a id="23340" class="Symbol">=</a>
<a id="23348" href="Relation.Binary.PropositionalEquality.Core.html#1130" class="Function">P.cong</a> <a id="23355" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="23361" href="Function.Base.html#1919" class="Function Operator">$</a> <a id="23363" href="Data.List.Relation.Unary.Any.Properties.html#23117" class="Function">to∘from</a> <a id="23371" href="Data.List.Relation.Unary.Any.Properties.html#23324" class="Bound">xs</a> <a id="23374" class="Symbol">(</a><a id="23375" href="Data.List.Relation.Unary.Any.Properties.html#23328" class="Bound">f</a> <a id="23377" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="23379" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a><a id="23384" class="Symbol">)</a> <a id="23386" href="Data.List.Relation.Unary.Any.Properties.html#23337" class="Bound">p</a>
<a id="23389" class="Comment">------------------------------------------------------------------------</a>
<a id="23462" class="Comment">-- reverse</a>
<a id="reverseAcc⁺"></a><a id="23474" href="Data.List.Relation.Unary.Any.Properties.html#23474" class="Function">reverseAcc⁺</a> <a id="23486" class="Symbol">:</a> <a id="23488" class="Symbol">∀</a> <a id="23490" href="Data.List.Relation.Unary.Any.Properties.html#23490" class="Bound">acc</a> <a id="23494" href="Data.List.Relation.Unary.Any.Properties.html#23494" class="Bound">xs</a> <a id="23497" class="Symbol">→</a> <a id="23499" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="23503" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="23505" href="Data.List.Relation.Unary.Any.Properties.html#23490" class="Bound">acc</a> <a id="23509" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="23511" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="23515" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="23517" href="Data.List.Relation.Unary.Any.Properties.html#23494" class="Bound">xs</a> <a id="23520" class="Symbol">→</a> <a id="23522" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="23526" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="23528" class="Symbol">(</a><a id="23529" href="Data.List.Base.html#9748" class="Function">reverseAcc</a> <a id="23540" href="Data.List.Relation.Unary.Any.Properties.html#23490" class="Bound">acc</a> <a id="23544" href="Data.List.Relation.Unary.Any.Properties.html#23494" class="Bound">xs</a><a id="23546" class="Symbol">)</a>
<a id="23548" href="Data.List.Relation.Unary.Any.Properties.html#23474" class="Function">reverseAcc⁺</a> <a id="23560" href="Data.List.Relation.Unary.Any.Properties.html#23560" class="Bound">acc</a> <a id="23564" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="23573" class="Symbol">(</a><a id="23574" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="23579" href="Data.List.Relation.Unary.Any.Properties.html#23579" class="Bound">ps</a><a id="23581" class="Symbol">)</a> <a id="23590" class="Symbol">=</a> <a id="23592" href="Data.List.Relation.Unary.Any.Properties.html#23579" class="Bound">ps</a>
<a id="23595" href="Data.List.Relation.Unary.Any.Properties.html#23474" class="Function">reverseAcc⁺</a> <a id="23607" href="Data.List.Relation.Unary.Any.Properties.html#23607" class="Bound">acc</a> <a id="23611" class="Symbol">(</a><a id="23612" href="Data.List.Relation.Unary.Any.Properties.html#23612" class="Bound">x</a> <a id="23614" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="23616" href="Data.List.Relation.Unary.Any.Properties.html#23616" class="Bound">xs</a><a id="23618" class="Symbol">)</a> <a id="23620" class="Symbol">(</a><a id="23621" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="23626" href="Data.List.Relation.Unary.Any.Properties.html#23626" class="Bound">ps</a><a id="23628" class="Symbol">)</a> <a id="23637" class="Symbol">=</a> <a id="23639" href="Data.List.Relation.Unary.Any.Properties.html#23474" class="Function">reverseAcc⁺</a> <a id="23651" class="Symbol">(</a><a id="23652" href="Data.List.Relation.Unary.Any.Properties.html#23612" class="Bound">x</a> <a id="23654" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="23656" href="Data.List.Relation.Unary.Any.Properties.html#23607" class="Bound">acc</a><a id="23659" class="Symbol">)</a> <a id="23661" href="Data.List.Relation.Unary.Any.Properties.html#23616" class="Bound">xs</a> <a id="23664" class="Symbol">(</a><a id="23665" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="23670" class="Symbol">(</a><a id="23671" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="23677" href="Data.List.Relation.Unary.Any.Properties.html#23626" class="Bound">ps</a><a id="23679" class="Symbol">))</a>
<a id="23682" href="Data.List.Relation.Unary.Any.Properties.html#23474" class="Function">reverseAcc⁺</a> <a id="23694" href="Data.List.Relation.Unary.Any.Properties.html#23694" class="Bound">acc</a> <a id="23698" class="Symbol">(</a><a id="23699" href="Data.List.Relation.Unary.Any.Properties.html#23699" class="Bound">x</a> <a id="23701" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="23703" href="Data.List.Relation.Unary.Any.Properties.html#23703" class="Bound">xs</a><a id="23705" class="Symbol">)</a> <a id="23707" class="Symbol">(</a><a id="23708" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="23713" class="Symbol">(</a><a id="23714" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="23719" href="Data.List.Relation.Unary.Any.Properties.html#23719" class="Bound">px</a><a id="23721" class="Symbol">))</a> <a id="23724" class="Symbol">=</a> <a id="23726" href="Data.List.Relation.Unary.Any.Properties.html#23474" class="Function">reverseAcc⁺</a> <a id="23738" class="Symbol">(</a><a id="23739" href="Data.List.Relation.Unary.Any.Properties.html#23699" class="Bound">x</a> <a id="23741" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="23743" href="Data.List.Relation.Unary.Any.Properties.html#23694" class="Bound">acc</a><a id="23746" class="Symbol">)</a> <a id="23748" href="Data.List.Relation.Unary.Any.Properties.html#23703" class="Bound">xs</a> <a id="23751" class="Symbol">(</a><a id="23752" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="23757" class="Symbol">(</a><a id="23758" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="23763" href="Data.List.Relation.Unary.Any.Properties.html#23719" class="Bound">px</a><a id="23765" class="Symbol">))</a>
<a id="23768" href="Data.List.Relation.Unary.Any.Properties.html#23474" class="Function">reverseAcc⁺</a> <a id="23780" href="Data.List.Relation.Unary.Any.Properties.html#23780" class="Bound">acc</a> <a id="23784" class="Symbol">(</a><a id="23785" href="Data.List.Relation.Unary.Any.Properties.html#23785" class="Bound">x</a> <a id="23787" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="23789" href="Data.List.Relation.Unary.Any.Properties.html#23789" class="Bound">xs</a><a id="23791" class="Symbol">)</a> <a id="23793" class="Symbol">(</a><a id="23794" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="23799" class="Symbol">(</a><a id="23800" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="23806" href="Data.List.Relation.Unary.Any.Properties.html#23806" class="Bound">y</a><a id="23807" class="Symbol">))</a> <a id="23810" class="Symbol">=</a> <a id="23812" href="Data.List.Relation.Unary.Any.Properties.html#23474" class="Function">reverseAcc⁺</a> <a id="23824" class="Symbol">(</a><a id="23825" href="Data.List.Relation.Unary.Any.Properties.html#23785" class="Bound">x</a> <a id="23827" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="23829" href="Data.List.Relation.Unary.Any.Properties.html#23780" class="Bound">acc</a><a id="23832" class="Symbol">)</a> <a id="23834" href="Data.List.Relation.Unary.Any.Properties.html#23789" class="Bound">xs</a> <a id="23837" class="Symbol">(</a><a id="23838" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="23843" href="Data.List.Relation.Unary.Any.Properties.html#23806" class="Bound">y</a><a id="23844" class="Symbol">)</a>
<a id="reverseAcc⁻"></a><a id="23847" href="Data.List.Relation.Unary.Any.Properties.html#23847" class="Function">reverseAcc⁻</a> <a id="23859" class="Symbol">:</a> <a id="23861" class="Symbol">∀</a> <a id="23863" href="Data.List.Relation.Unary.Any.Properties.html#23863" class="Bound">acc</a> <a id="23867" href="Data.List.Relation.Unary.Any.Properties.html#23867" class="Bound">xs</a> <a id="23870" class="Symbol">→</a> <a id="23872" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="23876" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="23878" class="Symbol">(</a><a id="23879" href="Data.List.Base.html#9748" class="Function">reverseAcc</a> <a id="23890" href="Data.List.Relation.Unary.Any.Properties.html#23863" class="Bound">acc</a> <a id="23894" href="Data.List.Relation.Unary.Any.Properties.html#23867" class="Bound">xs</a><a id="23896" class="Symbol">)</a> <a id="23898" class="Symbol">→</a> <a id="23900" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="23904" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="23906" href="Data.List.Relation.Unary.Any.Properties.html#23863" class="Bound">acc</a> <a id="23910" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="23912" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="23916" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="23918" href="Data.List.Relation.Unary.Any.Properties.html#23867" class="Bound">xs</a>
<a id="23921" href="Data.List.Relation.Unary.Any.Properties.html#23847" class="Function">reverseAcc⁻</a> <a id="23933" href="Data.List.Relation.Unary.Any.Properties.html#23933" class="Bound">acc</a> <a id="23937" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="23946" href="Data.List.Relation.Unary.Any.Properties.html#23946" class="Bound">ps</a> <a id="23949" class="Symbol">=</a> <a id="23951" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="23956" href="Data.List.Relation.Unary.Any.Properties.html#23946" class="Bound">ps</a>
<a id="23959" href="Data.List.Relation.Unary.Any.Properties.html#23847" class="Function">reverseAcc⁻</a> <a id="23971" href="Data.List.Relation.Unary.Any.Properties.html#23971" class="Bound">acc</a> <a id="23975" class="Symbol">(</a><a id="23976" href="Data.List.Relation.Unary.Any.Properties.html#23976" class="Bound">x</a> <a id="23978" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="23980" href="Data.List.Relation.Unary.Any.Properties.html#23980" class="Bound">xs</a><a id="23982" class="Symbol">)</a> <a id="23984" href="Data.List.Relation.Unary.Any.Properties.html#23984" class="Bound">ps</a> <a id="23987" class="Keyword">rewrite</a> <a id="23995" href="Data.List.Properties.html#31429" class="Function">ʳ++-defn</a> <a id="24004" href="Data.List.Relation.Unary.Any.Properties.html#23980" class="Bound">xs</a> <a id="24007" class="Symbol">{</a><a id="24008" href="Data.List.Relation.Unary.Any.Properties.html#23976" class="Bound">x</a> <a id="24010" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="24012" href="Data.List.Relation.Unary.Any.Properties.html#23971" class="Bound">acc</a><a id="24015" class="Symbol">}</a> <a id="24017" class="Keyword">with</a> <a id="24022" href="Data.List.Relation.Unary.Any.Properties.html#12422" class="Function">++⁻</a> <a id="24026" class="Symbol">(</a><a id="24027" href="Data.List.Base.html#9748" class="Function">reverseAcc</a> <a id="24038" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="24041" href="Data.List.Relation.Unary.Any.Properties.html#23980" class="Bound">xs</a><a id="24043" class="Symbol">)</a> <a id="24045" href="Data.List.Relation.Unary.Any.Properties.html#23984" class="Bound">ps</a>
<a id="24048" class="Symbol">...</a> <a id="24052" class="Symbol">|</a> <a id="24054" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="24059" class="Symbol">(</a><a id="24060" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="24065" href="Data.List.Relation.Unary.Any.Properties.html#24065" class="Bound">p'</a><a id="24067" class="Symbol">)</a> <a id="24069" class="Symbol">=</a> <a id="24071" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="24076" class="Symbol">(</a><a id="24077" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="24082" href="Data.List.Relation.Unary.Any.Properties.html#24065" class="Bound">p'</a><a id="24084" class="Symbol">)</a>
<a id="24086" class="Symbol">...</a> <a id="24090" class="Symbol">|</a> <a id="24092" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="24097" class="Symbol">(</a><a id="24098" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="24104" href="Data.List.Relation.Unary.Any.Properties.html#24104" class="Bound">ps'</a><a id="24107" class="Symbol">)</a> <a id="24109" class="Symbol">=</a> <a id="24111" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="24116" href="Data.List.Relation.Unary.Any.Properties.html#24104" class="Bound">ps'</a>
<a id="24120" class="Symbol">...</a> <a id="24124" class="Symbol">|</a> <a id="24126" href="Data.Sum.Base.html#784" class="InductiveConstructor">inj₁</a> <a id="24131" href="Data.List.Relation.Unary.Any.Properties.html#24131" class="Bound">ps'</a> <a id="24135" class="Keyword">with</a> <a id="24140" href="Data.List.Relation.Unary.Any.Properties.html#23847" class="Function">reverseAcc⁻</a> <a id="24152" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="24155" class="Bound">xs</a> <a id="24158" href="Data.List.Relation.Unary.Any.Properties.html#24131" class="Bound">ps'</a>
<a id="24162" class="Symbol">...</a> <a id="24168" class="Symbol">|</a> <a id="24170" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="24175" href="Data.List.Relation.Unary.Any.Properties.html#24175" class="Bound">ps''</a> <a id="24180" class="Symbol">=</a> <a id="24182" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="24187" class="Symbol">(</a><a id="24188" href="Data.List.Relation.Unary.Any.html#1272" class="InductiveConstructor">there</a> <a id="24194" href="Data.List.Relation.Unary.Any.Properties.html#24175" class="Bound">ps''</a><a id="24198" class="Symbol">)</a>
<a id="reverse⁺"></a><a id="24201" href="Data.List.Relation.Unary.Any.Properties.html#24201" class="Function">reverse⁺</a> <a id="24210" class="Symbol">:</a> <a id="24212" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="24216" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="24218" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="24221" class="Symbol">→</a> <a id="24223" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="24227" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="24229" class="Symbol">(</a><a id="24230" href="Data.List.Base.html#9817" class="Function">reverse</a> <a id="24238" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="24240" class="Symbol">)</a>
<a id="24242" href="Data.List.Relation.Unary.Any.Properties.html#24201" class="Function">reverse⁺</a> <a id="24251" href="Data.List.Relation.Unary.Any.Properties.html#24251" class="Bound">ps</a> <a id="24254" class="Symbol">=</a> <a id="24256" href="Data.List.Relation.Unary.Any.Properties.html#23474" class="Function">reverseAcc⁺</a> <a id="24268" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="24271" class="Symbol">_</a> <a id="24273" class="Symbol">(</a><a id="24274" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="24279" href="Data.List.Relation.Unary.Any.Properties.html#24251" class="Bound">ps</a><a id="24281" class="Symbol">)</a>
<a id="reverse⁻"></a><a id="24284" href="Data.List.Relation.Unary.Any.Properties.html#24284" class="Function">reverse⁻</a> <a id="24293" class="Symbol">:</a> <a id="24295" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="24299" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="24301" class="Symbol">(</a><a id="24302" href="Data.List.Base.html#9817" class="Function">reverse</a> <a id="24310" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="24312" class="Symbol">)</a> <a id="24314" class="Symbol">→</a> <a id="24316" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="24320" href="Data.List.Relation.Unary.Any.Properties.html#2440" class="Generalizable">P</a> <a id="24322" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a>
<a id="24325" href="Data.List.Relation.Unary.Any.Properties.html#24284" class="Function">reverse⁻</a> <a id="24334" href="Data.List.Relation.Unary.Any.Properties.html#24334" class="Bound">ps</a> <a id="24337" class="Keyword">with</a> <a id="24342" href="Data.List.Relation.Unary.Any.Properties.html#23847" class="Function">reverseAcc⁻</a> <a id="24354" href="Agda.Builtin.List.html#185" class="InductiveConstructor">[]</a> <a id="24357" class="Symbol">_</a> <a id="24359" href="Data.List.Relation.Unary.Any.Properties.html#24334" class="Bound">ps</a>
<a id="24362" class="Symbol">...</a> <a id="24366" class="Symbol">|</a> <a id="24368" href="Data.Sum.Base.html#809" class="InductiveConstructor">inj₂</a> <a id="24373" href="Data.List.Relation.Unary.Any.Properties.html#24373" class="Bound">ps'</a> <a id="24377" class="Symbol">=</a> <a id="24379" href="Data.List.Relation.Unary.Any.Properties.html#24373" class="Bound">ps'</a>
<a id="24384" class="Comment">------------------------------------------------------------------------</a>
<a id="24457" class="Comment">-- return</a>
<a id="24468" class="Keyword">module</a> <a id="24475" href="Data.List.Relation.Unary.Any.Properties.html#24475" class="Module">_</a> <a id="24477" class="Symbol">{</a><a id="24478" href="Data.List.Relation.Unary.Any.Properties.html#24478" class="Bound">P</a> <a id="24480" class="Symbol">:</a> <a id="24482" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="24484" class="Symbol">→</a> <a id="24486" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="24490" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a><a id="24491" class="Symbol">}</a> <a id="24493" class="Keyword">where</a>
<a id="24502" href="Data.List.Relation.Unary.Any.Properties.html#24502" class="Function">return⁺</a> <a id="24510" class="Symbol">:</a> <a id="24512" href="Data.List.Relation.Unary.Any.Properties.html#24478" class="Bound">P</a> <a id="24514" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="24516" class="Symbol">→</a> <a id="24518" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="24522" href="Data.List.Relation.Unary.Any.Properties.html#24478" class="Bound">P</a> <a id="24524" class="Symbol">(</a><a id="24525" href="Category.Monad.Indexed.html#644" class="Function">return</a> <a id="24532" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a><a id="24533" class="Symbol">)</a>
<a id="24537" href="Data.List.Relation.Unary.Any.Properties.html#24502" class="Function">return⁺</a> <a id="24545" class="Symbol">=</a> <a id="24547" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a>
<a id="24555" href="Data.List.Relation.Unary.Any.Properties.html#24555" class="Function">return⁻</a> <a id="24563" class="Symbol">:</a> <a id="24565" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="24569" href="Data.List.Relation.Unary.Any.Properties.html#24478" class="Bound">P</a> <a id="24571" class="Symbol">(</a><a id="24572" href="Category.Monad.Indexed.html#644" class="Function">return</a> <a id="24579" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a><a id="24580" class="Symbol">)</a> <a id="24582" class="Symbol">→</a> <a id="24584" href="Data.List.Relation.Unary.Any.Properties.html#24478" class="Bound">P</a> <a id="24586" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a>
<a id="24590" href="Data.List.Relation.Unary.Any.Properties.html#24555" class="Function">return⁻</a> <a id="24598" class="Symbol">(</a><a id="24599" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="24604" href="Data.List.Relation.Unary.Any.Properties.html#24604" class="Bound">p</a><a id="24605" class="Symbol">)</a> <a id="24607" class="Symbol">=</a> <a id="24609" href="Data.List.Relation.Unary.Any.Properties.html#24604" class="Bound">p</a>
<a id="24614" href="Data.List.Relation.Unary.Any.Properties.html#24614" class="Function">return⁺∘return⁻</a> <a id="24630" class="Symbol">:</a> <a id="24632" class="Symbol">(</a><a id="24633" href="Data.List.Relation.Unary.Any.Properties.html#24633" class="Bound">p</a> <a id="24635" class="Symbol">:</a> <a id="24637" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="24641" href="Data.List.Relation.Unary.Any.Properties.html#24478" class="Bound">P</a> <a id="24643" class="Symbol">(</a><a id="24644" href="Category.Monad.Indexed.html#644" class="Function">return</a> <a id="24651" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a><a id="24652" class="Symbol">))</a> <a id="24655" class="Symbol">→</a> <a id="24657" href="Data.List.Relation.Unary.Any.Properties.html#24502" class="Function">return⁺</a> <a id="24665" class="Symbol">(</a><a id="24666" href="Data.List.Relation.Unary.Any.Properties.html#24555" class="Function">return⁻</a> <a id="24674" href="Data.List.Relation.Unary.Any.Properties.html#24633" class="Bound">p</a><a id="24675" class="Symbol">)</a> <a id="24677" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="24679" href="Data.List.Relation.Unary.Any.Properties.html#24633" class="Bound">p</a>
<a id="24683" href="Data.List.Relation.Unary.Any.Properties.html#24614" class="Function">return⁺∘return⁻</a> <a id="24699" class="Symbol">(</a><a id="24700" href="Data.List.Relation.Unary.Any.html#1219" class="InductiveConstructor">here</a> <a id="24705" href="Data.List.Relation.Unary.Any.Properties.html#24705" class="Bound">p</a><a id="24706" class="Symbol">)</a> <a id="24708" class="Symbol">=</a> <a id="24710" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="24718" href="Data.List.Relation.Unary.Any.Properties.html#24718" class="Function">return⁻∘return⁺</a> <a id="24734" class="Symbol">:</a> <a id="24736" class="Symbol">(</a><a id="24737" href="Data.List.Relation.Unary.Any.Properties.html#24737" class="Bound">p</a> <a id="24739" class="Symbol">:</a> <a id="24741" href="Data.List.Relation.Unary.Any.Properties.html#24478" class="Bound">P</a> <a id="24743" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a><a id="24744" class="Symbol">)</a> <a id="24746" class="Symbol">→</a> <a id="24748" href="Data.List.Relation.Unary.Any.Properties.html#24555" class="Function">return⁻</a> <a id="24756" class="Symbol">(</a><a id="24757" href="Data.List.Relation.Unary.Any.Properties.html#24502" class="Function">return⁺</a> <a id="24765" href="Data.List.Relation.Unary.Any.Properties.html#24737" class="Bound">p</a><a id="24766" class="Symbol">)</a> <a id="24768" href="Agda.Builtin.Equality.html#151" class="Datatype Operator">≡</a> <a id="24770" href="Data.List.Relation.Unary.Any.Properties.html#24737" class="Bound">p</a>
<a id="24774" href="Data.List.Relation.Unary.Any.Properties.html#24718" class="Function">return⁻∘return⁺</a> <a id="24790" href="Data.List.Relation.Unary.Any.Properties.html#24790" class="Bound">p</a> <a id="24792" class="Symbol">=</a> <a id="24794" href="Agda.Builtin.Equality.html#208" class="InductiveConstructor">refl</a>
<a id="24802" href="Data.List.Relation.Unary.Any.Properties.html#24802" class="Function">return↔</a> <a id="24810" class="Symbol">:</a> <a id="24812" href="Data.List.Relation.Unary.Any.Properties.html#24478" class="Bound">P</a> <a id="24814" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="24816" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="24818" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="24822" href="Data.List.Relation.Unary.Any.Properties.html#24478" class="Bound">P</a> <a id="24824" class="Symbol">(</a><a id="24825" href="Category.Monad.Indexed.html#644" class="Function">return</a> <a id="24832" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a><a id="24833" class="Symbol">)</a>
<a id="24837" href="Data.List.Relation.Unary.Any.Properties.html#24802" class="Function">return↔</a> <a id="24845" class="Symbol">=</a> <a id="24847" href="Function.Inverse.html#2641" class="Function">inverse</a> <a id="24855" href="Data.List.Relation.Unary.Any.Properties.html#24502" class="Function">return⁺</a> <a id="24863" href="Data.List.Relation.Unary.Any.Properties.html#24555" class="Function">return⁻</a> <a id="24871" href="Data.List.Relation.Unary.Any.Properties.html#24718" class="Function">return⁻∘return⁺</a> <a id="24887" href="Data.List.Relation.Unary.Any.Properties.html#24614" class="Function">return⁺∘return⁻</a>
<a id="24904" class="Comment">------------------------------------------------------------------------</a>
<a id="24977" class="Comment">-- _∷_</a>
<a id="24985" class="Keyword">module</a> <a id="24992" href="Data.List.Relation.Unary.Any.Properties.html#24992" class="Module">_</a> <a id="24994" class="Symbol">(</a><a id="24995" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="24997" class="Symbol">:</a> <a id="24999" href="Relation.Unary.html#1101" class="Function">Pred</a> <a id="25004" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="25006" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a><a id="25007" class="Symbol">)</a> <a id="25009" class="Keyword">where</a>
<a id="25018" href="Data.List.Relation.Unary.Any.Properties.html#25018" class="Function">∷↔</a> <a id="25021" class="Symbol">:</a> <a id="25023" class="Symbol">(</a><a id="25024" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="25026" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="25028" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="25030" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25034" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="25036" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="25038" class="Symbol">)</a> <a id="25040" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="25042" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25046" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="25048" class="Symbol">(</a><a id="25049" href="Data.List.Relation.Unary.Any.Properties.html#2461" class="Generalizable">x</a> <a id="25051" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="25053" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a><a id="25055" class="Symbol">)</a>
<a id="25059" href="Data.List.Relation.Unary.Any.Properties.html#25018" class="Function">∷↔</a> <a id="25062" class="Symbol">{</a><a id="25063" class="Argument">x</a> <a id="25065" class="Symbol">=</a> <a id="25067" href="Data.List.Relation.Unary.Any.Properties.html#25067" class="Bound">x</a><a id="25068" class="Symbol">}</a> <a id="25070" class="Symbol">{</a><a id="25071" href="Data.List.Relation.Unary.Any.Properties.html#25071" class="Bound">xs</a><a id="25073" class="Symbol">}</a> <a id="25075" class="Symbol">=</a>
<a id="25081" class="Symbol">(</a><a id="25082" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="25084" href="Data.List.Relation.Unary.Any.Properties.html#25067" class="Bound">x</a> <a id="25094" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="25096" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25100" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="25102" href="Data.List.Relation.Unary.Any.Properties.html#25071" class="Bound">xs</a><a id="25104" class="Symbol">)</a> <a id="25107" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="25110" href="Data.List.Relation.Unary.Any.Properties.html#24802" class="Function">return↔</a> <a id="25118" class="Symbol">{</a><a id="25119" class="Argument">P</a> <a id="25121" class="Symbol">=</a> <a id="25123" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a><a id="25124" class="Symbol">}</a> <a id="25126" href="Data.Sum.Function.Propositional.html#2320" class="Function Operator">⊎-cong</a> <a id="25133" class="Symbol">(</a><a id="25134" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25138" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="25140" href="Data.List.Relation.Unary.Any.Properties.html#25071" class="Bound">xs</a> <a id="25143" href="Function.Related.html#10453" class="Function Operator">∎</a><a id="25144" class="Symbol">)</a> <a id="25146" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="25152" class="Symbol">(</a><a id="25153" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25157" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="25159" href="Data.List.Base.html#5025" class="Function Operator">[</a> <a id="25161" href="Data.List.Relation.Unary.Any.Properties.html#25067" class="Bound">x</a> <a id="25163" href="Data.List.Base.html#5025" class="Function Operator">]</a> <a id="25165" href="Data.Sum.Base.html#734" class="Datatype Operator">⊎</a> <a id="25167" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25171" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="25173" href="Data.List.Relation.Unary.Any.Properties.html#25071" class="Bound">xs</a><a id="25175" class="Symbol">)</a> <a id="25178" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="25181" href="Data.List.Relation.Unary.Any.Properties.html#13259" class="Function">++↔</a> <a id="25185" class="Symbol">{</a><a id="25186" class="Argument">P</a> <a id="25188" class="Symbol">=</a> <a id="25190" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a><a id="25191" class="Symbol">}</a> <a id="25193" class="Symbol">{</a><a id="25194" class="Argument">xs</a> <a id="25197" class="Symbol">=</a> <a id="25199" href="Data.List.Base.html#5025" class="Function Operator">[</a> <a id="25201" href="Data.List.Relation.Unary.Any.Properties.html#25067" class="Bound">x</a> <a id="25203" href="Data.List.Base.html#5025" class="Function Operator">]</a><a id="25204" class="Symbol">}</a> <a id="25206" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="25212" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25216" href="Data.List.Relation.Unary.Any.Properties.html#24995" class="Bound">P</a> <a id="25218" class="Symbol">(</a><a id="25219" href="Data.List.Relation.Unary.Any.Properties.html#25067" class="Bound">x</a> <a id="25221" href="Agda.Builtin.List.html#200" class="InductiveConstructor Operator">∷</a> <a id="25223" href="Data.List.Relation.Unary.Any.Properties.html#25071" class="Bound">xs</a><a id="25225" class="Symbol">)</a> <a id="25238" href="Function.Related.html#10453" class="Function Operator">∎</a>
<a id="25244" class="Keyword">where</a> <a id="25250" class="Keyword">open</a> <a id="25255" href="Function.Related.html#9774" class="Module">Related.EquationalReasoning</a>
<a id="25284" class="Comment">------------------------------------------------------------------------</a>
<a id="25357" class="Comment">-- _>>=_</a>
<a id="25367" class="Keyword">module</a> <a id="25374" href="Data.List.Relation.Unary.Any.Properties.html#25374" class="Module">_</a> <a id="25376" class="Symbol">{</a><a id="25377" href="Data.List.Relation.Unary.Any.Properties.html#25377" class="Bound">A</a> <a id="25379" href="Data.List.Relation.Unary.Any.Properties.html#25379" class="Bound">B</a> <a id="25381" class="Symbol">:</a> <a id="25383" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="25387" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="25388" class="Symbol">}</a> <a id="25390" class="Symbol">{</a><a id="25391" href="Data.List.Relation.Unary.Any.Properties.html#25391" class="Bound">P</a> <a id="25393" class="Symbol">:</a> <a id="25395" href="Data.List.Relation.Unary.Any.Properties.html#25379" class="Bound">B</a> <a id="25397" class="Symbol">→</a> <a id="25399" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="25403" href="Data.List.Relation.Unary.Any.Properties.html#2378" class="Generalizable">p</a><a id="25404" class="Symbol">}</a> <a id="25406" class="Symbol">{</a><a id="25407" href="Data.List.Relation.Unary.Any.Properties.html#25407" class="Bound">f</a> <a id="25409" class="Symbol">:</a> <a id="25411" href="Data.List.Relation.Unary.Any.Properties.html#25377" class="Bound">A</a> <a id="25413" class="Symbol">→</a> <a id="25415" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="25420" href="Data.List.Relation.Unary.Any.Properties.html#25379" class="Bound">B</a><a id="25421" class="Symbol">}</a> <a id="25423" class="Keyword">where</a>
<a id="25432" href="Data.List.Relation.Unary.Any.Properties.html#25432" class="Function">>>=↔</a> <a id="25437" class="Symbol">:</a> <a id="25439" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25443" class="Symbol">(</a><a id="25444" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25448" href="Data.List.Relation.Unary.Any.Properties.html#25391" class="Bound">P</a> <a id="25450" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="25452" href="Data.List.Relation.Unary.Any.Properties.html#25407" class="Bound">f</a><a id="25453" class="Symbol">)</a> <a id="25455" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="25458" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="25460" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25464" href="Data.List.Relation.Unary.Any.Properties.html#25391" class="Bound">P</a> <a id="25466" class="Symbol">(</a><a id="25467" href="Data.List.Relation.Unary.Any.Properties.html#2473" class="Generalizable">xs</a> <a id="25470" href="Category.Monad.Indexed.html#677" class="Function Operator">>>=</a> <a id="25474" href="Data.List.Relation.Unary.Any.Properties.html#25407" class="Bound">f</a><a id="25475" class="Symbol">)</a>
<a id="25479" href="Data.List.Relation.Unary.Any.Properties.html#25432" class="Function">>>=↔</a> <a id="25484" class="Symbol">{</a><a id="25485" class="Argument">xs</a> <a id="25488" class="Symbol">=</a> <a id="25490" href="Data.List.Relation.Unary.Any.Properties.html#25490" class="Bound">xs</a><a id="25492" class="Symbol">}</a> <a id="25494" class="Symbol">=</a>
<a id="25500" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25504" class="Symbol">(</a><a id="25505" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25509" href="Data.List.Relation.Unary.Any.Properties.html#25391" class="Bound">P</a> <a id="25511" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="25513" href="Data.List.Relation.Unary.Any.Properties.html#25407" class="Bound">f</a><a id="25514" class="Symbol">)</a> <a id="25516" href="Data.List.Relation.Unary.Any.Properties.html#25490" class="Bound">xs</a> <a id="25529" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="25532" href="Data.List.Relation.Unary.Any.Properties.html#11541" class="Function">map↔</a> <a id="25537" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="25543" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25547" class="Symbol">(</a><a id="25548" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25552" href="Data.List.Relation.Unary.Any.Properties.html#25391" class="Bound">P</a><a id="25553" class="Symbol">)</a> <a id="25555" class="Symbol">(</a><a id="25556" href="Data.List.Base.html#1544" class="Function">List.map</a> <a id="25565" href="Data.List.Relation.Unary.Any.Properties.html#25407" class="Bound">f</a> <a id="25567" href="Data.List.Relation.Unary.Any.Properties.html#25490" class="Bound">xs</a><a id="25569" class="Symbol">)</a> <a id="25572" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="25575" href="Data.List.Relation.Unary.Any.Properties.html#16297" class="Function">concat↔</a> <a id="25583" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="25589" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25593" href="Data.List.Relation.Unary.Any.Properties.html#25391" class="Bound">P</a> <a id="25595" class="Symbol">(</a><a id="25596" href="Data.List.Relation.Unary.Any.Properties.html#25490" class="Bound">xs</a> <a id="25599" href="Category.Monad.Indexed.html#677" class="Function Operator">>>=</a> <a id="25603" href="Data.List.Relation.Unary.Any.Properties.html#25407" class="Bound">f</a><a id="25604" class="Symbol">)</a> <a id="25618" href="Function.Related.html#10453" class="Function Operator">∎</a>
<a id="25624" class="Keyword">where</a> <a id="25630" class="Keyword">open</a> <a id="25635" href="Function.Related.html#9774" class="Module">Related.EquationalReasoning</a>
<a id="25664" class="Comment">------------------------------------------------------------------------</a>
<a id="25737" class="Comment">-- _⊛_</a>
<a id="⊛↔"></a><a id="25745" href="Data.List.Relation.Unary.Any.Properties.html#25745" class="Function">⊛↔</a> <a id="25748" class="Symbol">:</a> <a id="25750" class="Symbol">∀</a> <a id="25752" class="Symbol">{</a><a id="25753" href="Data.List.Relation.Unary.Any.Properties.html#25753" class="Bound">P</a> <a id="25755" class="Symbol">:</a> <a id="25757" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="25759" class="Symbol">→</a> <a id="25761" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="25765" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="25766" class="Symbol">}</a> <a id="25768" class="Symbol">{</a><a id="25769" href="Data.List.Relation.Unary.Any.Properties.html#25769" class="Bound">fs</a> <a id="25772" class="Symbol">:</a> <a id="25774" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="25779" class="Symbol">(</a><a id="25780" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="25782" class="Symbol">→</a> <a id="25784" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a><a id="25785" class="Symbol">)}</a> <a id="25788" class="Symbol">{</a><a id="25789" href="Data.List.Relation.Unary.Any.Properties.html#25789" class="Bound">xs</a> <a id="25792" class="Symbol">:</a> <a id="25794" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="25799" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="25800" class="Symbol">}</a> <a id="25802" class="Symbol">→</a>
<a id="25809" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25813" class="Symbol">(λ</a> <a id="25816" href="Data.List.Relation.Unary.Any.Properties.html#25816" class="Bound">f</a> <a id="25818" class="Symbol">→</a> <a id="25820" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25824" class="Symbol">(</a><a id="25825" href="Data.List.Relation.Unary.Any.Properties.html#25753" class="Bound">P</a> <a id="25827" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="25829" href="Data.List.Relation.Unary.Any.Properties.html#25816" class="Bound">f</a><a id="25830" class="Symbol">)</a> <a id="25832" href="Data.List.Relation.Unary.Any.Properties.html#25789" class="Bound">xs</a><a id="25834" class="Symbol">)</a> <a id="25836" href="Data.List.Relation.Unary.Any.Properties.html#25769" class="Bound">fs</a> <a id="25839" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="25841" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25845" href="Data.List.Relation.Unary.Any.Properties.html#25753" class="Bound">P</a> <a id="25847" class="Symbol">(</a><a id="25848" href="Data.List.Relation.Unary.Any.Properties.html#25769" class="Bound">fs</a> <a id="25851" href="Category.Applicative.Indexed.html#1034" class="Function Operator">⊛</a> <a id="25853" href="Data.List.Relation.Unary.Any.Properties.html#25789" class="Bound">xs</a><a id="25855" class="Symbol">)</a>
<a id="25857" href="Data.List.Relation.Unary.Any.Properties.html#25745" class="Function">⊛↔</a> <a id="25860" class="Symbol">{</a><a id="25861" class="Argument">P</a> <a id="25863" class="Symbol">=</a> <a id="25865" href="Data.List.Relation.Unary.Any.Properties.html#25865" class="Bound">P</a><a id="25866" class="Symbol">}</a> <a id="25868" class="Symbol">{</a><a id="25869" href="Data.List.Relation.Unary.Any.Properties.html#25869" class="Bound">fs</a><a id="25871" class="Symbol">}</a> <a id="25873" class="Symbol">{</a><a id="25874" href="Data.List.Relation.Unary.Any.Properties.html#25874" class="Bound">xs</a><a id="25876" class="Symbol">}</a> <a id="25878" class="Symbol">=</a>
<a id="25882" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25886" class="Symbol">(λ</a> <a id="25889" href="Data.List.Relation.Unary.Any.Properties.html#25889" class="Bound">f</a> <a id="25891" class="Symbol">→</a> <a id="25893" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25897" class="Symbol">(</a><a id="25898" href="Data.List.Relation.Unary.Any.Properties.html#25865" class="Bound">P</a> <a id="25900" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="25902" href="Data.List.Relation.Unary.Any.Properties.html#25889" class="Bound">f</a><a id="25903" class="Symbol">)</a> <a id="25905" href="Data.List.Relation.Unary.Any.Properties.html#25874" class="Bound">xs</a><a id="25907" class="Symbol">)</a> <a id="25909" href="Data.List.Relation.Unary.Any.Properties.html#25869" class="Bound">fs</a> <a id="25926" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="25929" href="Data.List.Relation.Unary.Any.Properties.html#3234" class="Function">Any-cong</a> <a id="25938" class="Symbol">(λ</a> <a id="25941" href="Data.List.Relation.Unary.Any.Properties.html#25941" class="Bound">_</a> <a id="25943" class="Symbol">→</a> <a id="25945" href="Data.List.Relation.Unary.Any.Properties.html#3234" class="Function">Any-cong</a> <a id="25954" class="Symbol">(λ</a> <a id="25957" href="Data.List.Relation.Unary.Any.Properties.html#25957" class="Bound">_</a> <a id="25959" class="Symbol">→</a> <a id="25961" href="Data.List.Relation.Unary.Any.Properties.html#24802" class="Function">return↔</a><a id="25968" class="Symbol">)</a> <a id="25970" class="Symbol">(_</a> <a id="25973" href="Function.Related.html#10453" class="Function Operator">∎</a><a id="25974" class="Symbol">))</a> <a id="25977" class="Symbol">(_</a> <a id="25980" href="Function.Related.html#10453" class="Function Operator">∎</a><a id="25981" class="Symbol">)</a> <a id="25983" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="25987" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="25991" class="Symbol">(λ</a> <a id="25994" href="Data.List.Relation.Unary.Any.Properties.html#25994" class="Bound">f</a> <a id="25996" class="Symbol">→</a> <a id="25998" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26002" class="Symbol">(</a><a id="26003" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26007" href="Data.List.Relation.Unary.Any.Properties.html#25865" class="Bound">P</a> <a id="26009" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="26011" href="Category.Monad.Indexed.html#644" class="Function">return</a> <a id="26018" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="26020" href="Data.List.Relation.Unary.Any.Properties.html#25994" class="Bound">f</a><a id="26021" class="Symbol">)</a> <a id="26023" href="Data.List.Relation.Unary.Any.Properties.html#25874" class="Bound">xs</a><a id="26025" class="Symbol">)</a> <a id="26027" href="Data.List.Relation.Unary.Any.Properties.html#25869" class="Bound">fs</a> <a id="26031" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="26034" href="Data.List.Relation.Unary.Any.Properties.html#3234" class="Function">Any-cong</a> <a id="26043" class="Symbol">(λ</a> <a id="26046" href="Data.List.Relation.Unary.Any.Properties.html#26046" class="Bound">_</a> <a id="26048" class="Symbol">→</a> <a id="26050" href="Data.List.Relation.Unary.Any.Properties.html#25432" class="Function">>>=↔</a> <a id="26055" class="Symbol">)</a> <a id="26057" class="Symbol">(_</a> <a id="26060" href="Function.Related.html#10453" class="Function Operator">∎</a><a id="26061" class="Symbol">)</a> <a id="26063" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="26067" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26071" class="Symbol">(λ</a> <a id="26074" href="Data.List.Relation.Unary.Any.Properties.html#26074" class="Bound">f</a> <a id="26076" class="Symbol">→</a> <a id="26078" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26082" href="Data.List.Relation.Unary.Any.Properties.html#25865" class="Bound">P</a> <a id="26084" class="Symbol">(</a><a id="26085" href="Data.List.Relation.Unary.Any.Properties.html#25874" class="Bound">xs</a> <a id="26088" href="Category.Monad.Indexed.html#677" class="Function Operator">>>=</a> <a id="26092" href="Category.Monad.Indexed.html#644" class="Function">return</a> <a id="26099" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="26101" href="Data.List.Relation.Unary.Any.Properties.html#26074" class="Bound">f</a><a id="26102" class="Symbol">))</a> <a id="26105" href="Data.List.Relation.Unary.Any.Properties.html#25869" class="Bound">fs</a> <a id="26111" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="26114" href="Data.List.Relation.Unary.Any.Properties.html#25432" class="Function">>>=↔</a> <a id="26119" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="26123" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26127" href="Data.List.Relation.Unary.Any.Properties.html#25865" class="Bound">P</a> <a id="26129" class="Symbol">(</a><a id="26130" href="Data.List.Relation.Unary.Any.Properties.html#25869" class="Bound">fs</a> <a id="26133" href="Category.Applicative.Indexed.html#1034" class="Function Operator">⊛</a> <a id="26135" href="Data.List.Relation.Unary.Any.Properties.html#25874" class="Bound">xs</a><a id="26137" class="Symbol">)</a> <a id="26167" href="Function.Related.html#10453" class="Function Operator">∎</a>
<a id="26171" class="Keyword">where</a> <a id="26177" class="Keyword">open</a> <a id="26182" href="Function.Related.html#9774" class="Module">Related.EquationalReasoning</a>
<a id="26211" class="Comment">-- An alternative introduction rule for _⊛_</a>
<a id="⊛⁺′"></a><a id="26256" href="Data.List.Relation.Unary.Any.Properties.html#26256" class="Function">⊛⁺′</a> <a id="26260" class="Symbol">:</a> <a id="26262" class="Symbol">∀</a> <a id="26264" class="Symbol">{</a><a id="26265" href="Data.List.Relation.Unary.Any.Properties.html#26265" class="Bound">P</a> <a id="26267" class="Symbol">:</a> <a id="26269" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="26271" class="Symbol">→</a> <a id="26273" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="26277" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="26278" class="Symbol">}</a> <a id="26280" class="Symbol">{</a><a id="26281" href="Data.List.Relation.Unary.Any.Properties.html#26281" class="Bound">Q</a> <a id="26283" class="Symbol">:</a> <a id="26285" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="26287" class="Symbol">→</a> <a id="26289" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="26293" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="26294" class="Symbol">}</a> <a id="26296" class="Symbol">{</a><a id="26297" href="Data.List.Relation.Unary.Any.Properties.html#26297" class="Bound">fs</a> <a id="26300" class="Symbol">:</a> <a id="26302" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="26307" class="Symbol">(</a><a id="26308" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="26310" class="Symbol">→</a> <a id="26312" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a><a id="26313" class="Symbol">)}</a> <a id="26316" class="Symbol">{</a><a id="26317" href="Data.List.Relation.Unary.Any.Properties.html#26317" class="Bound">xs</a><a id="26319" class="Symbol">}</a> <a id="26321" class="Symbol">→</a>
<a id="26329" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26333" class="Symbol">(</a><a id="26334" href="Data.List.Relation.Unary.Any.Properties.html#26265" class="Bound">P</a> <a id="26336" href="Relation.Unary.html#5766" class="Function Operator">⟨→⟩</a> <a id="26340" href="Data.List.Relation.Unary.Any.Properties.html#26281" class="Bound">Q</a><a id="26341" class="Symbol">)</a> <a id="26343" href="Data.List.Relation.Unary.Any.Properties.html#26297" class="Bound">fs</a> <a id="26346" class="Symbol">→</a> <a id="26348" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26352" href="Data.List.Relation.Unary.Any.Properties.html#26265" class="Bound">P</a> <a id="26354" href="Data.List.Relation.Unary.Any.Properties.html#26317" class="Bound">xs</a> <a id="26357" class="Symbol">→</a> <a id="26359" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26363" href="Data.List.Relation.Unary.Any.Properties.html#26281" class="Bound">Q</a> <a id="26365" class="Symbol">(</a><a id="26366" href="Data.List.Relation.Unary.Any.Properties.html#26297" class="Bound">fs</a> <a id="26369" href="Category.Applicative.Indexed.html#1034" class="Function Operator">⊛</a> <a id="26371" href="Data.List.Relation.Unary.Any.Properties.html#26317" class="Bound">xs</a><a id="26373" class="Symbol">)</a>
<a id="26375" href="Data.List.Relation.Unary.Any.Properties.html#26256" class="Function">⊛⁺′</a> <a id="26379" href="Data.List.Relation.Unary.Any.Properties.html#26379" class="Bound">pq</a> <a id="26382" href="Data.List.Relation.Unary.Any.Properties.html#26382" class="Bound">p</a> <a id="26384" class="Symbol">=</a>
<a id="26388" href="Function.Inverse.html#1523" class="Field">Inverse.to</a> <a id="26399" href="Data.List.Relation.Unary.Any.Properties.html#25745" class="Function">⊛↔</a> <a id="26402" href="Function.Equality.html#1064" class="Field Operator">⟨$⟩</a>
<a id="26410" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="26418" class="Symbol">(λ</a> <a id="26421" href="Data.List.Relation.Unary.Any.Properties.html#26421" class="Bound">pq</a> <a id="26424" class="Symbol">→</a> <a id="26426" href="Data.List.Relation.Unary.Any.html#1643" class="Function">Any.map</a> <a id="26434" class="Symbol">(λ</a> <a id="26437" class="Symbol">{</a><a id="26438" href="Data.List.Relation.Unary.Any.Properties.html#26438" class="Bound">x</a><a id="26439" class="Symbol">}</a> <a id="26441" class="Symbol">→</a> <a id="26443" href="Data.List.Relation.Unary.Any.Properties.html#26421" class="Bound">pq</a> <a id="26446" class="Symbol">{</a><a id="26447" href="Data.List.Relation.Unary.Any.Properties.html#26438" class="Bound">x</a><a id="26448" class="Symbol">})</a> <a id="26451" href="Data.List.Relation.Unary.Any.Properties.html#26382" class="Bound">p</a><a id="26452" class="Symbol">)</a> <a id="26454" href="Data.List.Relation.Unary.Any.Properties.html#26379" class="Bound">pq</a>
<a id="26458" class="Comment">------------------------------------------------------------------------</a>
<a id="26531" class="Comment">-- _⊗_</a>
<a id="⊗↔"></a><a id="26539" href="Data.List.Relation.Unary.Any.Properties.html#26539" class="Function">⊗↔</a> <a id="26542" class="Symbol">:</a> <a id="26544" class="Symbol">{</a><a id="26545" href="Data.List.Relation.Unary.Any.Properties.html#26545" class="Bound">P</a> <a id="26547" class="Symbol">:</a> <a id="26549" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="26551" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="26553" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="26555" class="Symbol">→</a> <a id="26557" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="26561" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="26562" class="Symbol">}</a> <a id="26564" class="Symbol">{</a><a id="26565" href="Data.List.Relation.Unary.Any.Properties.html#26565" class="Bound">xs</a> <a id="26568" class="Symbol">:</a> <a id="26570" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="26575" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="26576" class="Symbol">}</a> <a id="26578" class="Symbol">{</a><a id="26579" href="Data.List.Relation.Unary.Any.Properties.html#26579" class="Bound">ys</a> <a id="26582" class="Symbol">:</a> <a id="26584" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="26589" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a><a id="26590" class="Symbol">}</a> <a id="26592" class="Symbol">→</a>
<a id="26599" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26603" class="Symbol">(λ</a> <a id="26606" href="Data.List.Relation.Unary.Any.Properties.html#26606" class="Bound">x</a> <a id="26608" class="Symbol">→</a> <a id="26610" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26614" class="Symbol">(λ</a> <a id="26617" href="Data.List.Relation.Unary.Any.Properties.html#26617" class="Bound">y</a> <a id="26619" class="Symbol">→</a> <a id="26621" href="Data.List.Relation.Unary.Any.Properties.html#26545" class="Bound">P</a> <a id="26623" class="Symbol">(</a><a id="26624" href="Data.List.Relation.Unary.Any.Properties.html#26606" class="Bound">x</a> <a id="26626" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="26628" href="Data.List.Relation.Unary.Any.Properties.html#26617" class="Bound">y</a><a id="26629" class="Symbol">))</a> <a id="26632" href="Data.List.Relation.Unary.Any.Properties.html#26579" class="Bound">ys</a><a id="26634" class="Symbol">)</a> <a id="26636" href="Data.List.Relation.Unary.Any.Properties.html#26565" class="Bound">xs</a> <a id="26639" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="26641" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26645" href="Data.List.Relation.Unary.Any.Properties.html#26545" class="Bound">P</a> <a id="26647" class="Symbol">(</a><a id="26648" href="Data.List.Relation.Unary.Any.Properties.html#26565" class="Bound">xs</a> <a id="26651" href="Category.Applicative.Indexed.html#1462" class="Function Operator">⊗</a> <a id="26653" href="Data.List.Relation.Unary.Any.Properties.html#26579" class="Bound">ys</a><a id="26655" class="Symbol">)</a>
<a id="26657" href="Data.List.Relation.Unary.Any.Properties.html#26539" class="Function">⊗↔</a> <a id="26660" class="Symbol">{</a><a id="26661" class="Argument">P</a> <a id="26663" class="Symbol">=</a> <a id="26665" href="Data.List.Relation.Unary.Any.Properties.html#26665" class="Bound">P</a><a id="26666" class="Symbol">}</a> <a id="26668" class="Symbol">{</a><a id="26669" href="Data.List.Relation.Unary.Any.Properties.html#26669" class="Bound">xs</a><a id="26671" class="Symbol">}</a> <a id="26673" class="Symbol">{</a><a id="26674" href="Data.List.Relation.Unary.Any.Properties.html#26674" class="Bound">ys</a><a id="26676" class="Symbol">}</a> <a id="26678" class="Symbol">=</a>
<a id="26682" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26686" class="Symbol">(λ</a> <a id="26689" href="Data.List.Relation.Unary.Any.Properties.html#26689" class="Bound">x</a> <a id="26691" class="Symbol">→</a> <a id="26693" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26697" class="Symbol">(λ</a> <a id="26700" href="Data.List.Relation.Unary.Any.Properties.html#26700" class="Bound">y</a> <a id="26702" class="Symbol">→</a> <a id="26704" href="Data.List.Relation.Unary.Any.Properties.html#26665" class="Bound">P</a> <a id="26706" class="Symbol">(</a><a id="26707" href="Data.List.Relation.Unary.Any.Properties.html#26689" class="Bound">x</a> <a id="26709" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">,</a> <a id="26711" href="Data.List.Relation.Unary.Any.Properties.html#26700" class="Bound">y</a><a id="26712" class="Symbol">))</a> <a id="26715" href="Data.List.Relation.Unary.Any.Properties.html#26674" class="Bound">ys</a><a id="26717" class="Symbol">)</a> <a id="26719" href="Data.List.Relation.Unary.Any.Properties.html#26669" class="Bound">xs</a> <a id="26750" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="26753" href="Data.List.Relation.Unary.Any.Properties.html#24802" class="Function">return↔</a> <a id="26761" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="26765" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26769" class="Symbol">(λ</a> <a id="26772" href="Data.List.Relation.Unary.Any.Properties.html#26772" class="Bound Operator">_,_</a> <a id="26776" class="Symbol">→</a> <a id="26778" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26782" class="Symbol">(λ</a> <a id="26785" href="Data.List.Relation.Unary.Any.Properties.html#26785" class="Bound">x</a> <a id="26787" class="Symbol">→</a> <a id="26789" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26793" class="Symbol">(λ</a> <a id="26796" href="Data.List.Relation.Unary.Any.Properties.html#26796" class="Bound">y</a> <a id="26798" class="Symbol">→</a> <a id="26800" href="Data.List.Relation.Unary.Any.Properties.html#26665" class="Bound">P</a> <a id="26802" class="Symbol">(</a><a id="26803" href="Data.List.Relation.Unary.Any.Properties.html#26785" class="Bound">x</a> <a id="26805" href="Data.List.Relation.Unary.Any.Properties.html#26772" class="Bound Operator">,</a> <a id="26807" href="Data.List.Relation.Unary.Any.Properties.html#26796" class="Bound">y</a><a id="26808" class="Symbol">))</a> <a id="26811" href="Data.List.Relation.Unary.Any.Properties.html#26674" class="Bound">ys</a><a id="26813" class="Symbol">)</a> <a id="26815" href="Data.List.Relation.Unary.Any.Properties.html#26669" class="Bound">xs</a><a id="26817" class="Symbol">)</a> <a id="26819" class="Symbol">(</a><a id="26820" href="Category.Monad.Indexed.html#644" class="Function">return</a> <a id="26827" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">_,_</a><a id="26830" class="Symbol">)</a> <a id="26833" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="26836" href="Data.List.Relation.Unary.Any.Properties.html#25745" class="Function">⊛↔</a> <a id="26839" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="26843" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26847" class="Symbol">(λ</a> <a id="26850" href="Data.List.Relation.Unary.Any.Properties.html#26850" class="Bound">x,</a> <a id="26853" class="Symbol">→</a> <a id="26855" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26859" class="Symbol">(</a><a id="26860" href="Data.List.Relation.Unary.Any.Properties.html#26665" class="Bound">P</a> <a id="26862" href="Function.Base.html#1031" class="Function Operator">∘</a> <a id="26864" href="Data.List.Relation.Unary.Any.Properties.html#26850" class="Bound">x,</a><a id="26866" class="Symbol">)</a> <a id="26868" href="Data.List.Relation.Unary.Any.Properties.html#26674" class="Bound">ys</a><a id="26870" class="Symbol">)</a> <a id="26872" class="Symbol">(</a><a id="26873" href="Agda.Builtin.Sigma.html#236" class="InductiveConstructor Operator">_,_</a> <a id="26877" href="Category.Functor.html#608" class="Function Operator"><$></a> <a id="26881" href="Data.List.Relation.Unary.Any.Properties.html#26669" class="Bound">xs</a><a id="26883" class="Symbol">)</a> <a id="26911" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="26914" href="Data.List.Relation.Unary.Any.Properties.html#25745" class="Function">⊛↔</a> <a id="26917" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="26921" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="26925" href="Data.List.Relation.Unary.Any.Properties.html#26665" class="Bound">P</a> <a id="26927" class="Symbol">(</a><a id="26928" href="Data.List.Relation.Unary.Any.Properties.html#26669" class="Bound">xs</a> <a id="26931" href="Category.Applicative.Indexed.html#1462" class="Function Operator">⊗</a> <a id="26933" href="Data.List.Relation.Unary.Any.Properties.html#26674" class="Bound">ys</a><a id="26935" class="Symbol">)</a> <a id="26989" href="Function.Related.html#10453" class="Function Operator">∎</a>
<a id="26993" class="Keyword">where</a> <a id="26999" class="Keyword">open</a> <a id="27004" href="Function.Related.html#9774" class="Module">Related.EquationalReasoning</a>
<a id="⊗↔′"></a><a id="27033" href="Data.List.Relation.Unary.Any.Properties.html#27033" class="Function">⊗↔′</a> <a id="27037" class="Symbol">:</a> <a id="27039" class="Symbol">{</a><a id="27040" href="Data.List.Relation.Unary.Any.Properties.html#27040" class="Bound">P</a> <a id="27042" class="Symbol">:</a> <a id="27044" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a> <a id="27046" class="Symbol">→</a> <a id="27048" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="27052" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="27053" class="Symbol">}</a> <a id="27055" class="Symbol">{</a><a id="27056" href="Data.List.Relation.Unary.Any.Properties.html#27056" class="Bound">Q</a> <a id="27058" class="Symbol">:</a> <a id="27060" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a> <a id="27062" class="Symbol">→</a> <a id="27064" href="Agda.Primitive.html#326" class="Primitive">Set</a> <a id="27068" href="Data.List.Relation.Unary.Any.Properties.html#2384" class="Generalizable">ℓ</a><a id="27069" class="Symbol">}</a> <a id="27071" class="Symbol">{</a><a id="27072" href="Data.List.Relation.Unary.Any.Properties.html#27072" class="Bound">xs</a> <a id="27075" class="Symbol">:</a> <a id="27077" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="27082" href="Data.List.Relation.Unary.Any.Properties.html#2398" class="Generalizable">A</a><a id="27083" class="Symbol">}</a> <a id="27085" class="Symbol">{</a><a id="27086" href="Data.List.Relation.Unary.Any.Properties.html#27086" class="Bound">ys</a> <a id="27089" class="Symbol">:</a> <a id="27091" href="Agda.Builtin.List.html#148" class="Datatype">List</a> <a id="27096" href="Data.List.Relation.Unary.Any.Properties.html#2412" class="Generalizable">B</a><a id="27097" class="Symbol">}</a> <a id="27099" class="Symbol">→</a>
<a id="27107" class="Symbol">(</a><a id="27108" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="27112" href="Data.List.Relation.Unary.Any.Properties.html#27040" class="Bound">P</a> <a id="27114" href="Data.List.Relation.Unary.Any.Properties.html#27072" class="Bound">xs</a> <a id="27117" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="27119" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="27123" href="Data.List.Relation.Unary.Any.Properties.html#27056" class="Bound">Q</a> <a id="27125" href="Data.List.Relation.Unary.Any.Properties.html#27086" class="Bound">ys</a><a id="27127" class="Symbol">)</a> <a id="27129" href="Function.Inverse.html#2457" class="Function Operator">↔</a> <a id="27131" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="27135" class="Symbol">(</a><a id="27136" href="Data.List.Relation.Unary.Any.Properties.html#27040" class="Bound">P</a> <a id="27138" href="Relation.Unary.html#5466" class="Function Operator">⟨×⟩</a> <a id="27142" href="Data.List.Relation.Unary.Any.Properties.html#27056" class="Bound">Q</a><a id="27143" class="Symbol">)</a> <a id="27145" class="Symbol">(</a><a id="27146" href="Data.List.Relation.Unary.Any.Properties.html#27072" class="Bound">xs</a> <a id="27149" href="Category.Applicative.Indexed.html#1462" class="Function Operator">⊗</a> <a id="27151" href="Data.List.Relation.Unary.Any.Properties.html#27086" class="Bound">ys</a><a id="27153" class="Symbol">)</a>
<a id="27155" href="Data.List.Relation.Unary.Any.Properties.html#27033" class="Function">⊗↔′</a> <a id="27159" class="Symbol">{</a><a id="27160" class="Argument">P</a> <a id="27162" class="Symbol">=</a> <a id="27164" href="Data.List.Relation.Unary.Any.Properties.html#27164" class="Bound">P</a><a id="27165" class="Symbol">}</a> <a id="27167" class="Symbol">{</a><a id="27168" href="Data.List.Relation.Unary.Any.Properties.html#27168" class="Bound">Q</a><a id="27169" class="Symbol">}</a> <a id="27171" class="Symbol">{</a><a id="27172" href="Data.List.Relation.Unary.Any.Properties.html#27172" class="Bound">xs</a><a id="27174" class="Symbol">}</a> <a id="27176" class="Symbol">{</a><a id="27177" href="Data.List.Relation.Unary.Any.Properties.html#27177" class="Bound">ys</a><a id="27179" class="Symbol">}</a> <a id="27181" class="Symbol">=</a>
<a id="27185" class="Symbol">(</a><a id="27186" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="27190" href="Data.List.Relation.Unary.Any.Properties.html#27164" class="Bound">P</a> <a id="27192" href="Data.List.Relation.Unary.Any.Properties.html#27172" class="Bound">xs</a> <a id="27195" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="27197" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="27201" href="Data.List.Relation.Unary.Any.Properties.html#27168" class="Bound">Q</a> <a id="27203" href="Data.List.Relation.Unary.Any.Properties.html#27177" class="Bound">ys</a><a id="27205" class="Symbol">)</a> <a id="27226" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="27229" href="Data.List.Relation.Unary.Any.Properties.html#8046" class="Function">×↔</a> <a id="27232" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="27236" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="27240" class="Symbol">(λ</a> <a id="27243" href="Data.List.Relation.Unary.Any.Properties.html#27243" class="Bound">x</a> <a id="27245" class="Symbol">→</a> <a id="27247" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="27251" class="Symbol">(λ</a> <a id="27254" href="Data.List.Relation.Unary.Any.Properties.html#27254" class="Bound">y</a> <a id="27256" class="Symbol">→</a> <a id="27258" href="Data.List.Relation.Unary.Any.Properties.html#27164" class="Bound">P</a> <a id="27260" href="Data.List.Relation.Unary.Any.Properties.html#27243" class="Bound">x</a> <a id="27262" href="Data.Product.html#1167" class="Function Operator">×</a> <a id="27264" href="Data.List.Relation.Unary.Any.Properties.html#27168" class="Bound">Q</a> <a id="27266" href="Data.List.Relation.Unary.Any.Properties.html#27254" class="Bound">y</a><a id="27267" class="Symbol">)</a> <a id="27269" href="Data.List.Relation.Unary.Any.Properties.html#27177" class="Bound">ys</a><a id="27271" class="Symbol">)</a> <a id="27273" href="Data.List.Relation.Unary.Any.Properties.html#27172" class="Bound">xs</a> <a id="27277" href="Function.Related.html#10072" class="Function Operator">↔⟨</a> <a id="27280" href="Data.List.Relation.Unary.Any.Properties.html#26539" class="Function">⊗↔</a> <a id="27283" href="Function.Related.html#10072" class="Function Operator">⟩</a>
<a id="27287" href="Data.List.Relation.Unary.Any.html#1156" class="Datatype">Any</a> <a id="27291" class="Symbol">(</a><a id="27292" href="Data.List.Relation.Unary.Any.Properties.html#27164" class="Bound">P</a> <a id="27294" href="Relation.Unary.html#5466" class="Function Operator">⟨×⟩</a> <a id="27298" href="Data.List.Relation.Unary.Any.Properties.html#27168" class="Bound">Q</a><a id="27299" class="Symbol">)</a> <a id="27301" class="Symbol">(</a><a id="27302" href="Data.List.Relation.Unary.Any.Properties.html#27172" class="Bound">xs</a> <a id="27305" href="Category.Applicative.Indexed.html#1462" class="Function Operator">⊗</a> <a id="27307" href="Data.List.Relation.Unary.Any.Properties.html#27177" class="Bound">ys</a><a id="27309" class="Symbol">)</a> <a id="27328" href="Function.Related.html#10453" class="Function Operator">∎</a>
<a id="27332" class="Keyword">where</a> <a id="27338" class="Keyword">open</a> <a id="27343" href="Function.Related.html#9774" class="Module">Related.EquationalReasoning</a>
</pre></body></html>