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update before PR
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xyzw12345 committed Mar 11, 2024
1 parent 49689ee commit 5e3e894
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Expand Up @@ -8,8 +8,6 @@ open Line

variable {P : Type*} [EuclideanPlane P]

theorem perp_foot_unique' {A B : P} {l : Line P} (h : B LiesOn l) [_hne : PtNe A B] (hp : LIN A B ⟂ l) : perp_foot A l = B := sorry

theorem perp_of_angle_dvalue_eq_pi_div_two {A B C : P} [h1 : PtNe B A] [h2 : PtNe C A] (h : (ANG B A C).dvalue = ↑(π / 2)) : LIN B A ⟂ LIN C A := by
sorry
end EuclidGeom
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Expand Up @@ -17,26 +17,6 @@ theorem ang_acute_of_is_isoceles_variant {A B C : P} (h : ¬ Collinear A B C) (i
theorem midpt_eq_perp_foot_of_isIsoceles {A B C : P} [PtNe B C] (h : (▵ A B C).IsIsoceles) : (SEG B C).midpoint = perp_foot A (LIN B C) := sorry

theorem perp_foot_eq_midpt_of_is_isoceles {A B C : P} (not_collinear_ABC : ¬ Collinear A B C) (isoceles_ABC : (▵ A B C).IsIsoceles) : perp_foot A (LIN B C (ne_of_not_collinear not_collinear_ABC).1) = (SEG B C).midpoint := by
let D := (SEG B C).midpoint
haveI C_ne_B: PtNe C B := ⟨(ne_of_not_collinear not_collinear_ABC).1
have D_int_BC : D LiesInt (SEG B C) := by
apply SegND.midpt_lies_int (seg_nd := (SEG_nd B C))
have D_on_line_BC : D LiesOn (LIN B C) := by
apply SegND.lies_on_toLine_of_lie_on (s := SEG_nd B C)
show D LiesOn (SEG B C); exact D_int_BC.1
have : D ≠ A := by
by_contra h; absurd not_collinear_ABC
simp only [h.symm]; apply Seg.collinear_of_lies_on D_int_BC.1
apply Seg.source_lies_on; apply Seg.target_lies_on
haveI D_ne_A: PtNe D A := ⟨this⟩
have DB_eq_DC : (SEG D B).length = (SEG D C).length := by
calc
_= (SEG B D).length := by apply length_of_rev_eq_length'
_= _ := by apply Seg.dist_target_eq_dist_source_of_midpt (seg := (SEG B C))
apply perp_foot_unique'
exact D_on_line_BC
show LIN A D ⟂ LIN B C
sorry
sorry

end EuclidGeom

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