geometry.euclidean.angle.oriented.affine ⟷ Mathlib.Geometry.Euclidean.Angle.Oriented.Affine

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -330,7 +330,7 @@ theorem two_zsmul_oangle_of_vectorSpan_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P}
     (h₃₂₆₅ : vectorSpan ℝ ({p₃, p₂} : Set P) = vectorSpan ℝ ({p₆, p₅} : Set P)) :
     (2 : ℤ) • ∡ p₁ p₂ p₃ = (2 : ℤ) • ∡ p₄ p₅ p₆ :=
   by
-  simp_rw [vectorSpan_pair] at h₁₂₄₅ h₃₂₆₅ 
+  simp_rw [vectorSpan_pair] at h₁₂₄₅ h₃₂₆₅
   exact o.two_zsmul_oangle_of_span_eq_of_span_eq h₁₂₄₅ h₃₂₆₅
 #align euclidean_geometry.two_zsmul_oangle_of_vector_span_eq EuclideanGeometry.two_zsmul_oangle_of_vectorSpan_eq
 -/
@@ -342,7 +342,7 @@ theorem two_zsmul_oangle_of_parallel {p₁ p₂ p₃ p₄ p₅ p₆ : P}
     (h₁₂₄₅ : line[ℝ, p₁, p₂] ∥ line[ℝ, p₄, p₅]) (h₃₂₆₅ : line[ℝ, p₃, p₂] ∥ line[ℝ, p₆, p₅]) :
     (2 : ℤ) • ∡ p₁ p₂ p₃ = (2 : ℤ) • ∡ p₄ p₅ p₆ :=
   by
-  rw [AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq] at h₁₂₄₅ h₃₂₆₅ 
+  rw [AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq] at h₁₂₄₅ h₃₂₆₅
   exact two_zsmul_oangle_of_vector_span_eq h₁₂₄₅ h₃₂₆₅
 #align euclidean_geometry.two_zsmul_oangle_of_parallel EuclideanGeometry.two_zsmul_oangle_of_parallel
 -/
@@ -401,7 +401,7 @@ theorem oangle_add_cyc3 {p p₁ p₂ p₃ : P} (hp₁ : p₁ ≠ p) (hp₂ : p
 /-- Pons asinorum, oriented angle-at-point form. -/
 theorem oangle_eq_oangle_of_dist_eq {p₁ p₂ p₃ : P} (h : dist p₁ p₂ = dist p₁ p₃) :
     ∡ p₁ p₂ p₃ = ∡ p₂ p₃ p₁ := by
-  simp_rw [dist_eq_norm_vsub] at h 
+  simp_rw [dist_eq_norm_vsub] at h
   rw [oangle, oangle, ← vsub_sub_vsub_cancel_left p₃ p₂ p₁, ← vsub_sub_vsub_cancel_left p₂ p₃ p₁,
     o.oangle_sub_eq_oangle_sub_rev_of_norm_eq h]
 #align euclidean_geometry.oangle_eq_oangle_of_dist_eq EuclideanGeometry.oangle_eq_oangle_of_dist_eq
@@ -413,7 +413,7 @@ angle-at-point form. -/
 theorem oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq {p₁ p₂ p₃ : P} (hn : p₂ ≠ p₃)
     (h : dist p₁ p₂ = dist p₁ p₃) : ∡ p₃ p₁ p₂ = π - (2 : ℤ) • ∡ p₁ p₂ p₃ :=
   by
-  simp_rw [dist_eq_norm_vsub] at h 
+  simp_rw [dist_eq_norm_vsub] at h
   rw [oangle, oangle]
   convert o.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eq _ h using 1
   · rw [← neg_vsub_eq_vsub_rev p₁ p₃, ← neg_vsub_eq_vsub_rev p₁ p₂, o.oangle_neg_neg]
@@ -427,7 +427,7 @@ theorem oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq {p₁ p₂ p₃ : P} (hn :
 theorem abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq {p₁ p₂ p₃ : P}
     (h : dist p₁ p₂ = dist p₁ p₃) : |(∡ p₁ p₂ p₃).toReal| < π / 2 :=
   by
-  simp_rw [dist_eq_norm_vsub] at h 
+  simp_rw [dist_eq_norm_vsub] at h
   rw [oangle, ← vsub_sub_vsub_cancel_left p₃ p₂ p₁]
   exact o.abs_oangle_sub_right_toReal_lt_pi_div_two h
 #align euclidean_geometry.abs_oangle_right_to_real_lt_pi_div_two_of_dist_eq EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq
@@ -717,7 +717,7 @@ same ray. -/
 theorem Wbtw.oangle_eq_left {p₁ p₁' p₂ p₃ : P} (h : Wbtw ℝ p₂ p₁ p₁') (hp₁p₂ : p₁ ≠ p₂) :
     ∡ p₁ p₂ p₃ = ∡ p₁' p₂ p₃ := by
   by_cases hp₃p₂ : p₃ = p₂; · simp [hp₃p₂]
-  by_cases hp₁'p₂ : p₁' = p₂; · rw [hp₁'p₂, wbtw_self_iff] at h ; exact False.elim (hp₁p₂ h)
+  by_cases hp₁'p₂ : p₁' = p₂; · rw [hp₁'p₂, wbtw_self_iff] at h; exact False.elim (hp₁p₂ h)
   rw [← oangle_add hp₁'p₂ hp₁p₂ hp₃p₂, h.oangle₃₁₂_eq_zero, zero_add]
 #align wbtw.oangle_eq_left Wbtw.oangle_eq_left
 -/
@@ -851,14 +851,14 @@ theorem dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint {p₁ p₂ p : P}
       by
       rw [@dist_eq_norm_vsub' V, @dist_eq_norm_vsub' V, ←
         mul_self_inj (norm_nonneg _) (norm_nonneg _), ← real_inner_self_eq_norm_mul_norm, ←
-        real_inner_self_eq_norm_mul_norm] at hd 
+        real_inner_self_eq_norm_mul_norm] at hd
       simp_rw [vsub_midpoint, ← vsub_sub_vsub_cancel_left p₂ p₁ p, inner_sub_left, inner_add_right,
         inner_smul_right, hd, real_inner_comm (p -ᵥ p₁)]
       abel
     rw [@Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two V _ _ _ o,
-      or_iff_right (vsub_ne_zero.2 h.symm)] at hi 
+      or_iff_right (vsub_ne_zero.2 h.symm)] at hi
     rcases hi with ⟨r, hr⟩
-    rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr 
+    rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr
     exact ⟨r, hr.symm⟩
   · rcases hr with ⟨r, rfl⟩
     simp_rw [@dist_eq_norm_vsub V, vsub_vadd_eq_vsub_sub, left_vsub_midpoint, right_vsub_midpoint,
@@ -892,10 +892,10 @@ theorem Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (p₅ :
               (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))))
             hp₃p₄).1
         hc₅₁₂₃₄
-    rw [Set.insert_comm] at hc₅₁₂ hc₅₃₄ 
+    rw [Set.insert_comm] at hc₅₁₂ hc₅₃₄
     have hs₁₅₂ := oangle_eq_zero_or_eq_pi_iff_collinear.2 hc₅₁₂
     have hs₃₅₄ := oangle_eq_zero_or_eq_pi_iff_collinear.2 hc₅₃₄
-    rw [← Real.Angle.sign_eq_zero_iff] at hs₁₅₂ hs₃₅₄ 
+    rw [← Real.Angle.sign_eq_zero_iff] at hs₁₅₂ hs₃₅₄
     rw [hs₁₅₂, hs₃₅₄]
   · let s : Set (P × P × P) :=
       (fun x : line[ℝ, p₁, p₂] × V => (x.1, p₅, x.2 +ᵥ x.1)) ''
@@ -912,7 +912,7 @@ theorem Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (p₅ :
       by
       refine' ContinuousAt.continuousOn fun p hp => continuous_at_oangle _ _
       all_goals
-        simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_univ, true_and_iff, Prod.ext_iff] at hp 
+        simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_univ, true_and_iff, Prod.ext_iff] at hp
         obtain ⟨q₁, q₅, q₂⟩ := p
         dsimp only at hp ⊢
         obtain ⟨⟨⟨q, hq⟩, v⟩, hv, rfl, rfl, rfl⟩ := hp
@@ -922,7 +922,7 @@ theorem Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (p₅ :
         refine' hc₅₁₂ ((collinear_insert_iff_of_mem_affineSpan _).2 (collinear_pair _ _ _))
       · exact hq
       · refine' vadd_mem_of_mem_direction _ hq
-        rw [← exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)] at hvr 
+        rw [← exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)] at hvr
         obtain ⟨r, -, rfl⟩ := hvr
         rw [direction_affineSpan]
         exact smul_vsub_rev_mem_vectorSpan_pair _ _ _
@@ -930,15 +930,15 @@ theorem Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (p₅ :
       by
       intro p hp
       simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
-        Prod.ext_iff] at hp 
+        Prod.ext_iff] at hp
       obtain ⟨q₁, q₅, q₂⟩ := p
       dsimp only at hp ⊢
       obtain ⟨⟨⟨q, hq⟩, v⟩, hv, rfl, rfl, rfl⟩ := hp
       dsimp only [Subtype.coe_mk, Set.mem_setOf] at hv ⊢
       obtain ⟨hvr, hv0⟩ := hv
-      rw [← exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)] at hvr 
+      rw [← exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)] at hvr
       obtain ⟨r, -, rfl⟩ := hvr
-      change q ∈ line[ℝ, p₁, p₂] at hq 
+      change q ∈ line[ℝ, p₁, p₂] at hq
       rw [oangle_ne_zero_and_ne_pi_iff_affine_independent]
       refine'
         affineIndependent_of_ne_of_mem_of_not_mem_of_mem _ hq
@@ -1037,7 +1037,7 @@ theorem AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P} {p₁
     by
     refine' ContinuousAt.continuousOn fun p hp => continuous_at_oangle _ _
     all_goals
-      simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp 
+      simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp
       obtain ⟨p', hp', rfl⟩ := hp
       dsimp only
       rintro rfl
@@ -1046,7 +1046,7 @@ theorem AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P} {p₁
   have hsp : ∀ p : P × P × P, p ∈ sp → ∡ p.1 p.2.1 p.2.2 ≠ 0 ∧ ∡ p.1 p.2.1 p.2.2 ≠ π :=
     by
     intro p hp
-    simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp 
+    simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp
     obtain ⟨p', hp', rfl⟩ := hp
     dsimp only
     rw [oangle_ne_zero_and_ne_pi_iff_affine_independent]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,9 +3,9 @@ Copyright (c) 2022 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 -/
-import Mathbin.Analysis.Convex.Side
-import Mathbin.Geometry.Euclidean.Angle.Oriented.Rotation
-import Mathbin.Geometry.Euclidean.Angle.Unoriented.Affine
+import Analysis.Convex.Side
+import Geometry.Euclidean.Angle.Oriented.Rotation
+import Geometry.Euclidean.Angle.Unoriented.Affine
 
 #align_import geometry.euclidean.angle.oriented.affine from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module geometry.euclidean.angle.oriented.affine
-! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Side
 import Mathbin.Geometry.Euclidean.Angle.Oriented.Rotation
 import Mathbin.Geometry.Euclidean.Angle.Unoriented.Affine
 
+#align_import geometry.euclidean.angle.oriented.affine from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
+
 /-!
 # Oriented angles.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf9bbbcf0c1c1ead18280b0d010e417b10abb1b6

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module geometry.euclidean.angle.oriented.affine
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Geometry.Euclidean.Angle.Unoriented.Affine
 /-!
 # Oriented angles.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines oriented angles in Euclidean affine spaces.
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8

@@ -38,15 +38,18 @@ variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ
 
 local notation "o" => Module.Oriented.positiveOrientation
 
+#print EuclideanGeometry.oangle /-
 /-- The oriented angle at `p₂` between the line segments to `p₁` and `p₃`, modulo `2 * π`. If
 either of those points equals `p₂`, this is 0. See `euclidean_geometry.angle` for the
 corresponding unoriented angle definition. -/
 def oangle (p₁ p₂ p₃ : P) : Real.Angle :=
   o.oangle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂)
 #align euclidean_geometry.oangle EuclideanGeometry.oangle
+-/
 
 scoped notation "∡" => EuclideanGeometry.oangle
 
+#print EuclideanGeometry.continuousAt_oangle /-
 /-- Oriented angles are continuous when neither end point equals the middle point. -/
 theorem continuousAt_oangle {x : P × P × P} (hx12 : x.1 ≠ x.2.1) (hx32 : x.2.2 ≠ x.2.1) :
     ContinuousAt (fun y : P × P × P => ∡ y.1 y.2.1 y.2.2) x :=
@@ -59,165 +62,223 @@ theorem continuousAt_oangle {x : P × P × P} (hx12 : x.1 ≠ x.2.1) (hx32 : x.2
       ((continuous_fst.vsub continuous_snd.fst).prod_mk
           (continuous_snd.snd.vsub continuous_snd.fst)).ContinuousAt
 #align euclidean_geometry.continuous_at_oangle EuclideanGeometry.continuousAt_oangle
+-/
 
+#print EuclideanGeometry.oangle_self_left /-
 /-- The angle ∡AAB at a point. -/
 @[simp]
 theorem oangle_self_left (p₁ p₂ : P) : ∡ p₁ p₁ p₂ = 0 := by simp [oangle]
 #align euclidean_geometry.oangle_self_left EuclideanGeometry.oangle_self_left
+-/
 
+#print EuclideanGeometry.oangle_self_right /-
 /-- The angle ∡ABB at a point. -/
 @[simp]
 theorem oangle_self_right (p₁ p₂ : P) : ∡ p₁ p₂ p₂ = 0 := by simp [oangle]
 #align euclidean_geometry.oangle_self_right EuclideanGeometry.oangle_self_right
+-/
 
+#print EuclideanGeometry.oangle_self_left_right /-
 /-- The angle ∡ABA at a point. -/
 @[simp]
 theorem oangle_self_left_right (p₁ p₂ : P) : ∡ p₁ p₂ p₁ = 0 :=
   o.oangle_self _
 #align euclidean_geometry.oangle_self_left_right EuclideanGeometry.oangle_self_left_right
+-/
 
+#print EuclideanGeometry.left_ne_of_oangle_ne_zero /-
 /-- If the angle between three points is nonzero, the first two points are not equal. -/
 theorem left_ne_of_oangle_ne_zero {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ ≠ 0) : p₁ ≠ p₂ := by
   rw [← @vsub_ne_zero V]; exact o.left_ne_zero_of_oangle_ne_zero h
 #align euclidean_geometry.left_ne_of_oangle_ne_zero EuclideanGeometry.left_ne_of_oangle_ne_zero
+-/
 
+#print EuclideanGeometry.right_ne_of_oangle_ne_zero /-
 /-- If the angle between three points is nonzero, the last two points are not equal. -/
 theorem right_ne_of_oangle_ne_zero {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ ≠ 0) : p₃ ≠ p₂ := by
   rw [← @vsub_ne_zero V]; exact o.right_ne_zero_of_oangle_ne_zero h
 #align euclidean_geometry.right_ne_of_oangle_ne_zero EuclideanGeometry.right_ne_of_oangle_ne_zero
+-/
 
+#print EuclideanGeometry.left_ne_right_of_oangle_ne_zero /-
 /-- If the angle between three points is nonzero, the first and third points are not equal. -/
 theorem left_ne_right_of_oangle_ne_zero {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ ≠ 0) : p₁ ≠ p₃ := by
   rw [← (vsub_left_injective p₂).ne_iff]; exact o.ne_of_oangle_ne_zero h
 #align euclidean_geometry.left_ne_right_of_oangle_ne_zero EuclideanGeometry.left_ne_right_of_oangle_ne_zero
+-/
 
+#print EuclideanGeometry.left_ne_of_oangle_eq_pi /-
 /-- If the angle between three points is `π`, the first two points are not equal. -/
 theorem left_ne_of_oangle_eq_pi {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = π) : p₁ ≠ p₂ :=
   left_ne_of_oangle_ne_zero (h.symm ▸ Real.Angle.pi_ne_zero : ∡ p₁ p₂ p₃ ≠ 0)
 #align euclidean_geometry.left_ne_of_oangle_eq_pi EuclideanGeometry.left_ne_of_oangle_eq_pi
+-/
 
+#print EuclideanGeometry.right_ne_of_oangle_eq_pi /-
 /-- If the angle between three points is `π`, the last two points are not equal. -/
 theorem right_ne_of_oangle_eq_pi {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = π) : p₃ ≠ p₂ :=
   right_ne_of_oangle_ne_zero (h.symm ▸ Real.Angle.pi_ne_zero : ∡ p₁ p₂ p₃ ≠ 0)
 #align euclidean_geometry.right_ne_of_oangle_eq_pi EuclideanGeometry.right_ne_of_oangle_eq_pi
+-/
 
+#print EuclideanGeometry.left_ne_right_of_oangle_eq_pi /-
 /-- If the angle between three points is `π`, the first and third points are not equal. -/
 theorem left_ne_right_of_oangle_eq_pi {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = π) : p₁ ≠ p₃ :=
   left_ne_right_of_oangle_ne_zero (h.symm ▸ Real.Angle.pi_ne_zero : ∡ p₁ p₂ p₃ ≠ 0)
 #align euclidean_geometry.left_ne_right_of_oangle_eq_pi EuclideanGeometry.left_ne_right_of_oangle_eq_pi
+-/
 
+#print EuclideanGeometry.left_ne_of_oangle_eq_pi_div_two /-
 /-- If the angle between three points is `π / 2`, the first two points are not equal. -/
 theorem left_ne_of_oangle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = (π / 2 : ℝ)) : p₁ ≠ p₂ :=
   left_ne_of_oangle_ne_zero (h.symm ▸ Real.Angle.pi_div_two_ne_zero : ∡ p₁ p₂ p₃ ≠ 0)
 #align euclidean_geometry.left_ne_of_oangle_eq_pi_div_two EuclideanGeometry.left_ne_of_oangle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.right_ne_of_oangle_eq_pi_div_two /-
 /-- If the angle between three points is `π / 2`, the last two points are not equal. -/
 theorem right_ne_of_oangle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = (π / 2 : ℝ)) : p₃ ≠ p₂ :=
   right_ne_of_oangle_ne_zero (h.symm ▸ Real.Angle.pi_div_two_ne_zero : ∡ p₁ p₂ p₃ ≠ 0)
 #align euclidean_geometry.right_ne_of_oangle_eq_pi_div_two EuclideanGeometry.right_ne_of_oangle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.left_ne_right_of_oangle_eq_pi_div_two /-
 /-- If the angle between three points is `π / 2`, the first and third points are not equal. -/
 theorem left_ne_right_of_oangle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = (π / 2 : ℝ)) :
     p₁ ≠ p₃ :=
   left_ne_right_of_oangle_ne_zero (h.symm ▸ Real.Angle.pi_div_two_ne_zero : ∡ p₁ p₂ p₃ ≠ 0)
 #align euclidean_geometry.left_ne_right_of_oangle_eq_pi_div_two EuclideanGeometry.left_ne_right_of_oangle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.left_ne_of_oangle_eq_neg_pi_div_two /-
 /-- If the angle between three points is `-π / 2`, the first two points are not equal. -/
 theorem left_ne_of_oangle_eq_neg_pi_div_two {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = (-π / 2 : ℝ)) :
     p₁ ≠ p₂ :=
   left_ne_of_oangle_ne_zero (h.symm ▸ Real.Angle.neg_pi_div_two_ne_zero : ∡ p₁ p₂ p₃ ≠ 0)
 #align euclidean_geometry.left_ne_of_oangle_eq_neg_pi_div_two EuclideanGeometry.left_ne_of_oangle_eq_neg_pi_div_two
+-/
 
+#print EuclideanGeometry.right_ne_of_oangle_eq_neg_pi_div_two /-
 /-- If the angle between three points is `-π / 2`, the last two points are not equal. -/
 theorem right_ne_of_oangle_eq_neg_pi_div_two {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = (-π / 2 : ℝ)) :
     p₃ ≠ p₂ :=
   right_ne_of_oangle_ne_zero (h.symm ▸ Real.Angle.neg_pi_div_two_ne_zero : ∡ p₁ p₂ p₃ ≠ 0)
 #align euclidean_geometry.right_ne_of_oangle_eq_neg_pi_div_two EuclideanGeometry.right_ne_of_oangle_eq_neg_pi_div_two
+-/
 
+#print EuclideanGeometry.left_ne_right_of_oangle_eq_neg_pi_div_two /-
 /-- If the angle between three points is `-π / 2`, the first and third points are not equal. -/
 theorem left_ne_right_of_oangle_eq_neg_pi_div_two {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = (-π / 2 : ℝ)) :
     p₁ ≠ p₃ :=
   left_ne_right_of_oangle_ne_zero (h.symm ▸ Real.Angle.neg_pi_div_two_ne_zero : ∡ p₁ p₂ p₃ ≠ 0)
 #align euclidean_geometry.left_ne_right_of_oangle_eq_neg_pi_div_two EuclideanGeometry.left_ne_right_of_oangle_eq_neg_pi_div_two
+-/
 
+#print EuclideanGeometry.left_ne_of_oangle_sign_ne_zero /-
 /-- If the sign of the angle between three points is nonzero, the first two points are not
 equal. -/
 theorem left_ne_of_oangle_sign_ne_zero {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign ≠ 0) : p₁ ≠ p₂ :=
   left_ne_of_oangle_ne_zero (Real.Angle.sign_ne_zero_iff.1 h).1
 #align euclidean_geometry.left_ne_of_oangle_sign_ne_zero EuclideanGeometry.left_ne_of_oangle_sign_ne_zero
+-/
 
+#print EuclideanGeometry.right_ne_of_oangle_sign_ne_zero /-
 /-- If the sign of the angle between three points is nonzero, the last two points are not
 equal. -/
 theorem right_ne_of_oangle_sign_ne_zero {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign ≠ 0) : p₃ ≠ p₂ :=
   right_ne_of_oangle_ne_zero (Real.Angle.sign_ne_zero_iff.1 h).1
 #align euclidean_geometry.right_ne_of_oangle_sign_ne_zero EuclideanGeometry.right_ne_of_oangle_sign_ne_zero
+-/
 
+#print EuclideanGeometry.left_ne_right_of_oangle_sign_ne_zero /-
 /-- If the sign of the angle between three points is nonzero, the first and third points are not
 equal. -/
 theorem left_ne_right_of_oangle_sign_ne_zero {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign ≠ 0) : p₁ ≠ p₃ :=
   left_ne_right_of_oangle_ne_zero (Real.Angle.sign_ne_zero_iff.1 h).1
 #align euclidean_geometry.left_ne_right_of_oangle_sign_ne_zero EuclideanGeometry.left_ne_right_of_oangle_sign_ne_zero
+-/
 
+#print EuclideanGeometry.left_ne_of_oangle_sign_eq_one /-
 /-- If the sign of the angle between three points is positive, the first two points are not
 equal. -/
 theorem left_ne_of_oangle_sign_eq_one {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign = 1) : p₁ ≠ p₂ :=
   left_ne_of_oangle_sign_ne_zero (h.symm ▸ by decide : (∡ p₁ p₂ p₃).sign ≠ 0)
 #align euclidean_geometry.left_ne_of_oangle_sign_eq_one EuclideanGeometry.left_ne_of_oangle_sign_eq_one
+-/
 
+#print EuclideanGeometry.right_ne_of_oangle_sign_eq_one /-
 /-- If the sign of the angle between three points is positive, the last two points are not
 equal. -/
 theorem right_ne_of_oangle_sign_eq_one {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign = 1) : p₃ ≠ p₂ :=
   right_ne_of_oangle_sign_ne_zero (h.symm ▸ by decide : (∡ p₁ p₂ p₃).sign ≠ 0)
 #align euclidean_geometry.right_ne_of_oangle_sign_eq_one EuclideanGeometry.right_ne_of_oangle_sign_eq_one
+-/
 
+#print EuclideanGeometry.left_ne_right_of_oangle_sign_eq_one /-
 /-- If the sign of the angle between three points is positive, the first and third points are not
 equal. -/
 theorem left_ne_right_of_oangle_sign_eq_one {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign = 1) : p₁ ≠ p₃ :=
   left_ne_right_of_oangle_sign_ne_zero (h.symm ▸ by decide : (∡ p₁ p₂ p₃).sign ≠ 0)
 #align euclidean_geometry.left_ne_right_of_oangle_sign_eq_one EuclideanGeometry.left_ne_right_of_oangle_sign_eq_one
+-/
 
+#print EuclideanGeometry.left_ne_of_oangle_sign_eq_neg_one /-
 /-- If the sign of the angle between three points is negative, the first two points are not
 equal. -/
 theorem left_ne_of_oangle_sign_eq_neg_one {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign = -1) : p₁ ≠ p₂ :=
   left_ne_of_oangle_sign_ne_zero (h.symm ▸ by decide : (∡ p₁ p₂ p₃).sign ≠ 0)
 #align euclidean_geometry.left_ne_of_oangle_sign_eq_neg_one EuclideanGeometry.left_ne_of_oangle_sign_eq_neg_one
+-/
 
+#print EuclideanGeometry.right_ne_of_oangle_sign_eq_neg_one /-
 /-- If the sign of the angle between three points is negative, the last two points are not equal.
 -/
 theorem right_ne_of_oangle_sign_eq_neg_one {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign = -1) : p₃ ≠ p₂ :=
   right_ne_of_oangle_sign_ne_zero (h.symm ▸ by decide : (∡ p₁ p₂ p₃).sign ≠ 0)
 #align euclidean_geometry.right_ne_of_oangle_sign_eq_neg_one EuclideanGeometry.right_ne_of_oangle_sign_eq_neg_one
+-/
 
+#print EuclideanGeometry.left_ne_right_of_oangle_sign_eq_neg_one /-
 /-- If the sign of the angle between three points is negative, the first and third points are not
 equal. -/
 theorem left_ne_right_of_oangle_sign_eq_neg_one {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign = -1) :
     p₁ ≠ p₃ :=
   left_ne_right_of_oangle_sign_ne_zero (h.symm ▸ by decide : (∡ p₁ p₂ p₃).sign ≠ 0)
 #align euclidean_geometry.left_ne_right_of_oangle_sign_eq_neg_one EuclideanGeometry.left_ne_right_of_oangle_sign_eq_neg_one
+-/
 
+#print EuclideanGeometry.oangle_rev /-
 /-- Reversing the order of the points passed to `oangle` negates the angle. -/
 theorem oangle_rev (p₁ p₂ p₃ : P) : ∡ p₃ p₂ p₁ = -∡ p₁ p₂ p₃ :=
   o.oangle_rev _ _
 #align euclidean_geometry.oangle_rev EuclideanGeometry.oangle_rev
+-/
 
+#print EuclideanGeometry.oangle_add_oangle_rev /-
 /-- Adding an angle to that with the order of the points reversed results in 0. -/
 @[simp]
 theorem oangle_add_oangle_rev (p₁ p₂ p₃ : P) : ∡ p₁ p₂ p₃ + ∡ p₃ p₂ p₁ = 0 :=
   o.oangle_add_oangle_rev _ _
 #align euclidean_geometry.oangle_add_oangle_rev EuclideanGeometry.oangle_add_oangle_rev
+-/
 
+#print EuclideanGeometry.oangle_eq_zero_iff_oangle_rev_eq_zero /-
 /-- An oriented angle is zero if and only if the angle with the order of the points reversed is
 zero. -/
 theorem oangle_eq_zero_iff_oangle_rev_eq_zero {p₁ p₂ p₃ : P} : ∡ p₁ p₂ p₃ = 0 ↔ ∡ p₃ p₂ p₁ = 0 :=
   o.oangle_eq_zero_iff_oangle_rev_eq_zero
 #align euclidean_geometry.oangle_eq_zero_iff_oangle_rev_eq_zero EuclideanGeometry.oangle_eq_zero_iff_oangle_rev_eq_zero
+-/
 
+#print EuclideanGeometry.oangle_eq_pi_iff_oangle_rev_eq_pi /-
 /-- An oriented angle is `π` if and only if the angle with the order of the points reversed is
 `π`. -/
 theorem oangle_eq_pi_iff_oangle_rev_eq_pi {p₁ p₂ p₃ : P} : ∡ p₁ p₂ p₃ = π ↔ ∡ p₃ p₂ p₁ = π :=
   o.oangle_eq_pi_iff_oangle_rev_eq_pi
 #align euclidean_geometry.oangle_eq_pi_iff_oangle_rev_eq_pi EuclideanGeometry.oangle_eq_pi_iff_oangle_rev_eq_pi
+-/
 
+#print EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent /-
 /-- An oriented angle is not zero or `π` if and only if the three points are affinely
 independent. -/
 theorem oangle_ne_zero_and_ne_pi_iff_affineIndependent {p₁ p₂ p₃ : P} :
@@ -230,14 +291,18 @@ theorem oangle_ne_zero_and_ne_pi_iff_affineIndependent {p₁ p₂ p₃ : P} :
   ext i
   fin_cases i <;> rfl
 #align euclidean_geometry.oangle_ne_zero_and_ne_pi_iff_affine_independent EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent
+-/
 
+#print EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear /-
 /-- An oriented angle is zero or `π` if and only if the three points are collinear. -/
 theorem oangle_eq_zero_or_eq_pi_iff_collinear {p₁ p₂ p₃ : P} :
     ∡ p₁ p₂ p₃ = 0 ∨ ∡ p₁ p₂ p₃ = π ↔ Collinear ℝ ({p₁, p₂, p₃} : Set P) := by
   rw [← not_iff_not, not_or, oangle_ne_zero_and_ne_pi_iff_affine_independent,
     affineIndependent_iff_not_collinear_set]
 #align euclidean_geometry.oangle_eq_zero_or_eq_pi_iff_collinear EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear
+-/
 
+#print EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq /-
 /-- If twice the oriented angles between two triples of points are equal, one triple is affinely
 independent if and only if the other is. -/
 theorem affineIndependent_iff_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P}
@@ -245,7 +310,9 @@ theorem affineIndependent_iff_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ p₅ p
     AffineIndependent ℝ ![p₁, p₂, p₃] ↔ AffineIndependent ℝ ![p₄, p₅, p₆] := by
   simp_rw [← oangle_ne_zero_and_ne_pi_iff_affine_independent, ← Real.Angle.two_zsmul_ne_zero_iff, h]
 #align euclidean_geometry.affine_independent_iff_of_two_zsmul_oangle_eq EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq
+-/
 
+#print EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq /-
 /-- If twice the oriented angles between two triples of points are equal, one triple is collinear
 if and only if the other is. -/
 theorem collinear_iff_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P}
@@ -253,7 +320,9 @@ theorem collinear_iff_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P}
     Collinear ℝ ({p₁, p₂, p₃} : Set P) ↔ Collinear ℝ ({p₄, p₅, p₆} : Set P) := by
   simp_rw [← oangle_eq_zero_or_eq_pi_iff_collinear, ← Real.Angle.two_zsmul_eq_zero_iff, h]
 #align euclidean_geometry.collinear_iff_of_two_zsmul_oangle_eq EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq
+-/
 
+#print EuclideanGeometry.two_zsmul_oangle_of_vectorSpan_eq /-
 /-- If corresponding pairs of points in two angles have the same vector span, twice those angles
 are equal. -/
 theorem two_zsmul_oangle_of_vectorSpan_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P}
@@ -264,7 +333,9 @@ theorem two_zsmul_oangle_of_vectorSpan_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P}
   simp_rw [vectorSpan_pair] at h₁₂₄₅ h₃₂₆₅ 
   exact o.two_zsmul_oangle_of_span_eq_of_span_eq h₁₂₄₅ h₃₂₆₅
 #align euclidean_geometry.two_zsmul_oangle_of_vector_span_eq EuclideanGeometry.two_zsmul_oangle_of_vectorSpan_eq
+-/
 
+#print EuclideanGeometry.two_zsmul_oangle_of_parallel /-
 /-- If the lines determined by corresponding pairs of points in two angles are parallel, twice
 those angles are equal. -/
 theorem two_zsmul_oangle_of_parallel {p₁ p₂ p₃ p₄ p₅ p₆ : P}
@@ -274,7 +345,9 @@ theorem two_zsmul_oangle_of_parallel {p₁ p₂ p₃ p₄ p₅ p₆ : P}
   rw [AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq] at h₁₂₄₅ h₃₂₆₅ 
   exact two_zsmul_oangle_of_vector_span_eq h₁₂₄₅ h₃₂₆₅
 #align euclidean_geometry.two_zsmul_oangle_of_parallel EuclideanGeometry.two_zsmul_oangle_of_parallel
+-/
 
+#print EuclideanGeometry.oangle_add /-
 /-- Given three points not equal to `p`, the angle between the first and the second at `p` plus
 the angle between the second and the third equals the angle between the first and the third. -/
 @[simp]
@@ -282,7 +355,9 @@ theorem oangle_add {p p₁ p₂ p₃ : P} (hp₁ : p₁ ≠ p) (hp₂ : p₂ ≠
     ∡ p₁ p p₂ + ∡ p₂ p p₃ = ∡ p₁ p p₃ :=
   o.oangle_add (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₂) (vsub_ne_zero.2 hp₃)
 #align euclidean_geometry.oangle_add EuclideanGeometry.oangle_add
+-/
 
+#print EuclideanGeometry.oangle_add_swap /-
 /-- Given three points not equal to `p`, the angle between the second and the third at `p` plus
 the angle between the first and the second equals the angle between the first and the third. -/
 @[simp]
@@ -290,7 +365,9 @@ theorem oangle_add_swap {p p₁ p₂ p₃ : P} (hp₁ : p₁ ≠ p) (hp₂ : p
     ∡ p₂ p p₃ + ∡ p₁ p p₂ = ∡ p₁ p p₃ :=
   o.oangle_add_swap (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₂) (vsub_ne_zero.2 hp₃)
 #align euclidean_geometry.oangle_add_swap EuclideanGeometry.oangle_add_swap
+-/
 
+#print EuclideanGeometry.oangle_sub_left /-
 /-- Given three points not equal to `p`, the angle between the first and the third at `p` minus
 the angle between the first and the second equals the angle between the second and the third. -/
 @[simp]
@@ -298,7 +375,9 @@ theorem oangle_sub_left {p p₁ p₂ p₃ : P} (hp₁ : p₁ ≠ p) (hp₂ : p
     ∡ p₁ p p₃ - ∡ p₁ p p₂ = ∡ p₂ p p₃ :=
   o.oangle_sub_left (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₂) (vsub_ne_zero.2 hp₃)
 #align euclidean_geometry.oangle_sub_left EuclideanGeometry.oangle_sub_left
+-/
 
+#print EuclideanGeometry.oangle_sub_right /-
 /-- Given three points not equal to `p`, the angle between the first and the third at `p` minus
 the angle between the second and the third equals the angle between the first and the second. -/
 @[simp]
@@ -306,7 +385,9 @@ theorem oangle_sub_right {p p₁ p₂ p₃ : P} (hp₁ : p₁ ≠ p) (hp₂ : p
     ∡ p₁ p p₃ - ∡ p₂ p p₃ = ∡ p₁ p p₂ :=
   o.oangle_sub_right (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₂) (vsub_ne_zero.2 hp₃)
 #align euclidean_geometry.oangle_sub_right EuclideanGeometry.oangle_sub_right
+-/
 
+#print EuclideanGeometry.oangle_add_cyc3 /-
 /-- Given three points not equal to `p`, adding the angles between them at `p` in cyclic order
 results in 0. -/
 @[simp]
@@ -314,7 +395,9 @@ theorem oangle_add_cyc3 {p p₁ p₂ p₃ : P} (hp₁ : p₁ ≠ p) (hp₂ : p
     ∡ p₁ p p₂ + ∡ p₂ p p₃ + ∡ p₃ p p₁ = 0 :=
   o.oangle_add_cyc3 (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₂) (vsub_ne_zero.2 hp₃)
 #align euclidean_geometry.oangle_add_cyc3 EuclideanGeometry.oangle_add_cyc3
+-/
 
+#print EuclideanGeometry.oangle_eq_oangle_of_dist_eq /-
 /-- Pons asinorum, oriented angle-at-point form. -/
 theorem oangle_eq_oangle_of_dist_eq {p₁ p₂ p₃ : P} (h : dist p₁ p₂ = dist p₁ p₃) :
     ∡ p₁ p₂ p₃ = ∡ p₂ p₃ p₁ := by
@@ -322,7 +405,9 @@ theorem oangle_eq_oangle_of_dist_eq {p₁ p₂ p₃ : P} (h : dist p₁ p₂ = d
   rw [oangle, oangle, ← vsub_sub_vsub_cancel_left p₃ p₂ p₁, ← vsub_sub_vsub_cancel_left p₂ p₃ p₁,
     o.oangle_sub_eq_oangle_sub_rev_of_norm_eq h]
 #align euclidean_geometry.oangle_eq_oangle_of_dist_eq EuclideanGeometry.oangle_eq_oangle_of_dist_eq
+-/
 
+#print EuclideanGeometry.oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq /-
 /-- The angle at the apex of an isosceles triangle is `π` minus twice a base angle, oriented
 angle-at-point form. -/
 theorem oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq {p₁ p₂ p₃ : P} (hn : p₂ ≠ p₃)
@@ -335,7 +420,9 @@ theorem oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq {p₁ p₂ p₃ : P} (hn :
   · rw [← o.oangle_sub_eq_oangle_sub_rev_of_norm_eq h]; simp
   · simpa using hn
 #align euclidean_geometry.oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq EuclideanGeometry.oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq
+-/
 
+#print EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq /-
 /-- A base angle of an isosceles triangle is acute, oriented angle-at-point form. -/
 theorem abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq {p₁ p₂ p₃ : P}
     (h : dist p₁ p₂ = dist p₁ p₃) : |(∡ p₁ p₂ p₃).toReal| < π / 2 :=
@@ -344,48 +431,62 @@ theorem abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq {p₁ p₂ p₃ : P}
   rw [oangle, ← vsub_sub_vsub_cancel_left p₃ p₂ p₁]
   exact o.abs_oangle_sub_right_toReal_lt_pi_div_two h
 #align euclidean_geometry.abs_oangle_right_to_real_lt_pi_div_two_of_dist_eq EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq
+-/
 
+#print EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq /-
 /-- A base angle of an isosceles triangle is acute, oriented angle-at-point form. -/
 theorem abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq {p₁ p₂ p₃ : P}
     (h : dist p₁ p₂ = dist p₁ p₃) : |(∡ p₂ p₃ p₁).toReal| < π / 2 :=
   oangle_eq_oangle_of_dist_eq h ▸ abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq h
 #align euclidean_geometry.abs_oangle_left_to_real_lt_pi_div_two_of_dist_eq EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq
+-/
 
+#print EuclideanGeometry.cos_oangle_eq_cos_angle /-
 /-- The cosine of the oriented angle at `p` between two points not equal to `p` equals that of the
 unoriented angle. -/
 theorem cos_oangle_eq_cos_angle {p p₁ p₂ : P} (hp₁ : p₁ ≠ p) (hp₂ : p₂ ≠ p) :
     Real.Angle.cos (∡ p₁ p p₂) = Real.cos (∠ p₁ p p₂) :=
   o.cos_oangle_eq_cos_angle (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₂)
 #align euclidean_geometry.cos_oangle_eq_cos_angle EuclideanGeometry.cos_oangle_eq_cos_angle
+-/
 
+#print EuclideanGeometry.oangle_eq_angle_or_eq_neg_angle /-
 /-- The oriented angle at `p` between two points not equal to `p` is plus or minus the unoriented
 angle. -/
 theorem oangle_eq_angle_or_eq_neg_angle {p p₁ p₂ : P} (hp₁ : p₁ ≠ p) (hp₂ : p₂ ≠ p) :
     ∡ p₁ p p₂ = ∠ p₁ p p₂ ∨ ∡ p₁ p p₂ = -∠ p₁ p p₂ :=
   o.oangle_eq_angle_or_eq_neg_angle (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₂)
 #align euclidean_geometry.oangle_eq_angle_or_eq_neg_angle EuclideanGeometry.oangle_eq_angle_or_eq_neg_angle
+-/
 
+#print EuclideanGeometry.angle_eq_abs_oangle_toReal /-
 /-- The unoriented angle at `p` between two points not equal to `p` is the absolute value of the
 oriented angle. -/
 theorem angle_eq_abs_oangle_toReal {p p₁ p₂ : P} (hp₁ : p₁ ≠ p) (hp₂ : p₂ ≠ p) :
     ∠ p₁ p p₂ = |(∡ p₁ p p₂).toReal| :=
   o.angle_eq_abs_oangle_toReal (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₂)
 #align euclidean_geometry.angle_eq_abs_oangle_to_real EuclideanGeometry.angle_eq_abs_oangle_toReal
+-/
 
+#print EuclideanGeometry.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero /-
 /-- If the sign of the oriented angle at `p` between two points is zero, either one of the points
 equals `p` or the unoriented angle is 0 or π. -/
 theorem eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero {p p₁ p₂ : P}
     (h : (∡ p₁ p p₂).sign = 0) : p₁ = p ∨ p₂ = p ∨ ∠ p₁ p p₂ = 0 ∨ ∠ p₁ p p₂ = π := by
   convert o.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero h <;> simp
 #align euclidean_geometry.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero EuclideanGeometry.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero
+-/
 
+#print EuclideanGeometry.oangle_eq_of_angle_eq_of_sign_eq /-
 /-- If two unoriented angles are equal, and the signs of the corresponding oriented angles are
 equal, then the oriented angles are equal (even in degenerate cases). -/
 theorem oangle_eq_of_angle_eq_of_sign_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P} (h : ∠ p₁ p₂ p₃ = ∠ p₄ p₅ p₆)
     (hs : (∡ p₁ p₂ p₃).sign = (∡ p₄ p₅ p₆).sign) : ∡ p₁ p₂ p₃ = ∡ p₄ p₅ p₆ :=
   o.oangle_eq_of_angle_eq_of_sign_eq h hs
 #align euclidean_geometry.oangle_eq_of_angle_eq_of_sign_eq EuclideanGeometry.oangle_eq_of_angle_eq_of_sign_eq
+-/
 
+#print EuclideanGeometry.angle_eq_iff_oangle_eq_of_sign_eq /-
 /-- If the signs of two nondegenerate oriented angles between points are equal, the oriented
 angles are equal if and only if the unoriented angles are equal. -/
 theorem angle_eq_iff_oangle_eq_of_sign_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P} (hp₁ : p₁ ≠ p₂) (hp₃ : p₃ ≠ p₂)
@@ -394,33 +495,43 @@ theorem angle_eq_iff_oangle_eq_of_sign_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P} (h
   o.angle_eq_iff_oangle_eq_of_sign_eq (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₃) (vsub_ne_zero.2 hp₄)
     (vsub_ne_zero.2 hp₆) hs
 #align euclidean_geometry.angle_eq_iff_oangle_eq_of_sign_eq EuclideanGeometry.angle_eq_iff_oangle_eq_of_sign_eq
+-/
 
+#print EuclideanGeometry.oangle_eq_angle_of_sign_eq_one /-
 /-- The oriented angle between three points equals the unoriented angle if the sign is
 positive. -/
 theorem oangle_eq_angle_of_sign_eq_one {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign = 1) :
     ∡ p₁ p₂ p₃ = ∠ p₁ p₂ p₃ :=
   o.oangle_eq_angle_of_sign_eq_one h
 #align euclidean_geometry.oangle_eq_angle_of_sign_eq_one EuclideanGeometry.oangle_eq_angle_of_sign_eq_one
+-/
 
+#print EuclideanGeometry.oangle_eq_neg_angle_of_sign_eq_neg_one /-
 /-- The oriented angle between three points equals minus the unoriented angle if the sign is
 negative. -/
 theorem oangle_eq_neg_angle_of_sign_eq_neg_one {p₁ p₂ p₃ : P} (h : (∡ p₁ p₂ p₃).sign = -1) :
     ∡ p₁ p₂ p₃ = -∠ p₁ p₂ p₃ :=
   o.oangle_eq_neg_angle_of_sign_eq_neg_one h
 #align euclidean_geometry.oangle_eq_neg_angle_of_sign_eq_neg_one EuclideanGeometry.oangle_eq_neg_angle_of_sign_eq_neg_one
+-/
 
+#print EuclideanGeometry.oangle_eq_zero_iff_angle_eq_zero /-
 /-- The unoriented angle at `p` between two points not equal to `p` is zero if and only if the
 unoriented angle is zero. -/
 theorem oangle_eq_zero_iff_angle_eq_zero {p p₁ p₂ : P} (hp₁ : p₁ ≠ p) (hp₂ : p₂ ≠ p) :
     ∡ p₁ p p₂ = 0 ↔ ∠ p₁ p p₂ = 0 :=
   o.oangle_eq_zero_iff_angle_eq_zero (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₂)
 #align euclidean_geometry.oangle_eq_zero_iff_angle_eq_zero EuclideanGeometry.oangle_eq_zero_iff_angle_eq_zero
+-/
 
+#print EuclideanGeometry.oangle_eq_pi_iff_angle_eq_pi /-
 /-- The oriented angle between three points is `π` if and only if the unoriented angle is `π`. -/
 theorem oangle_eq_pi_iff_angle_eq_pi {p₁ p₂ p₃ : P} : ∡ p₁ p₂ p₃ = π ↔ ∠ p₁ p₂ p₃ = π :=
   o.oangle_eq_pi_iff_angle_eq_pi
 #align euclidean_geometry.oangle_eq_pi_iff_angle_eq_pi EuclideanGeometry.oangle_eq_pi_iff_angle_eq_pi
+-/
 
+#print EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_pi_div_two /-
 /-- If the oriented angle between three points is `π / 2`, so is the unoriented angle. -/
 theorem angle_eq_pi_div_two_of_oangle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = ↑(π / 2)) :
     ∠ p₁ p₂ p₃ = π / 2 :=
@@ -428,7 +539,9 @@ theorem angle_eq_pi_div_two_of_oangle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : 
   rw [angle, ← InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two]
   exact o.inner_eq_zero_of_oangle_eq_pi_div_two h
 #align euclidean_geometry.angle_eq_pi_div_two_of_oangle_eq_pi_div_two EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.angle_rev_eq_pi_div_two_of_oangle_eq_pi_div_two /-
 /-- If the oriented angle between three points is `π / 2`, so is the unoriented angle
 (reversed). -/
 theorem angle_rev_eq_pi_div_two_of_oangle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ = ↑(π / 2)) :
@@ -436,7 +549,9 @@ theorem angle_rev_eq_pi_div_two_of_oangle_eq_pi_div_two {p₁ p₂ p₃ : P} (h
   rw [angle_comm]
   exact angle_eq_pi_div_two_of_oangle_eq_pi_div_two h
 #align euclidean_geometry.angle_rev_eq_pi_div_two_of_oangle_eq_pi_div_two EuclideanGeometry.angle_rev_eq_pi_div_two_of_oangle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_neg_pi_div_two /-
 /-- If the oriented angle between three points is `-π / 2`, the unoriented angle is `π / 2`. -/
 theorem angle_eq_pi_div_two_of_oangle_eq_neg_pi_div_two {p₁ p₂ p₃ : P}
     (h : ∡ p₁ p₂ p₃ = ↑(-π / 2)) : ∠ p₁ p₂ p₃ = π / 2 :=
@@ -444,7 +559,9 @@ theorem angle_eq_pi_div_two_of_oangle_eq_neg_pi_div_two {p₁ p₂ p₃ : P}
   rw [angle, ← InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two]
   exact o.inner_eq_zero_of_oangle_eq_neg_pi_div_two h
 #align euclidean_geometry.angle_eq_pi_div_two_of_oangle_eq_neg_pi_div_two EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_neg_pi_div_two
+-/
 
+#print EuclideanGeometry.angle_rev_eq_pi_div_two_of_oangle_eq_neg_pi_div_two /-
 /-- If the oriented angle between three points is `-π / 2`, the unoriented angle (reversed) is
 `π / 2`. -/
 theorem angle_rev_eq_pi_div_two_of_oangle_eq_neg_pi_div_two {p₁ p₂ p₃ : P}
@@ -453,7 +570,9 @@ theorem angle_rev_eq_pi_div_two_of_oangle_eq_neg_pi_div_two {p₁ p₂ p₃ : P}
   rw [angle_comm]
   exact angle_eq_pi_div_two_of_oangle_eq_neg_pi_div_two h
 #align euclidean_geometry.angle_rev_eq_pi_div_two_of_oangle_eq_neg_pi_div_two EuclideanGeometry.angle_rev_eq_pi_div_two_of_oangle_eq_neg_pi_div_two
+-/
 
+#print EuclideanGeometry.oangle_swap₁₂_sign /-
 /-- Swapping the first and second points in an oriented angle negates the sign of that angle. -/
 theorem oangle_swap₁₂_sign (p₁ p₂ p₃ : P) : -(∡ p₁ p₂ p₃).sign = (∡ p₂ p₁ p₃).sign :=
   by
@@ -464,40 +583,54 @@ theorem oangle_swap₁₂_sign (p₁ p₂ p₃ : P) : -(∡ p₁ p₂ p₃).sign
   rw [o.oangle_sign_smul_add_smul_right]
   simp
 #align euclidean_geometry.oangle_swap₁₂_sign EuclideanGeometry.oangle_swap₁₂_sign
+-/
 
+#print EuclideanGeometry.oangle_swap₁₃_sign /-
 /-- Swapping the first and third points in an oriented angle negates the sign of that angle. -/
 theorem oangle_swap₁₃_sign (p₁ p₂ p₃ : P) : -(∡ p₁ p₂ p₃).sign = (∡ p₃ p₂ p₁).sign := by
   rw [oangle_rev, Real.Angle.sign_neg, neg_neg]
 #align euclidean_geometry.oangle_swap₁₃_sign EuclideanGeometry.oangle_swap₁₃_sign
+-/
 
+#print EuclideanGeometry.oangle_swap₂₃_sign /-
 /-- Swapping the second and third points in an oriented angle negates the sign of that angle. -/
 theorem oangle_swap₂₃_sign (p₁ p₂ p₃ : P) : -(∡ p₁ p₂ p₃).sign = (∡ p₁ p₃ p₂).sign := by
   rw [oangle_swap₁₃_sign, ← oangle_swap₁₂_sign, oangle_swap₁₃_sign]
 #align euclidean_geometry.oangle_swap₂₃_sign EuclideanGeometry.oangle_swap₂₃_sign
+-/
 
+#print EuclideanGeometry.oangle_rotate_sign /-
 /-- Rotating the points in an oriented angle does not change the sign of that angle. -/
 theorem oangle_rotate_sign (p₁ p₂ p₃ : P) : (∡ p₂ p₃ p₁).sign = (∡ p₁ p₂ p₃).sign := by
   rw [← oangle_swap₁₂_sign, oangle_swap₁₃_sign]
 #align euclidean_geometry.oangle_rotate_sign EuclideanGeometry.oangle_rotate_sign
+-/
 
+#print EuclideanGeometry.oangle_eq_pi_iff_sbtw /-
 /-- The oriented angle between three points is π if and only if the second point is strictly
 between the other two. -/
 theorem oangle_eq_pi_iff_sbtw {p₁ p₂ p₃ : P} : ∡ p₁ p₂ p₃ = π ↔ Sbtw ℝ p₁ p₂ p₃ := by
   rw [oangle_eq_pi_iff_angle_eq_pi, angle_eq_pi_iff_sbtw]
 #align euclidean_geometry.oangle_eq_pi_iff_sbtw EuclideanGeometry.oangle_eq_pi_iff_sbtw
+-/
 
+#print Sbtw.oangle₁₂₃_eq_pi /-
 /-- If the second of three points is strictly between the other two, the oriented angle at that
 point is π. -/
 theorem Sbtw.oangle₁₂₃_eq_pi {p₁ p₂ p₃ : P} (h : Sbtw ℝ p₁ p₂ p₃) : ∡ p₁ p₂ p₃ = π :=
   oangle_eq_pi_iff_sbtw.2 h
 #align sbtw.oangle₁₂₃_eq_pi Sbtw.oangle₁₂₃_eq_pi
+-/
 
+#print Sbtw.oangle₃₂₁_eq_pi /-
 /-- If the second of three points is strictly between the other two, the oriented angle at that
 point (reversed) is π. -/
 theorem Sbtw.oangle₃₂₁_eq_pi {p₁ p₂ p₃ : P} (h : Sbtw ℝ p₁ p₂ p₃) : ∡ p₃ p₂ p₁ = π := by
   rw [oangle_eq_pi_iff_oangle_rev_eq_pi, ← h.oangle₁₂₃_eq_pi]
 #align sbtw.oangle₃₂₁_eq_pi Sbtw.oangle₃₂₁_eq_pi
+-/
 
+#print Wbtw.oangle₂₁₃_eq_zero /-
 /-- If the second of three points is weakly between the other two, the oriented angle at the
 first point is zero. -/
 theorem Wbtw.oangle₂₁₃_eq_zero {p₁ p₂ p₃ : P} (h : Wbtw ℝ p₁ p₂ p₃) : ∡ p₂ p₁ p₃ = 0 :=
@@ -507,49 +640,65 @@ theorem Wbtw.oangle₂₁₃_eq_zero {p₁ p₂ p₃ : P} (h : Wbtw ℝ p₁ p
   rw [oangle_eq_zero_iff_angle_eq_zero hp₂p₁ hp₃p₁]
   exact h.angle₂₁₃_eq_zero_of_ne hp₂p₁
 #align wbtw.oangle₂₁₃_eq_zero Wbtw.oangle₂₁₃_eq_zero
+-/
 
+#print Sbtw.oangle₂₁₃_eq_zero /-
 /-- If the second of three points is strictly between the other two, the oriented angle at the
 first point is zero. -/
 theorem Sbtw.oangle₂₁₃_eq_zero {p₁ p₂ p₃ : P} (h : Sbtw ℝ p₁ p₂ p₃) : ∡ p₂ p₁ p₃ = 0 :=
   h.Wbtw.oangle₂₁₃_eq_zero
 #align sbtw.oangle₂₁₃_eq_zero Sbtw.oangle₂₁₃_eq_zero
+-/
 
+#print Wbtw.oangle₃₁₂_eq_zero /-
 /-- If the second of three points is weakly between the other two, the oriented angle at the
 first point (reversed) is zero. -/
 theorem Wbtw.oangle₃₁₂_eq_zero {p₁ p₂ p₃ : P} (h : Wbtw ℝ p₁ p₂ p₃) : ∡ p₃ p₁ p₂ = 0 := by
   rw [oangle_eq_zero_iff_oangle_rev_eq_zero, h.oangle₂₁₃_eq_zero]
 #align wbtw.oangle₃₁₂_eq_zero Wbtw.oangle₃₁₂_eq_zero
+-/
 
+#print Sbtw.oangle₃₁₂_eq_zero /-
 /-- If the second of three points is strictly between the other two, the oriented angle at the
 first point (reversed) is zero. -/
 theorem Sbtw.oangle₃₁₂_eq_zero {p₁ p₂ p₃ : P} (h : Sbtw ℝ p₁ p₂ p₃) : ∡ p₃ p₁ p₂ = 0 :=
   h.Wbtw.oangle₃₁₂_eq_zero
 #align sbtw.oangle₃₁₂_eq_zero Sbtw.oangle₃₁₂_eq_zero
+-/
 
+#print Wbtw.oangle₂₃₁_eq_zero /-
 /-- If the second of three points is weakly between the other two, the oriented angle at the
 third point is zero. -/
 theorem Wbtw.oangle₂₃₁_eq_zero {p₁ p₂ p₃ : P} (h : Wbtw ℝ p₁ p₂ p₃) : ∡ p₂ p₃ p₁ = 0 :=
   h.symm.oangle₂₁₃_eq_zero
 #align wbtw.oangle₂₃₁_eq_zero Wbtw.oangle₂₃₁_eq_zero
+-/
 
+#print Sbtw.oangle₂₃₁_eq_zero /-
 /-- If the second of three points is strictly between the other two, the oriented angle at the
 third point is zero. -/
 theorem Sbtw.oangle₂₃₁_eq_zero {p₁ p₂ p₃ : P} (h : Sbtw ℝ p₁ p₂ p₃) : ∡ p₂ p₃ p₁ = 0 :=
   h.Wbtw.oangle₂₃₁_eq_zero
 #align sbtw.oangle₂₃₁_eq_zero Sbtw.oangle₂₃₁_eq_zero
+-/
 
+#print Wbtw.oangle₁₃₂_eq_zero /-
 /-- If the second of three points is weakly between the other two, the oriented angle at the
 third point (reversed) is zero. -/
 theorem Wbtw.oangle₁₃₂_eq_zero {p₁ p₂ p₃ : P} (h : Wbtw ℝ p₁ p₂ p₃) : ∡ p₁ p₃ p₂ = 0 :=
   h.symm.oangle₃₁₂_eq_zero
 #align wbtw.oangle₁₃₂_eq_zero Wbtw.oangle₁₃₂_eq_zero
+-/
 
+#print Sbtw.oangle₁₃₂_eq_zero /-
 /-- If the second of three points is strictly between the other two, the oriented angle at the
 third point (reversed) is zero. -/
 theorem Sbtw.oangle₁₃₂_eq_zero {p₁ p₂ p₃ : P} (h : Sbtw ℝ p₁ p₂ p₃) : ∡ p₁ p₃ p₂ = 0 :=
   h.Wbtw.oangle₁₃₂_eq_zero
 #align sbtw.oangle₁₃₂_eq_zero Sbtw.oangle₁₃₂_eq_zero
+-/
 
+#print EuclideanGeometry.oangle_eq_zero_iff_wbtw /-
 /-- The oriented angle between three points is zero if and only if one of the first and third
 points is weakly between the other two. -/
 theorem oangle_eq_zero_iff_wbtw {p₁ p₂ p₃ : P} :
@@ -560,7 +709,9 @@ theorem oangle_eq_zero_iff_wbtw {p₁ p₂ p₃ : P} :
   rw [oangle_eq_zero_iff_angle_eq_zero hp₁p₂ hp₃p₂, angle_eq_zero_iff_ne_and_wbtw]
   simp [hp₁p₂, hp₃p₂]
 #align euclidean_geometry.oangle_eq_zero_iff_wbtw EuclideanGeometry.oangle_eq_zero_iff_wbtw
+-/
 
+#print Wbtw.oangle_eq_left /-
 /-- An oriented angle is unchanged by replacing the first point by one weakly further away on the
 same ray. -/
 theorem Wbtw.oangle_eq_left {p₁ p₁' p₂ p₃ : P} (h : Wbtw ℝ p₂ p₁ p₁') (hp₁p₂ : p₁ ≠ p₂) :
@@ -569,25 +720,33 @@ theorem Wbtw.oangle_eq_left {p₁ p₁' p₂ p₃ : P} (h : Wbtw ℝ p₂ p₁ p
   by_cases hp₁'p₂ : p₁' = p₂; · rw [hp₁'p₂, wbtw_self_iff] at h ; exact False.elim (hp₁p₂ h)
   rw [← oangle_add hp₁'p₂ hp₁p₂ hp₃p₂, h.oangle₃₁₂_eq_zero, zero_add]
 #align wbtw.oangle_eq_left Wbtw.oangle_eq_left
+-/
 
+#print Sbtw.oangle_eq_left /-
 /-- An oriented angle is unchanged by replacing the first point by one strictly further away on
 the same ray. -/
 theorem Sbtw.oangle_eq_left {p₁ p₁' p₂ p₃ : P} (h : Sbtw ℝ p₂ p₁ p₁') : ∡ p₁ p₂ p₃ = ∡ p₁' p₂ p₃ :=
   h.Wbtw.oangle_eq_left h.ne_left
 #align sbtw.oangle_eq_left Sbtw.oangle_eq_left
+-/
 
+#print Wbtw.oangle_eq_right /-
 /-- An oriented angle is unchanged by replacing the third point by one weakly further away on the
 same ray. -/
 theorem Wbtw.oangle_eq_right {p₁ p₂ p₃ p₃' : P} (h : Wbtw ℝ p₂ p₃ p₃') (hp₃p₂ : p₃ ≠ p₂) :
     ∡ p₁ p₂ p₃ = ∡ p₁ p₂ p₃' := by rw [oangle_rev, h.oangle_eq_left hp₃p₂, ← oangle_rev]
 #align wbtw.oangle_eq_right Wbtw.oangle_eq_right
+-/
 
+#print Sbtw.oangle_eq_right /-
 /-- An oriented angle is unchanged by replacing the third point by one strictly further away on
 the same ray. -/
 theorem Sbtw.oangle_eq_right {p₁ p₂ p₃ p₃' : P} (h : Sbtw ℝ p₂ p₃ p₃') : ∡ p₁ p₂ p₃ = ∡ p₁ p₂ p₃' :=
   h.Wbtw.oangle_eq_right h.ne_left
 #align sbtw.oangle_eq_right Sbtw.oangle_eq_right
+-/
 
+#print EuclideanGeometry.oangle_midpoint_left /-
 /-- An oriented angle is unchanged by replacing the first point with the midpoint of the segment
 between it and the second point. -/
 @[simp]
@@ -596,14 +755,18 @@ theorem oangle_midpoint_left (p₁ p₂ p₃ : P) : ∡ (midpoint ℝ p₁ p₂)
   by_cases h : p₁ = p₂; · simp [h]
   exact (sbtw_midpoint_of_ne ℝ h).symm.oangle_eq_left
 #align euclidean_geometry.oangle_midpoint_left EuclideanGeometry.oangle_midpoint_left
+-/
 
+#print EuclideanGeometry.oangle_midpoint_rev_left /-
 /-- An oriented angle is unchanged by replacing the first point with the midpoint of the segment
 between the second point and that point. -/
 @[simp]
 theorem oangle_midpoint_rev_left (p₁ p₂ p₃ : P) : ∡ (midpoint ℝ p₂ p₁) p₂ p₃ = ∡ p₁ p₂ p₃ := by
   rw [midpoint_comm, oangle_midpoint_left]
 #align euclidean_geometry.oangle_midpoint_rev_left EuclideanGeometry.oangle_midpoint_rev_left
+-/
 
+#print EuclideanGeometry.oangle_midpoint_right /-
 /-- An oriented angle is unchanged by replacing the third point with the midpoint of the segment
 between it and the second point. -/
 @[simp]
@@ -612,28 +775,36 @@ theorem oangle_midpoint_right (p₁ p₂ p₃ : P) : ∡ p₁ p₂ (midpoint ℝ
   by_cases h : p₃ = p₂; · simp [h]
   exact (sbtw_midpoint_of_ne ℝ h).symm.oangle_eq_right
 #align euclidean_geometry.oangle_midpoint_right EuclideanGeometry.oangle_midpoint_right
+-/
 
+#print EuclideanGeometry.oangle_midpoint_rev_right /-
 /-- An oriented angle is unchanged by replacing the third point with the midpoint of the segment
 between the second point and that point. -/
 @[simp]
 theorem oangle_midpoint_rev_right (p₁ p₂ p₃ : P) : ∡ p₁ p₂ (midpoint ℝ p₂ p₃) = ∡ p₁ p₂ p₃ := by
   rw [midpoint_comm, oangle_midpoint_right]
 #align euclidean_geometry.oangle_midpoint_rev_right EuclideanGeometry.oangle_midpoint_rev_right
+-/
 
+#print Sbtw.oangle_eq_add_pi_left /-
 /-- Replacing the first point by one on the same line but the opposite ray adds π to the oriented
 angle. -/
 theorem Sbtw.oangle_eq_add_pi_left {p₁ p₁' p₂ p₃ : P} (h : Sbtw ℝ p₁ p₂ p₁') (hp₃p₂ : p₃ ≠ p₂) :
     ∡ p₁ p₂ p₃ = ∡ p₁' p₂ p₃ + π := by
   rw [← h.oangle₁₂₃_eq_pi, oangle_add_swap h.left_ne h.right_ne hp₃p₂]
 #align sbtw.oangle_eq_add_pi_left Sbtw.oangle_eq_add_pi_left
+-/
 
+#print Sbtw.oangle_eq_add_pi_right /-
 /-- Replacing the third point by one on the same line but the opposite ray adds π to the oriented
 angle. -/
 theorem Sbtw.oangle_eq_add_pi_right {p₁ p₂ p₃ p₃' : P} (h : Sbtw ℝ p₃ p₂ p₃') (hp₁p₂ : p₁ ≠ p₂) :
     ∡ p₁ p₂ p₃ = ∡ p₁ p₂ p₃' + π := by
   rw [← h.oangle₃₂₁_eq_pi, oangle_add hp₁p₂ h.right_ne h.left_ne]
 #align sbtw.oangle_eq_add_pi_right Sbtw.oangle_eq_add_pi_right
+-/
 
+#print Sbtw.oangle_eq_left_right /-
 /-- Replacing both the first and third points by ones on the same lines but the opposite rays
 does not change the oriented angle (vertically opposite angles). -/
 theorem Sbtw.oangle_eq_left_right {p₁ p₁' p₂ p₃ p₃' : P} (h₁ : Sbtw ℝ p₁ p₂ p₁')
@@ -641,7 +812,9 @@ theorem Sbtw.oangle_eq_left_right {p₁ p₁' p₂ p₃ p₃' : P} (h₁ : Sbtw
   rw [h₁.oangle_eq_add_pi_left h₃.left_ne, h₃.oangle_eq_add_pi_right h₁.right_ne, add_assoc,
     Real.Angle.coe_pi_add_coe_pi, add_zero]
 #align sbtw.oangle_eq_left_right Sbtw.oangle_eq_left_right
+-/
 
+#print Collinear.two_zsmul_oangle_eq_left /-
 /-- Replacing the first point by one on the same line does not change twice the oriented angle. -/
 theorem Collinear.two_zsmul_oangle_eq_left {p₁ p₁' p₂ p₃ : P}
     (h : Collinear ℝ ({p₁, p₂, p₁'} : Set P)) (hp₁p₂ : p₁ ≠ p₂) (hp₁'p₂ : p₁' ≠ p₂) :
@@ -654,14 +827,18 @@ theorem Collinear.two_zsmul_oangle_eq_left {p₁ p₁' p₂ p₃ : P}
   · rw [hw.oangle_eq_left hp₁'p₂]
   · rw [hw.symm.oangle_eq_left hp₁p₂]
 #align collinear.two_zsmul_oangle_eq_left Collinear.two_zsmul_oangle_eq_left
+-/
 
+#print Collinear.two_zsmul_oangle_eq_right /-
 /-- Replacing the third point by one on the same line does not change twice the oriented angle. -/
 theorem Collinear.two_zsmul_oangle_eq_right {p₁ p₂ p₃ p₃' : P}
     (h : Collinear ℝ ({p₃, p₂, p₃'} : Set P)) (hp₃p₂ : p₃ ≠ p₂) (hp₃'p₂ : p₃' ≠ p₂) :
     (2 : ℤ) • ∡ p₁ p₂ p₃ = (2 : ℤ) • ∡ p₁ p₂ p₃' := by
   rw [oangle_rev, smul_neg, h.two_zsmul_oangle_eq_left hp₃p₂ hp₃'p₂, ← smul_neg, ← oangle_rev]
 #align collinear.two_zsmul_oangle_eq_right Collinear.two_zsmul_oangle_eq_right
+-/
 
+#print EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint /-
 /-- Two different points are equidistant from a third point if and only if that third point
 equals some multiple of a `π / 2` rotation of the vector between those points, plus the midpoint
 of those points. -/
@@ -689,10 +866,12 @@ theorem dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint {p₁ p₂ p : P}
       real_inner_self_eq_norm_mul_norm, inner_sub_sub_self]
     simp [-neg_vsub_eq_vsub_rev]
 #align euclidean_geometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint
+-/
 
 open AffineSubspace
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Collinear.oangle_sign_of_sameRay_vsub /-
 /-- Given two pairs of distinct points on the same line, such that the vectors between those
 pairs of points are on the same ray (oriented in the same direction on that line), and a fifth
 point, the angles at the fifth point between each of those two pairs of points have the same
@@ -790,7 +969,9 @@ theorem Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (p₅ :
       simp
     convert Real.Angle.sign_eq_of_continuousOn hco hf hsp hp₃p₄s hp₁p₂s
 #align collinear.oangle_sign_of_same_ray_vsub Collinear.oangle_sign_of_sameRay_vsub
+-/
 
+#print Sbtw.oangle_sign_eq /-
 /-- Given three points in strict order on the same line, and a fourth point, the angles at the
 fourth point between the first and second or second and third points have the same sign. -/
 theorem Sbtw.oangle_sign_eq {p₁ p₂ p₃ : P} (p₄ : P) (h : Sbtw ℝ p₁ p₂ p₃) :
@@ -798,7 +979,9 @@ theorem Sbtw.oangle_sign_eq {p₁ p₂ p₃ : P} (p₄ : P) (h : Sbtw ℝ p₁ p
   haveI hc : Collinear ℝ ({p₁, p₂, p₂, p₃} : Set P) := by simpa using h.wbtw.collinear
   hc.oangle_sign_of_same_ray_vsub _ h.left_ne h.ne_right h.wbtw.same_ray_vsub
 #align sbtw.oangle_sign_eq Sbtw.oangle_sign_eq
+-/
 
+#print Wbtw.oangle_sign_eq_of_ne_left /-
 /-- Given three points in weak order on the same line, with the first not equal to the second,
 and a fourth point, the angles at the fourth point between the first and second or first and
 third points have the same sign. -/
@@ -808,14 +991,18 @@ theorem Wbtw.oangle_sign_eq_of_ne_left {p₁ p₂ p₃ : P} (p₄ : P) (h : Wbtw
     simpa [Set.insert_comm p₂] using h.collinear
   hc.oangle_sign_of_same_ray_vsub _ hne (h.left_ne_right_of_ne_left hne.symm) h.same_ray_vsub_left
 #align wbtw.oangle_sign_eq_of_ne_left Wbtw.oangle_sign_eq_of_ne_left
+-/
 
+#print Sbtw.oangle_sign_eq_left /-
 /-- Given three points in strict order on the same line, and a fourth point, the angles at the
 fourth point between the first and second or first and third points have the same sign. -/
 theorem Sbtw.oangle_sign_eq_left {p₁ p₂ p₃ : P} (p₄ : P) (h : Sbtw ℝ p₁ p₂ p₃) :
     (∡ p₁ p₄ p₂).sign = (∡ p₁ p₄ p₃).sign :=
   h.Wbtw.oangle_sign_eq_of_ne_left _ h.left_ne
 #align sbtw.oangle_sign_eq_left Sbtw.oangle_sign_eq_left
+-/
 
+#print Wbtw.oangle_sign_eq_of_ne_right /-
 /-- Given three points in weak order on the same line, with the second not equal to the third,
 and a fourth point, the angles at the fourth point between the second and third or first and
 third points have the same sign. -/
@@ -823,14 +1010,18 @@ theorem Wbtw.oangle_sign_eq_of_ne_right {p₁ p₂ p₃ : P} (p₄ : P) (h : Wbt
     (hne : p₂ ≠ p₃) : (∡ p₂ p₄ p₃).sign = (∡ p₁ p₄ p₃).sign := by
   simp_rw [oangle_rev p₃, Real.Angle.sign_neg, h.symm.oangle_sign_eq_of_ne_left _ hne.symm]
 #align wbtw.oangle_sign_eq_of_ne_right Wbtw.oangle_sign_eq_of_ne_right
+-/
 
+#print Sbtw.oangle_sign_eq_right /-
 /-- Given three points in strict order on the same line, and a fourth point, the angles at the
 fourth point between the second and third or first and third points have the same sign. -/
 theorem Sbtw.oangle_sign_eq_right {p₁ p₂ p₃ : P} (p₄ : P) (h : Sbtw ℝ p₁ p₂ p₃) :
     (∡ p₂ p₄ p₃).sign = (∡ p₁ p₄ p₃).sign :=
   h.Wbtw.oangle_sign_eq_of_ne_right _ h.ne_right
 #align sbtw.oangle_sign_eq_right Sbtw.oangle_sign_eq_right
+-/
 
+#print AffineSubspace.SSameSide.oangle_sign_eq /-
 /-- Given two points in an affine subspace, the angles between those two points at two other
 points on the same side of that subspace have the same sign. -/
 theorem AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P} {p₁ p₂ p₃ p₄ : P}
@@ -865,7 +1056,9 @@ theorem AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P} {p₁
   have hp₄ : (p₁, p₄, p₂) ∈ sp := Set.mem_image_of_mem _ hp₃p₄
   convert Real.Angle.sign_eq_of_continuousOn hc hf hsp hp₃ hp₄
 #align affine_subspace.s_same_side.oangle_sign_eq AffineSubspace.SSameSide.oangle_sign_eq
+-/
 
+#print AffineSubspace.SOppSide.oangle_sign_eq_neg /-
 /-- Given two points in an affine subspace, the angles between those two points at two other
 points on opposite sides of that subspace have opposite signs. -/
 theorem AffineSubspace.SOppSide.oangle_sign_eq_neg {s : AffineSubspace ℝ P} {p₁ p₂ p₃ p₄ : P}
@@ -878,6 +1071,7 @@ theorem AffineSubspace.SOppSide.oangle_sign_eq_neg {s : AffineSubspace ℝ P} {p
     ← oangle_rotate_sign p₁, ← oangle_rotate_sign p₁, oangle_swap₁₃_sign,
     (sbtw_pointReflection_of_ne ℝ hp₁p₃).symm.oangle_sign_eq _]
 #align affine_subspace.s_opp_side.oangle_sign_eq_neg AffineSubspace.SOppSide.oangle_sign_eq_neg
+-/
 
 end EuclideanGeometry
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -36,9 +36,6 @@ namespace EuclideanGeometry
 variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P] [hd2 : Fact (finrank ℝ V = 2)] [Module.Oriented ℝ V (Fin 2)]
 
-include hd2
-
--- mathport name: expro
 local notation "o" => Module.Oriented.positiveOrientation
 
 /-- The oriented angle at `p₂` between the line segments to `p₁` and `p₃`, modulo `2 * π`. If
@@ -48,7 +45,6 @@ def oangle (p₁ p₂ p₃ : P) : Real.Angle :=
   o.oangle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂)
 #align euclidean_geometry.oangle EuclideanGeometry.oangle
 
--- mathport name: oangle
 scoped notation "∡" => EuclideanGeometry.oangle
 
 /-- Oriented angles are continuous when neither end point equals the middle point. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -724,7 +724,7 @@ theorem Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (p₅ :
     rw [hs₁₅₂, hs₃₅₄]
   · let s : Set (P × P × P) :=
       (fun x : line[ℝ, p₁, p₂] × V => (x.1, p₅, x.2 +ᵥ x.1)) ''
-        Set.univ ×ˢ { v | SameRay ℝ (p₂ -ᵥ p₁) v ∧ v ≠ 0 }
+        Set.univ ×ˢ {v | SameRay ℝ (p₂ -ᵥ p₁) v ∧ v ≠ 0}
     have hco : IsConnected s :=
       haveI : ConnectedSpace line[ℝ, p₁, p₂] := AddTorsor.connectedSpace _ _
       (is_connected_univ.prod
@@ -842,7 +842,7 @@ theorem AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P} {p₁
     (∡ p₁ p₄ p₂).sign = (∡ p₁ p₃ p₂).sign :=
   by
   by_cases h : p₁ = p₂; · simp [h]
-  let sp : Set (P × P × P) := (fun p : P => (p₁, p, p₂)) '' { p | s.s_same_side p₃ p }
+  let sp : Set (P × P × P) := (fun p : P => (p₁, p, p₂)) '' {p | s.s_same_side p₃ p}
   have hc : IsConnected sp :=
     (is_connected_set_of_s_same_side hp₃p₄.2.1 hp₃p₄.nonempty).image _
       (continuous_const.prod_mk (Continuous.Prod.mk_left _)).ContinuousOn

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -265,7 +265,7 @@ theorem two_zsmul_oangle_of_vectorSpan_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P}
     (h₃₂₆₅ : vectorSpan ℝ ({p₃, p₂} : Set P) = vectorSpan ℝ ({p₆, p₅} : Set P)) :
     (2 : ℤ) • ∡ p₁ p₂ p₃ = (2 : ℤ) • ∡ p₄ p₅ p₆ :=
   by
-  simp_rw [vectorSpan_pair] at h₁₂₄₅ h₃₂₆₅
+  simp_rw [vectorSpan_pair] at h₁₂₄₅ h₃₂₆₅ 
   exact o.two_zsmul_oangle_of_span_eq_of_span_eq h₁₂₄₅ h₃₂₆₅
 #align euclidean_geometry.two_zsmul_oangle_of_vector_span_eq EuclideanGeometry.two_zsmul_oangle_of_vectorSpan_eq
 
@@ -275,7 +275,7 @@ theorem two_zsmul_oangle_of_parallel {p₁ p₂ p₃ p₄ p₅ p₆ : P}
     (h₁₂₄₅ : line[ℝ, p₁, p₂] ∥ line[ℝ, p₄, p₅]) (h₃₂₆₅ : line[ℝ, p₃, p₂] ∥ line[ℝ, p₆, p₅]) :
     (2 : ℤ) • ∡ p₁ p₂ p₃ = (2 : ℤ) • ∡ p₄ p₅ p₆ :=
   by
-  rw [AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq] at h₁₂₄₅ h₃₂₆₅
+  rw [AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq] at h₁₂₄₅ h₃₂₆₅ 
   exact two_zsmul_oangle_of_vector_span_eq h₁₂₄₅ h₃₂₆₅
 #align euclidean_geometry.two_zsmul_oangle_of_parallel EuclideanGeometry.two_zsmul_oangle_of_parallel
 
@@ -322,7 +322,7 @@ theorem oangle_add_cyc3 {p p₁ p₂ p₃ : P} (hp₁ : p₁ ≠ p) (hp₂ : p
 /-- Pons asinorum, oriented angle-at-point form. -/
 theorem oangle_eq_oangle_of_dist_eq {p₁ p₂ p₃ : P} (h : dist p₁ p₂ = dist p₁ p₃) :
     ∡ p₁ p₂ p₃ = ∡ p₂ p₃ p₁ := by
-  simp_rw [dist_eq_norm_vsub] at h
+  simp_rw [dist_eq_norm_vsub] at h 
   rw [oangle, oangle, ← vsub_sub_vsub_cancel_left p₃ p₂ p₁, ← vsub_sub_vsub_cancel_left p₂ p₃ p₁,
     o.oangle_sub_eq_oangle_sub_rev_of_norm_eq h]
 #align euclidean_geometry.oangle_eq_oangle_of_dist_eq EuclideanGeometry.oangle_eq_oangle_of_dist_eq
@@ -332,7 +332,7 @@ angle-at-point form. -/
 theorem oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq {p₁ p₂ p₃ : P} (hn : p₂ ≠ p₃)
     (h : dist p₁ p₂ = dist p₁ p₃) : ∡ p₃ p₁ p₂ = π - (2 : ℤ) • ∡ p₁ p₂ p₃ :=
   by
-  simp_rw [dist_eq_norm_vsub] at h
+  simp_rw [dist_eq_norm_vsub] at h 
   rw [oangle, oangle]
   convert o.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eq _ h using 1
   · rw [← neg_vsub_eq_vsub_rev p₁ p₃, ← neg_vsub_eq_vsub_rev p₁ p₂, o.oangle_neg_neg]
@@ -344,7 +344,7 @@ theorem oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq {p₁ p₂ p₃ : P} (hn :
 theorem abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq {p₁ p₂ p₃ : P}
     (h : dist p₁ p₂ = dist p₁ p₃) : |(∡ p₁ p₂ p₃).toReal| < π / 2 :=
   by
-  simp_rw [dist_eq_norm_vsub] at h
+  simp_rw [dist_eq_norm_vsub] at h 
   rw [oangle, ← vsub_sub_vsub_cancel_left p₃ p₂ p₁]
   exact o.abs_oangle_sub_right_toReal_lt_pi_div_two h
 #align euclidean_geometry.abs_oangle_right_to_real_lt_pi_div_two_of_dist_eq EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq
@@ -570,7 +570,7 @@ same ray. -/
 theorem Wbtw.oangle_eq_left {p₁ p₁' p₂ p₃ : P} (h : Wbtw ℝ p₂ p₁ p₁') (hp₁p₂ : p₁ ≠ p₂) :
     ∡ p₁ p₂ p₃ = ∡ p₁' p₂ p₃ := by
   by_cases hp₃p₂ : p₃ = p₂; · simp [hp₃p₂]
-  by_cases hp₁'p₂ : p₁' = p₂; · rw [hp₁'p₂, wbtw_self_iff] at h; exact False.elim (hp₁p₂ h)
+  by_cases hp₁'p₂ : p₁' = p₂; · rw [hp₁'p₂, wbtw_self_iff] at h ; exact False.elim (hp₁p₂ h)
   rw [← oangle_add hp₁'p₂ hp₁p₂ hp₃p₂, h.oangle₃₁₂_eq_zero, zero_add]
 #align wbtw.oangle_eq_left Wbtw.oangle_eq_left
 
@@ -678,14 +678,14 @@ theorem dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint {p₁ p₂ p : P}
       by
       rw [@dist_eq_norm_vsub' V, @dist_eq_norm_vsub' V, ←
         mul_self_inj (norm_nonneg _) (norm_nonneg _), ← real_inner_self_eq_norm_mul_norm, ←
-        real_inner_self_eq_norm_mul_norm] at hd
+        real_inner_self_eq_norm_mul_norm] at hd 
       simp_rw [vsub_midpoint, ← vsub_sub_vsub_cancel_left p₂ p₁ p, inner_sub_left, inner_add_right,
         inner_smul_right, hd, real_inner_comm (p -ᵥ p₁)]
       abel
     rw [@Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two V _ _ _ o,
-      or_iff_right (vsub_ne_zero.2 h.symm)] at hi
+      or_iff_right (vsub_ne_zero.2 h.symm)] at hi 
     rcases hi with ⟨r, hr⟩
-    rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr
+    rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr 
     exact ⟨r, hr.symm⟩
   · rcases hr with ⟨r, rfl⟩
     simp_rw [@dist_eq_norm_vsub V, vsub_vadd_eq_vsub_sub, left_vsub_midpoint, right_vsub_midpoint,
@@ -717,10 +717,10 @@ theorem Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (p₅ :
               (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))))
             hp₃p₄).1
         hc₅₁₂₃₄
-    rw [Set.insert_comm] at hc₅₁₂ hc₅₃₄
+    rw [Set.insert_comm] at hc₅₁₂ hc₅₃₄ 
     have hs₁₅₂ := oangle_eq_zero_or_eq_pi_iff_collinear.2 hc₅₁₂
     have hs₃₅₄ := oangle_eq_zero_or_eq_pi_iff_collinear.2 hc₅₃₄
-    rw [← Real.Angle.sign_eq_zero_iff] at hs₁₅₂ hs₃₅₄
+    rw [← Real.Angle.sign_eq_zero_iff] at hs₁₅₂ hs₃₅₄ 
     rw [hs₁₅₂, hs₃₅₄]
   · let s : Set (P × P × P) :=
       (fun x : line[ℝ, p₁, p₂] × V => (x.1, p₅, x.2 +ᵥ x.1)) ''
@@ -737,17 +737,17 @@ theorem Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (p₅ :
       by
       refine' ContinuousAt.continuousOn fun p hp => continuous_at_oangle _ _
       all_goals
-        simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_univ, true_and_iff, Prod.ext_iff] at hp
+        simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_univ, true_and_iff, Prod.ext_iff] at hp 
         obtain ⟨q₁, q₅, q₂⟩ := p
-        dsimp only at hp⊢
+        dsimp only at hp ⊢
         obtain ⟨⟨⟨q, hq⟩, v⟩, hv, rfl, rfl, rfl⟩ := hp
-        dsimp only [Subtype.coe_mk, Set.mem_setOf] at hv⊢
+        dsimp only [Subtype.coe_mk, Set.mem_setOf] at hv ⊢
         obtain ⟨hvr, -⟩ := hv
         rintro rfl
         refine' hc₅₁₂ ((collinear_insert_iff_of_mem_affineSpan _).2 (collinear_pair _ _ _))
       · exact hq
       · refine' vadd_mem_of_mem_direction _ hq
-        rw [← exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)] at hvr
+        rw [← exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)] at hvr 
         obtain ⟨r, -, rfl⟩ := hvr
         rw [direction_affineSpan]
         exact smul_vsub_rev_mem_vectorSpan_pair _ _ _
@@ -755,15 +755,15 @@ theorem Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (p₅ :
       by
       intro p hp
       simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
-        Prod.ext_iff] at hp
+        Prod.ext_iff] at hp 
       obtain ⟨q₁, q₅, q₂⟩ := p
-      dsimp only at hp⊢
+      dsimp only at hp ⊢
       obtain ⟨⟨⟨q, hq⟩, v⟩, hv, rfl, rfl, rfl⟩ := hp
-      dsimp only [Subtype.coe_mk, Set.mem_setOf] at hv⊢
+      dsimp only [Subtype.coe_mk, Set.mem_setOf] at hv ⊢
       obtain ⟨hvr, hv0⟩ := hv
-      rw [← exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)] at hvr
+      rw [← exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)] at hvr 
       obtain ⟨r, -, rfl⟩ := hvr
-      change q ∈ line[ℝ, p₁, p₂] at hq
+      change q ∈ line[ℝ, p₁, p₂] at hq 
       rw [oangle_ne_zero_and_ne_pi_iff_affine_independent]
       refine'
         affineIndependent_of_ne_of_mem_of_not_mem_of_mem _ hq
@@ -850,7 +850,7 @@ theorem AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P} {p₁
     by
     refine' ContinuousAt.continuousOn fun p hp => continuous_at_oangle _ _
     all_goals
-      simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp
+      simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp 
       obtain ⟨p', hp', rfl⟩ := hp
       dsimp only
       rintro rfl
@@ -859,7 +859,7 @@ theorem AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P} {p₁
   have hsp : ∀ p : P × P × P, p ∈ sp → ∡ p.1 p.2.1 p.2.2 ≠ 0 ∧ ∡ p.1 p.2.1 p.2.2 ≠ π :=
     by
     intro p hp
-    simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp
+    simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp 
     obtain ⟨p', hp', rfl⟩ := hp
     dsimp only
     rw [oangle_ne_zero_and_ne_pi_iff_affine_independent]

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -29,7 +29,7 @@ noncomputable section
 
 open FiniteDimensional Complex
 
-open Affine EuclideanGeometry Real RealInnerProductSpace ComplexConjugate
+open scoped Affine EuclideanGeometry Real RealInnerProductSpace ComplexConjugate
 
 namespace EuclideanGeometry
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -81,24 +81,18 @@ theorem oangle_self_left_right (p₁ p₂ : P) : ∡ p₁ p₂ p₁ = 0 :=
 #align euclidean_geometry.oangle_self_left_right EuclideanGeometry.oangle_self_left_right
 
 /-- If the angle between three points is nonzero, the first two points are not equal. -/
-theorem left_ne_of_oangle_ne_zero {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ ≠ 0) : p₁ ≠ p₂ :=
-  by
-  rw [← @vsub_ne_zero V]
-  exact o.left_ne_zero_of_oangle_ne_zero h
+theorem left_ne_of_oangle_ne_zero {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ ≠ 0) : p₁ ≠ p₂ := by
+  rw [← @vsub_ne_zero V]; exact o.left_ne_zero_of_oangle_ne_zero h
 #align euclidean_geometry.left_ne_of_oangle_ne_zero EuclideanGeometry.left_ne_of_oangle_ne_zero
 
 /-- If the angle between three points is nonzero, the last two points are not equal. -/
-theorem right_ne_of_oangle_ne_zero {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ ≠ 0) : p₃ ≠ p₂ :=
-  by
-  rw [← @vsub_ne_zero V]
-  exact o.right_ne_zero_of_oangle_ne_zero h
+theorem right_ne_of_oangle_ne_zero {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ ≠ 0) : p₃ ≠ p₂ := by
+  rw [← @vsub_ne_zero V]; exact o.right_ne_zero_of_oangle_ne_zero h
 #align euclidean_geometry.right_ne_of_oangle_ne_zero EuclideanGeometry.right_ne_of_oangle_ne_zero
 
 /-- If the angle between three points is nonzero, the first and third points are not equal. -/
-theorem left_ne_right_of_oangle_ne_zero {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ ≠ 0) : p₁ ≠ p₃ :=
-  by
-  rw [← (vsub_left_injective p₂).ne_iff]
-  exact o.ne_of_oangle_ne_zero h
+theorem left_ne_right_of_oangle_ne_zero {p₁ p₂ p₃ : P} (h : ∡ p₁ p₂ p₃ ≠ 0) : p₁ ≠ p₃ := by
+  rw [← (vsub_left_injective p₂).ne_iff]; exact o.ne_of_oangle_ne_zero h
 #align euclidean_geometry.left_ne_right_of_oangle_ne_zero EuclideanGeometry.left_ne_right_of_oangle_ne_zero
 
 /-- If the angle between three points is `π`, the first two points are not equal. -/
@@ -342,8 +336,7 @@ theorem oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq {p₁ p₂ p₃ : P} (hn :
   rw [oangle, oangle]
   convert o.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eq _ h using 1
   · rw [← neg_vsub_eq_vsub_rev p₁ p₃, ← neg_vsub_eq_vsub_rev p₁ p₂, o.oangle_neg_neg]
-  · rw [← o.oangle_sub_eq_oangle_sub_rev_of_norm_eq h]
-    simp
+  · rw [← o.oangle_sub_eq_oangle_sub_rev_of_norm_eq h]; simp
   · simpa using hn
 #align euclidean_geometry.oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq EuclideanGeometry.oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq
 
@@ -577,9 +570,7 @@ same ray. -/
 theorem Wbtw.oangle_eq_left {p₁ p₁' p₂ p₃ : P} (h : Wbtw ℝ p₂ p₁ p₁') (hp₁p₂ : p₁ ≠ p₂) :
     ∡ p₁ p₂ p₃ = ∡ p₁' p₂ p₃ := by
   by_cases hp₃p₂ : p₃ = p₂; · simp [hp₃p₂]
-  by_cases hp₁'p₂ : p₁' = p₂;
-  · rw [hp₁'p₂, wbtw_self_iff] at h
-    exact False.elim (hp₁p₂ h)
+  by_cases hp₁'p₂ : p₁' = p₂; · rw [hp₁'p₂, wbtw_self_iff] at h; exact False.elim (hp₁p₂ h)
   rw [← oangle_add hp₁'p₂ hp₁p₂ hp₃p₂, h.oangle₃₁₂_eq_zero, zero_add]
 #align wbtw.oangle_eq_left Wbtw.oangle_eq_left
 
@@ -850,8 +841,7 @@ theorem AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P} {p₁
     (hp₁ : p₁ ∈ s) (hp₂ : p₂ ∈ s) (hp₃p₄ : s.SSameSide p₃ p₄) :
     (∡ p₁ p₄ p₂).sign = (∡ p₁ p₃ p₂).sign :=
   by
-  by_cases h : p₁ = p₂
-  · simp [h]
+  by_cases h : p₁ = p₂; · simp [h]
   let sp : Set (P × P × P) := (fun p : P => (p₁, p, p₂)) '' { p | s.s_same_side p₃ p }
   have hc : IsConnected sp :=
     (is_connected_set_of_s_same_side hp₃p₄.2.1 hp₃p₄.nonempty).image _
@@ -886,9 +876,7 @@ theorem AffineSubspace.SOppSide.oangle_sign_eq_neg {s : AffineSubspace ℝ P} {p
     (hp₁ : p₁ ∈ s) (hp₂ : p₂ ∈ s) (hp₃p₄ : s.SOppSide p₃ p₄) :
     (∡ p₁ p₄ p₂).sign = -(∡ p₁ p₃ p₂).sign :=
   by
-  have hp₁p₃ : p₁ ≠ p₃ := by
-    rintro rfl
-    exact hp₃p₄.left_not_mem hp₁
+  have hp₁p₃ : p₁ ≠ p₃ := by rintro rfl; exact hp₃p₄.left_not_mem hp₁
   rw [←
     (hp₃p₄.symm.trans (s_opp_side_point_reflection hp₁ hp₃p₄.left_not_mem)).oangle_sign_eq hp₁ hp₂,
     ← oangle_rotate_sign p₁, ← oangle_rotate_sign p₁, oangle_swap₁₃_sign,

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module geometry.euclidean.angle.oriented.affine
-! leanprover-community/mathlib commit fb319896dcaa409bd4a3cc0f8484297ef9dae2c3
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -33,9 +33,8 @@ open Affine EuclideanGeometry Real RealInnerProductSpace ComplexConjugate
 
 namespace EuclideanGeometry
 
-variable {V : Type _} {P : Type _} [InnerProductSpace ℝ V] [MetricSpace P]
-
-variable [NormedAddTorsor V P] [hd2 : Fact (finrank ℝ V = 2)] [Module.Oriented ℝ V (Fin 2)]
+variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
+  [NormedAddTorsor V P] [hd2 : Fact (finrank ℝ V = 2)] [Module.Oriented ℝ V (Fin 2)]
 
 include hd2
 
@@ -692,7 +691,7 @@ theorem dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint {p₁ p₂ p : P}
       simp_rw [vsub_midpoint, ← vsub_sub_vsub_cancel_left p₂ p₁ p, inner_sub_left, inner_add_right,
         inner_smul_right, hd, real_inner_comm (p -ᵥ p₁)]
       abel
-    rw [@Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two V _ _ o,
+    rw [@Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two V _ _ _ o,
       or_iff_right (vsub_ne_zero.2 h.symm)] at hi
     rcases hi with ⟨r, hr⟩
     rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

@@ -33,6 +33,7 @@ namespace EuclideanGeometry
 variable {V : Type*} {P : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P] [hd2 : Fact (finrank ℝ V = 2)] [Module.Oriented ℝ V (Fin 2)]
 
+/-- A fixed choice of positive orientation of Euclidean space `ℝ²` -/
 abbrev o := @Module.Oriented.positiveOrientation
 
 /-- The oriented angle at `p₂` between the line segments to `p₁` and `p₃`, modulo `2 * π`. If

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -707,7 +707,7 @@ theorem _root_.Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (
     have hf : ContinuousOn (fun p : P × P × P => ∡ p.1 p.2.1 p.2.2) s := by
       refine' ContinuousAt.continuousOn fun p hp => continuousAt_oangle _ _
       all_goals
-        simp_rw [Set.mem_image, Set.mem_prod, Set.mem_univ, true_and_iff, Prod.ext_iff] at hp
+        simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_univ, true_and_iff, Prod.ext_iff] at hp
         obtain ⟨q₁, q₅, q₂⟩ := p
         dsimp only at hp ⊢
         obtain ⟨⟨⟨q, hq⟩, v⟩, hv, rfl, rfl, rfl⟩ := hp
@@ -723,7 +723,7 @@ theorem _root_.Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (
         exact smul_vsub_rev_mem_vectorSpan_pair _ _ _
     have hsp : ∀ p : P × P × P, p ∈ s → ∡ p.1 p.2.1 p.2.2 ≠ 0 ∧ ∡ p.1 p.2.1 p.2.2 ≠ π := by
       intro p hp
-      simp_rw [Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
+      simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
         Prod.ext_iff] at hp
       obtain ⟨q₁, q₅, q₂⟩ := p
       dsimp only at hp ⊢
@@ -741,13 +741,13 @@ theorem _root_.Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (
         rw [direction_affineSpan]
         exact smul_vsub_rev_mem_vectorSpan_pair _ _ _
     have hp₁p₂s : (p₁, p₅, p₂) ∈ s := by
-      simp_rw [Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
+      simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
         Prod.ext_iff]
       refine' ⟨⟨⟨p₁, left_mem_affineSpan_pair ℝ _ _⟩, p₂ -ᵥ p₁⟩,
         ⟨SameRay.rfl, vsub_ne_zero.2 hp₁p₂.symm⟩, _⟩
       simp
     have hp₃p₄s : (p₃, p₅, p₄) ∈ s := by
-      simp_rw [Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
+      simp_rw [s, Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
         Prod.ext_iff]
       refine' ⟨⟨⟨p₃, hc.mem_affineSpan_of_mem_of_ne (Set.mem_insert _ _)
         (Set.mem_insert_of_mem _ (Set.mem_insert _ _))
@@ -809,7 +809,7 @@ theorem _root_.AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P
   have hf : ContinuousOn (fun p : P × P × P => ∡ p.1 p.2.1 p.2.2) sp := by
     refine' ContinuousAt.continuousOn fun p hp => continuousAt_oangle _ _
     all_goals
-      simp_rw [Set.mem_image, Set.mem_setOf] at hp
+      simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp
       obtain ⟨p', hp', rfl⟩ := hp
       dsimp only
       rintro rfl
@@ -817,7 +817,7 @@ theorem _root_.AffineSubspace.SSameSide.oangle_sign_eq {s : AffineSubspace ℝ P
     · exact hp'.2.2 hp₂
   have hsp : ∀ p : P × P × P, p ∈ sp → ∡ p.1 p.2.1 p.2.2 ≠ 0 ∧ ∡ p.1 p.2.1 p.2.2 ≠ π := by
     intro p hp
-    simp_rw [Set.mem_image, Set.mem_setOf] at hp
+    simp_rw [sp, Set.mem_image, Set.mem_setOf] at hp
     obtain ⟨p', hp', rfl⟩ := hp
     dsimp only
     rw [oangle_ne_zero_and_ne_pi_iff_affineIndependent]

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -741,12 +741,14 @@ theorem _root_.Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (
         rw [direction_affineSpan]
         exact smul_vsub_rev_mem_vectorSpan_pair _ _ _
     have hp₁p₂s : (p₁, p₅, p₂) ∈ s := by
-      simp_rw [Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff, Prod.ext_iff]
+      simp_rw [Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
+        Prod.ext_iff]
       refine' ⟨⟨⟨p₁, left_mem_affineSpan_pair ℝ _ _⟩, p₂ -ᵥ p₁⟩,
         ⟨SameRay.rfl, vsub_ne_zero.2 hp₁p₂.symm⟩, _⟩
       simp
     have hp₃p₄s : (p₃, p₅, p₄) ∈ s := by
-      simp_rw [Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff, Prod.ext_iff]
+      simp_rw [Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff,
+        Prod.ext_iff]
       refine' ⟨⟨⟨p₃, hc.mem_affineSpan_of_mem_of_ne (Set.mem_insert _ _)
         (Set.mem_insert_of_mem _ (Set.mem_insert _ _))
         (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_insert _ _))) hp₁p₂⟩, p₄ -ᵥ p₃⟩,

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -714,7 +714,7 @@ theorem _root_.Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (
         dsimp only [Subtype.coe_mk, Set.mem_setOf] at hv ⊢
         obtain ⟨hvr, -⟩ := hv
         rintro rfl
-        refine' hc₅₁₂ ((collinear_insert_iff_of_mem_affineSpan _).2 (collinear_pair _ _ _))
+        refine hc₅₁₂ ((collinear_insert_iff_of_mem_affineSpan ?_).2 (collinear_pair _ _ _))
       · exact hq
       · refine' vadd_mem_of_mem_direction _ hq
         rw [← exists_nonneg_left_iff_sameRay (vsub_ne_zero.2 hp₁p₂.symm)] at hvr

Make all the notations that unambiguously should inherit the docstring of their definition actually inherit it.

Also write a few docstrings by hand. I only wrote the ones I was competent to write and which I was sure of. Some docstrings come from mathlib3 as they were lost during the early port.

This PR is only intended as a first pass There are many more docstrings to add.

@@ -42,7 +42,7 @@ def oangle (p₁ p₂ p₃ : P) : Real.Angle :=
   o.oangle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂)
 #align euclidean_geometry.oangle EuclideanGeometry.oangle
 
-scoped notation "∡" => EuclideanGeometry.oangle
+@[inherit_doc] scoped notation "∡" => EuclideanGeometry.oangle
 
 /-- Oriented angles are continuous when neither end point equals the middle point. -/
 theorem continuousAt_oangle {x : P × P × P} (hx12 : x.1 ≠ x.2.1) (hx32 : x.2.2 ≠ x.2.1) :

Mathlib already knew it formed a DistribMulAction.

This also cleans up some duplicate definitions from @urkud's #2968.

@@ -742,7 +742,7 @@ theorem _root_.Collinear.oangle_sign_of_sameRay_vsub {p₁ p₂ p₃ p₄ : P} (
         exact smul_vsub_rev_mem_vectorSpan_pair _ _ _
     have hp₁p₂s : (p₁, p₅, p₂) ∈ s := by
       simp_rw [Set.mem_image, Set.mem_prod, Set.mem_setOf, Set.mem_univ, true_and_iff, Prod.ext_iff]
-      refine' ⟨⟨⟨p₁, left_mem_affineSpan_pair _ _ _⟩, p₂ -ᵥ p₁⟩,
+      refine' ⟨⟨⟨p₁, left_mem_affineSpan_pair ℝ _ _⟩, p₂ -ᵥ p₁⟩,
         ⟨SameRay.rfl, vsub_ne_zero.2 hp₁p₂.symm⟩, _⟩
       simp
     have hp₃p₄s : (p₃, p₅, p₄) ∈ s := by

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -30,7 +30,7 @@ open scoped Affine EuclideanGeometry Real RealInnerProductSpace ComplexConjugate
 
 namespace EuclideanGeometry
 
-variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
+variable {V : Type*} {P : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P] [hd2 : Fact (finrank ℝ V = 2)] [Module.Oriented ℝ V (Fin 2)]
 
 abbrev o := @Module.Oriented.positiveOrientation

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module geometry.euclidean.angle.oriented.affine
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Convex.Side
 import Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation
 import Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine
 
+#align_import geometry.euclidean.angle.oriented.affine from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-!
 # Oriented angles.
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -552,7 +552,7 @@ same ray. -/
 theorem _root_.Wbtw.oangle_eq_left {p₁ p₁' p₂ p₃ : P} (h : Wbtw ℝ p₂ p₁ p₁') (hp₁p₂ : p₁ ≠ p₂) :
     ∡ p₁ p₂ p₃ = ∡ p₁' p₂ p₃ := by
   by_cases hp₃p₂ : p₃ = p₂; · simp [hp₃p₂]
-  by_cases hp₁'p₂ : p₁' = p₂; · rw [hp₁'p₂, wbtw_self_iff] at h ; exact False.elim (hp₁p₂ h)
+  by_cases hp₁'p₂ : p₁' = p₂; · rw [hp₁'p₂, wbtw_self_iff] at h; exact False.elim (hp₁p₂ h)
   rw [← oangle_add hp₁'p₂ hp₁p₂ hp₃p₂, h.oangle₃₁₂_eq_zero, zero_add]
 #align wbtw.oangle_eq_left Wbtw.oangle_eq_left
 

Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>