geometry.euclidean.angle.sphere ⟷ Mathlib.Geometry.Euclidean.Angle.Sphere

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

@@ -162,7 +162,7 @@ theorem two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi {s : Sphere P} {p₁
     (hp₁ : p₁ ∈ s) (hp₂ : p₂ ∈ s) (hp₃ : p₃ ∈ s) (hp₂p₁ : p₂ ≠ p₁) (hp₂p₃ : p₂ ≠ p₃)
     (hp₁p₃ : p₁ ≠ p₃) : (2 : ℤ) • ∡ p₃ p₁ s.center + (2 : ℤ) • ∡ p₁ p₂ p₃ = π := by
   rw [← oangle_center_eq_two_zsmul_oangle hp₁ hp₂ hp₃ hp₂p₁ hp₂p₃,
-    oangle_eq_pi_sub_two_zsmul_oangle_center_right hp₁ hp₃ hp₁p₃, add_sub_cancel'_right]
+    oangle_eq_pi_sub_two_zsmul_oangle_center_right hp₁ hp₃ hp₁p₃, add_sub_cancel]
 #align euclidean_geometry.sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi EuclideanGeometry.Sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi
 -/
 
@@ -201,7 +201,7 @@ theorem tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center {s : Sphere
   rw [← hr, ← oangle_midpoint_rev_left, oangle, vadd_vsub_assoc]
   nth_rw 1 [show p₂ -ᵥ p₁ = (2 : ℝ) • (midpoint ℝ p₁ p₂ -ᵥ p₁) by simp]
   rw [map_smul, smul_smul, add_comm, o.tan_oangle_add_right_smul_rotation_pi_div_two,
-    mul_div_cancel _ (two_ne_zero' ℝ)]
+    mul_div_cancel_right₀ _ (two_ne_zero' ℝ)]
   simpa using h.symm
 #align euclidean_geometry.sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center
 -/
@@ -235,7 +235,7 @@ theorem dist_div_cos_oangle_center_div_two_eq_radius {s : Sphere P} {p₁ p₂ :
     tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center hp₁ hp₂ h, ←
     oangle_midpoint_rev_left, oangle, vadd_vsub_assoc,
     show p₂ -ᵥ p₁ = (2 : ℝ) • (midpoint ℝ p₁ p₂ -ᵥ p₁) by simp, map_smul, smul_smul,
-    div_mul_cancel _ (two_ne_zero' ℝ), @dist_eq_norm_vsub' V, @dist_eq_norm_vsub' V,
+    div_mul_cancel₀ _ (two_ne_zero' ℝ), @dist_eq_norm_vsub' V, @dist_eq_norm_vsub' V,
     vadd_vsub_assoc, add_comm, o.oangle_add_right_smul_rotation_pi_div_two, Real.Angle.cos_coe,
     Real.cos_arctan, one_div, div_inv_eq_mul, ←
     mul_self_inj (mul_nonneg (norm_nonneg _) (Real.sqrt_nonneg _)) (norm_nonneg _),
@@ -257,7 +257,7 @@ the radius at one of those points. -/
 theorem dist_div_cos_oangle_center_eq_two_mul_radius {s : Sphere P} {p₁ p₂ : P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) (h : p₁ ≠ p₂) : dist p₁ p₂ / Real.Angle.cos (∡ p₂ p₁ s.center) = 2 * s.radius :=
   by
-  rw [← dist_div_cos_oangle_center_div_two_eq_radius hp₁ hp₂ h, mul_div_cancel' _ (two_ne_zero' ℝ)]
+  rw [← dist_div_cos_oangle_center_div_two_eq_radius hp₁ hp₂ h, mul_div_cancel₀ _ (two_ne_zero' ℝ)]
 #align euclidean_geometry.sphere.dist_div_cos_oangle_center_eq_two_mul_radius EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius
 -/
 
@@ -286,7 +286,7 @@ theorem dist_div_sin_oangle_eq_two_mul_radius {s : Sphere P} {p₁ p₂ p₃ : P
     (hp₂ : p₂ ∈ s) (hp₃ : p₃ ∈ s) (hp₁p₂ : p₁ ≠ p₂) (hp₁p₃ : p₁ ≠ p₃) (hp₂p₃ : p₂ ≠ p₃) :
     dist p₁ p₃ / |Real.Angle.sin (∡ p₁ p₂ p₃)| = 2 * s.radius := by
   rw [← dist_div_sin_oangle_div_two_eq_radius hp₁ hp₂ hp₃ hp₁p₂ hp₁p₃ hp₂p₃,
-    mul_div_cancel' _ (two_ne_zero' ℝ)]
+    mul_div_cancel₀ _ (two_ne_zero' ℝ)]
 #align euclidean_geometry.sphere.dist_div_sin_oangle_eq_two_mul_radius EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius
 -/
 

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

@@ -39,7 +39,7 @@ theorem oangle_eq_two_zsmul_oangle_sub_of_norm_eq {x y z : V} (hxyne : x ≠ y)
   by
   have hy : y ≠ 0 := by
     rintro rfl
-    rw [norm_zero, norm_eq_zero] at hxy 
+    rw [norm_zero, norm_eq_zero] at hxy
     exact hxyne hxy
   have hx : x ≠ 0 := norm_ne_zero_iff.1 (hxy.symm ▸ norm_ne_zero_iff.2 hy)
   have hz : z ≠ 0 := norm_ne_zero_iff.1 (hxz ▸ norm_ne_zero_iff.2 hx)
@@ -95,7 +95,7 @@ theorem oangle_center_eq_two_zsmul_oangle {s : Sphere P} {p₁ p₂ p₃ : P} (h
     (hp₂ : p₂ ∈ s) (hp₃ : p₃ ∈ s) (hp₂p₁ : p₂ ≠ p₁) (hp₂p₃ : p₂ ≠ p₃) :
     ∡ p₁ s.center p₃ = (2 : ℤ) • ∡ p₁ p₂ p₃ :=
   by
-  rw [mem_sphere, @dist_eq_norm_vsub V] at hp₁ hp₂ hp₃ 
+  rw [mem_sphere, @dist_eq_norm_vsub V] at hp₁ hp₂ hp₃
   rw [oangle, oangle, o.oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real _ _ hp₂ hp₁ hp₃] <;>
     simp [hp₂p₁, hp₂p₃]
 #align euclidean_geometry.sphere.oangle_center_eq_two_zsmul_oangle EuclideanGeometry.Sphere.oangle_center_eq_two_zsmul_oangle
@@ -109,7 +109,7 @@ theorem two_zsmul_oangle_eq {s : Sphere P} {p₁ p₂ p₃ p₄ : P} (hp₁ : p
     (hp₃ : p₃ ∈ s) (hp₄ : p₄ ∈ s) (hp₂p₁ : p₂ ≠ p₁) (hp₂p₄ : p₂ ≠ p₄) (hp₃p₁ : p₃ ≠ p₁)
     (hp₃p₄ : p₃ ≠ p₄) : (2 : ℤ) • ∡ p₁ p₂ p₄ = (2 : ℤ) • ∡ p₁ p₃ p₄ :=
   by
-  rw [mem_sphere, @dist_eq_norm_vsub V] at hp₁ hp₂ hp₃ hp₄ 
+  rw [mem_sphere, @dist_eq_norm_vsub V] at hp₁ hp₂ hp₃ hp₄
   rw [oangle, oangle, ← vsub_sub_vsub_cancel_right p₁ p₂ s.center, ←
       vsub_sub_vsub_cancel_right p₄ p₂ s.center,
       o.two_zsmul_oangle_sub_eq_two_zsmul_oangle_sub_of_norm_eq _ _ _ _ hp₂ hp₃ hp₁ hp₄] <;>
@@ -128,7 +128,7 @@ theorem Cospherical.two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P}
     (hp₃p₁ : p₃ ≠ p₁) (hp₃p₄ : p₃ ≠ p₄) : (2 : ℤ) • ∡ p₁ p₂ p₄ = (2 : ℤ) • ∡ p₁ p₃ p₄ :=
   by
   obtain ⟨s, hs⟩ := cospherical_iff_exists_sphere.1 h
-  simp_rw [Set.insert_subset_iff, Set.singleton_subset_iff, sphere.mem_coe] at hs 
+  simp_rw [Set.insert_subset_iff, Set.singleton_subset_iff, sphere.mem_coe] at hs
   exact sphere.two_zsmul_oangle_eq hs.1 hs.2.1 hs.2.2.1 hs.2.2.2 hp₂p₁ hp₂p₄ hp₃p₁ hp₃p₄
 #align euclidean_geometry.cospherical.two_zsmul_oangle_eq EuclideanGeometry.Cospherical.two_zsmul_oangle_eq
 -/
@@ -494,7 +494,7 @@ theorem cospherical_or_collinear_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P
     have hc' : Collinear ℝ ({p₁, p₃, p₄} : Set P) := by
       rwa [← collinear_iff_of_two_zsmul_oangle_eq h]
     refine' Or.inr _
-    rw [Set.insert_comm p₁ p₂] at hc 
+    rw [Set.insert_comm p₁ p₂] at hc
     rwa [Set.insert_comm p₁ p₂,
       hc'.collinear_insert_iff_of_ne (Set.mem_insert _ _)
         (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))) he]

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

@@ -3,8 +3,8 @@ 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.Geometry.Euclidean.Angle.Oriented.RightAngle
-import Mathbin.Geometry.Euclidean.Circumcenter
+import Geometry.Euclidean.Angle.Oriented.RightAngle
+import Geometry.Euclidean.Circumcenter
 
 #align_import geometry.euclidean.angle.sphere from "leanprover-community/mathlib"@"cff8231f04dfa33fd8f2f45792eebd862ef30cad"
 

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

@@ -2,15 +2,12 @@
 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.sphere
-! leanprover-community/mathlib commit cff8231f04dfa33fd8f2f45792eebd862ef30cad
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Geometry.Euclidean.Angle.Oriented.RightAngle
 import Mathbin.Geometry.Euclidean.Circumcenter
 
+#align_import geometry.euclidean.angle.sphere from "leanprover-community/mathlib"@"cff8231f04dfa33fd8f2f45792eebd862ef30cad"
+
 /-!
 # Angles in circles and sphere.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -131,7 +131,7 @@ theorem Cospherical.two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P}
     (hp₃p₁ : p₃ ≠ p₁) (hp₃p₄ : p₃ ≠ p₄) : (2 : ℤ) • ∡ p₁ p₂ p₄ = (2 : ℤ) • ∡ p₁ p₃ p₄ :=
   by
   obtain ⟨s, hs⟩ := cospherical_iff_exists_sphere.1 h
-  simp_rw [Set.insert_subset, Set.singleton_subset_iff, sphere.mem_coe] at hs 
+  simp_rw [Set.insert_subset_iff, Set.singleton_subset_iff, sphere.mem_coe] at hs 
   exact sphere.two_zsmul_oangle_eq hs.1 hs.2.1 hs.2.2.1 hs.2.2.2 hp₂p₁ hp₂p₄ hp₃p₁ hp₃p₄
 #align euclidean_geometry.cospherical.two_zsmul_oangle_eq EuclideanGeometry.Cospherical.two_zsmul_oangle_eq
 -/
@@ -456,7 +456,7 @@ theorem cospherical_of_two_zsmul_oangle_eq_of_not_collinear {p₁ p₂ p₃ p₄
   let t₂ : Affine.Triangle ℝ P := ⟨![p₁, p₃, p₄], affineIndependent_iff_not_collinear_set.2 hn'⟩
   rw [cospherical_iff_exists_sphere]
   refine' ⟨t₂.circumsphere, _⟩
-  simp_rw [Set.insert_subset, Set.singleton_subset_iff]
+  simp_rw [Set.insert_subset_iff, Set.singleton_subset_iff]
   refine' ⟨t₂.mem_circumsphere 0, _, t₂.mem_circumsphere 1, t₂.mem_circumsphere 2⟩
   rw [Affine.Triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq
       (by decide : (0 : Fin 3) ≠ 1) (by decide : (0 : Fin 3) ≠ 2) (by decide)
@@ -492,7 +492,7 @@ theorem cospherical_or_collinear_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P
       let t : Affine.Triangle ℝ P := ⟨![p₂, p₃, p₄], affineIndependent_iff_not_collinear_set.2 hl⟩
       rw [cospherical_iff_exists_sphere]
       refine' ⟨t.circumsphere, _⟩
-      simp_rw [Set.insert_subset, Set.singleton_subset_iff]
+      simp_rw [Set.insert_subset_iff, Set.singleton_subset_iff]
       exact ⟨t.mem_circumsphere 0, t.mem_circumsphere 1, t.mem_circumsphere 2⟩
     have hc' : Collinear ℝ ({p₁, p₃, p₄} : Set P) := by
       rwa [← collinear_iff_of_two_zsmul_oangle_eq h]

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -34,6 +34,7 @@ variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
 
 variable [Fact (finrank ℝ V = 2)] (o : Orientation ℝ V (Fin 2))
 
+#print Orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq /-
 /-- Angle at center of a circle equals twice angle at circumference, oriented vector angle
 form. -/
 theorem oangle_eq_two_zsmul_oangle_sub_of_norm_eq {x y z : V} (hxyne : x ≠ y) (hxzne : x ≠ z)
@@ -55,7 +56,9 @@ theorem oangle_eq_two_zsmul_oangle_sub_of_norm_eq {x y z : V} (hxyne : x ≠ y)
       rw [o.oangle_sub_right (sub_ne_zero_of_ne hxyne) (sub_ne_zero_of_ne hxzne) hx]
     _ = (2 : ℤ) • o.oangle (y - x) (z - x) := by rw [← oangle_neg_neg, neg_sub, neg_sub]
 #align orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq Orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq
+-/
 
+#print Orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real /-
 /-- Angle at center of a circle equals twice angle at circumference, oriented vector angle
 form with radius specified. -/
 theorem oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real {x y z : V} (hxyne : x ≠ y) (hxzne : x ≠ z)
@@ -63,7 +66,9 @@ theorem oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real {x y z : V} (hxyne : x 
     o.oangle y z = (2 : ℤ) • o.oangle (y - x) (z - x) :=
   o.oangle_eq_two_zsmul_oangle_sub_of_norm_eq hxyne hxzne (hy.symm ▸ hx) (hz.symm ▸ hx)
 #align orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real Orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real
+-/
 
+#print Orientation.two_zsmul_oangle_sub_eq_two_zsmul_oangle_sub_of_norm_eq /-
 /-- Oriented vector angle version of "angles in same segment are equal" and "opposite angles of
 a cyclic quadrilateral add to π", for oriented angles mod π (for which those are the same
 result), represented here as equality of twice the angles. -/
@@ -74,6 +79,7 @@ theorem two_zsmul_oangle_sub_eq_two_zsmul_oangle_sub_of_norm_eq {x₁ x₂ y z :
   o.oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real hx₁yne hx₁zne hx₁ hy hz ▸
     o.oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real hx₂yne hx₂zne hx₂ hy hz
 #align orientation.two_zsmul_oangle_sub_eq_two_zsmul_oangle_sub_of_norm_eq Orientation.two_zsmul_oangle_sub_eq_two_zsmul_oangle_sub_of_norm_eq
+-/
 
 end Orientation
 
@@ -86,6 +92,7 @@ local notation "o" => Module.Oriented.positiveOrientation
 
 namespace Sphere
 
+#print EuclideanGeometry.Sphere.oangle_center_eq_two_zsmul_oangle /-
 /-- Angle at center of a circle equals twice angle at circumference, oriented angle version. -/
 theorem oangle_center_eq_two_zsmul_oangle {s : Sphere P} {p₁ p₂ p₃ : P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) (hp₃ : p₃ ∈ s) (hp₂p₁ : p₂ ≠ p₁) (hp₂p₃ : p₂ ≠ p₃) :
@@ -95,7 +102,9 @@ theorem oangle_center_eq_two_zsmul_oangle {s : Sphere P} {p₁ p₂ p₃ : P} (h
   rw [oangle, oangle, o.oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real _ _ hp₂ hp₁ hp₃] <;>
     simp [hp₂p₁, hp₂p₃]
 #align euclidean_geometry.sphere.oangle_center_eq_two_zsmul_oangle EuclideanGeometry.Sphere.oangle_center_eq_two_zsmul_oangle
+-/
 
+#print EuclideanGeometry.Sphere.two_zsmul_oangle_eq /-
 /-- Oriented angle version of "angles in same segment are equal" and "opposite angles of a
 cyclic quadrilateral add to π", for oriented angles mod π (for which those are the same result),
 represented here as equality of twice the angles. -/
@@ -109,9 +118,11 @@ theorem two_zsmul_oangle_eq {s : Sphere P} {p₁ p₂ p₃ p₄ : P} (hp₁ : p
       o.two_zsmul_oangle_sub_eq_two_zsmul_oangle_sub_of_norm_eq _ _ _ _ hp₂ hp₃ hp₁ hp₄] <;>
     simp [hp₂p₁, hp₂p₄, hp₃p₁, hp₃p₄]
 #align euclidean_geometry.sphere.two_zsmul_oangle_eq EuclideanGeometry.Sphere.two_zsmul_oangle_eq
+-/
 
 end Sphere
 
+#print EuclideanGeometry.Cospherical.two_zsmul_oangle_eq /-
 /-- Oriented angle version of "angles in same segment are equal" and "opposite angles of a
 cyclic quadrilateral add to π", for oriented angles mod π (for which those are the same result),
 represented here as equality of twice the angles. -/
@@ -123,9 +134,11 @@ theorem Cospherical.two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P}
   simp_rw [Set.insert_subset, Set.singleton_subset_iff, sphere.mem_coe] at hs 
   exact sphere.two_zsmul_oangle_eq hs.1 hs.2.1 hs.2.2.1 hs.2.2.2 hp₂p₁ hp₂p₄ hp₃p₁ hp₃p₄
 #align euclidean_geometry.cospherical.two_zsmul_oangle_eq EuclideanGeometry.Cospherical.two_zsmul_oangle_eq
+-/
 
 namespace Sphere
 
+#print EuclideanGeometry.Sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_left /-
 /-- The angle at the apex of an isosceles triangle is `π` minus twice a base angle, oriented
 angle-at-point form where the apex is given as the center of a circle. -/
 theorem oangle_eq_pi_sub_two_zsmul_oangle_center_left {s : Sphere P} {p₁ p₂ : P} (hp₁ : p₁ ∈ s)
@@ -133,7 +146,9 @@ theorem oangle_eq_pi_sub_two_zsmul_oangle_center_left {s : Sphere P} {p₁ p₂
   rw [oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq h.symm
       (dist_center_eq_dist_center_of_mem_sphere' hp₂ hp₁)]
 #align euclidean_geometry.sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_left EuclideanGeometry.Sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_left
+-/
 
+#print EuclideanGeometry.Sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_right /-
 /-- The angle at the apex of an isosceles triangle is `π` minus twice a base angle, oriented
 angle-at-point form where the apex is given as the center of a circle. -/
 theorem oangle_eq_pi_sub_two_zsmul_oangle_center_right {s : Sphere P} {p₁ p₂ : P} (hp₁ : p₁ ∈ s)
@@ -141,7 +156,9 @@ theorem oangle_eq_pi_sub_two_zsmul_oangle_center_right {s : Sphere P} {p₁ p₂
   rw [oangle_eq_pi_sub_two_zsmul_oangle_center_left hp₁ hp₂ h,
     oangle_eq_oangle_of_dist_eq (dist_center_eq_dist_center_of_mem_sphere' hp₂ hp₁)]
 #align euclidean_geometry.sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_right EuclideanGeometry.Sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_right
+-/
 
+#print EuclideanGeometry.Sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi /-
 /-- Twice a base angle of an isosceles triangle with apex at the center of a circle, plus twice
 the angle at the apex of a triangle with the same base but apex on the circle, equals `π`. -/
 theorem two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi {s : Sphere P} {p₁ p₂ p₃ : P}
@@ -150,21 +167,27 @@ theorem two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi {s : Sphere P} {p₁
   rw [← oangle_center_eq_two_zsmul_oangle hp₁ hp₂ hp₃ hp₂p₁ hp₂p₃,
     oangle_eq_pi_sub_two_zsmul_oangle_center_right hp₁ hp₃ hp₁p₃, add_sub_cancel'_right]
 #align euclidean_geometry.sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi EuclideanGeometry.Sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi
+-/
 
+#print EuclideanGeometry.Sphere.abs_oangle_center_left_toReal_lt_pi_div_two /-
 /-- A base angle of an isosceles triangle with apex at the center of a circle is acute. -/
 theorem abs_oangle_center_left_toReal_lt_pi_div_two {s : Sphere P} {p₁ p₂ : P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) : |(∡ s.center p₂ p₁).toReal| < π / 2 :=
   abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq
     (dist_center_eq_dist_center_of_mem_sphere' hp₂ hp₁)
 #align euclidean_geometry.sphere.abs_oangle_center_left_to_real_lt_pi_div_two EuclideanGeometry.Sphere.abs_oangle_center_left_toReal_lt_pi_div_two
+-/
 
+#print EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two /-
 /-- A base angle of an isosceles triangle with apex at the center of a circle is acute. -/
 theorem abs_oangle_center_right_toReal_lt_pi_div_two {s : Sphere P} {p₁ p₂ : P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) : |(∡ p₂ p₁ s.center).toReal| < π / 2 :=
   abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq
     (dist_center_eq_dist_center_of_mem_sphere' hp₂ hp₁)
 #align euclidean_geometry.sphere.abs_oangle_center_right_to_real_lt_pi_div_two EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two
+-/
 
+#print EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center /-
 /-- Given two points on a circle, the center of that circle may be expressed explicitly as a
 multiple (by half the tangent of the angle between the chord and the radius at one of those
 points) of a `π / 2` rotation of the vector between those points, plus the midpoint of those
@@ -184,7 +207,9 @@ theorem tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center {s : Sphere
     mul_div_cancel _ (two_ne_zero' ℝ)]
   simpa using h.symm
 #align euclidean_geometry.sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center
+-/
 
+#print EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center /-
 /-- Given three points on a circle, the center of that circle may be expressed explicitly as a
 multiple (by half the inverse of the tangent of the angle at one of those points) of a `π / 2`
 rotation of the vector between the other two points, plus the midpoint of those points. -/
@@ -199,7 +224,9 @@ theorem inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center {s : Sp
   rw [add_comm,
     two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi hp₁ hp₂ hp₃ hp₁p₂.symm hp₂p₃ hp₁p₃]
 #align euclidean_geometry.sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center
+-/
 
+#print EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius /-
 /-- Given two points on a circle, the radius of that circle may be expressed explicitly as half
 the distance between those two points divided by the cosine of the angle between the chord and
 the radius at one of those points. -/
@@ -224,7 +251,9 @@ theorem dist_div_cos_oangle_center_div_two_eq_radius {s : Sphere P} {p₁ p₂ :
     rw [← mul_assoc, mul_comm _ ‖Real.Angle.tan _‖, ← mul_assoc, Real.norm_eq_abs, abs_mul_abs_self]
   ring
 #align euclidean_geometry.sphere.dist_div_cos_oangle_center_div_two_eq_radius EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius
+-/
 
+#print EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius /-
 /-- Given two points on a circle, twice the radius of that circle may be expressed explicitly as
 the distance between those two points divided by the cosine of the angle between the chord and
 the radius at one of those points. -/
@@ -233,7 +262,9 @@ theorem dist_div_cos_oangle_center_eq_two_mul_radius {s : Sphere P} {p₁ p₂ :
   by
   rw [← dist_div_cos_oangle_center_div_two_eq_radius hp₁ hp₂ h, mul_div_cancel' _ (two_ne_zero' ℝ)]
 #align euclidean_geometry.sphere.dist_div_cos_oangle_center_eq_two_mul_radius EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius
+-/
 
+#print EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius /-
 /-- Given three points on a circle, the radius of that circle may be expressed explicitly as half
 the distance between two of those points divided by the absolute value of the sine of the angle
 at the third point (a version of the law of sines or sine rule). -/
@@ -248,7 +279,9 @@ theorem dist_div_sin_oangle_div_two_eq_radius {s : Sphere P} {p₁ p₂ p₃ : P
     _root_.abs_of_nonneg (Real.Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two.2 _)]
   exact (abs_oangle_center_right_to_real_lt_pi_div_two hp₁ hp₃).le
 #align euclidean_geometry.sphere.dist_div_sin_oangle_div_two_eq_radius EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius
+-/
 
+#print EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius /-
 /-- Given three points on a circle, twice the radius of that circle may be expressed explicitly as
 the distance between two of those points divided by the absolute value of the sine of the angle
 at the third point (a version of the law of sines or sine rule). -/
@@ -258,6 +291,7 @@ theorem dist_div_sin_oangle_eq_two_mul_radius {s : Sphere P} {p₁ p₂ p₃ : P
   rw [← dist_div_sin_oangle_div_two_eq_radius hp₁ hp₂ hp₃ hp₁p₂ hp₁p₃ hp₂p₃,
     mul_div_cancel' _ (two_ne_zero' ℝ)]
 #align euclidean_geometry.sphere.dist_div_sin_oangle_eq_two_mul_radius EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius
+-/
 
 end Sphere
 
@@ -274,6 +308,7 @@ variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ
 
 local notation "o" => Module.Oriented.positiveOrientation
 
+#print Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter /-
 /-- The circumcenter of a triangle may be expressed explicitly as a multiple (by half the inverse
 of the tangent of the angle at one of the vertices) of a `π / 2` rotation of the vector between
 the other two vertices, plus the midpoint of those vertices. -/
@@ -287,7 +322,9 @@ theorem inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter (
     (t.mem_circumsphere _) (t.mem_circumsphere _) (t.Independent.Injective.Ne h₁₂)
     (t.Independent.Injective.Ne h₁₃) (t.Independent.Injective.Ne h₂₃)
 #align affine.triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter
+-/
 
+#print Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius /-
 /-- The circumradius of a triangle may be expressed explicitly as half the length of a side
 divided by the absolute value of the sine of the angle at the third point (a version of the law
 of sines or sine rule). -/
@@ -301,7 +338,9 @@ theorem dist_div_sin_oangle_div_two_eq_circumradius (t : Triangle ℝ P) {i₁ i
     (t.mem_circumsphere _) (t.Independent.Injective.Ne h₁₂) (t.Independent.Injective.Ne h₁₃)
     (t.Independent.Injective.Ne h₂₃)
 #align affine.triangle.dist_div_sin_oangle_div_two_eq_circumradius Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius
+-/
 
+#print Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius /-
 /-- Twice the circumradius of a triangle may be expressed explicitly as the length of a side
 divided by the absolute value of the sine of the angle at the third point (a version of the law
 of sines or sine rule). -/
@@ -314,7 +353,9 @@ theorem dist_div_sin_oangle_eq_two_mul_circumradius (t : Triangle ℝ P) {i₁ i
     (t.mem_circumsphere _) (t.Independent.Injective.Ne h₁₂) (t.Independent.Injective.Ne h₁₃)
     (t.Independent.Injective.Ne h₂₃)
 #align affine.triangle.dist_div_sin_oangle_eq_two_mul_circumradius Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius
+-/
 
+#print Affine.Triangle.circumsphere_eq_of_dist_of_oangle /-
 /-- The circumsphere of a triangle may be expressed explicitly in terms of two points and the
 angle at the third point. -/
 theorem circumsphere_eq_of_dist_of_oangle (t : Triangle ℝ P) {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂)
@@ -330,8 +371,10 @@ theorem circumsphere_eq_of_dist_of_oangle (t : Triangle ℝ P) {i₁ i₂ i₃ :
     (t.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter h₁₂ h₁₃ h₂₃).symm
     (t.dist_div_sin_oangle_div_two_eq_circumradius h₁₂ h₁₃ h₂₃).symm
 #align affine.triangle.circumsphere_eq_of_dist_of_oangle Affine.Triangle.circumsphere_eq_of_dist_of_oangle
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ⟨«expr +ᵥ »(«expr • »(«expr / »(«expr ⁻¹»((_ : exprℝ())), 2), _), _), «expr / »(«expr / »(_, _), 2)⟩]] -/
+#print Affine.Triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq /-
 /-- If two triangles have two points the same, and twice the angle at the third point the same,
 they have the same circumsphere. -/
 theorem circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq {t₁ t₂ : Triangle ℝ P}
@@ -352,7 +395,9 @@ theorem circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq {t₁ t
   · rw [h₁, h₃]
   · exact Real.Angle.abs_sin_eq_of_two_zsmul_eq h₂
 #align affine.triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq Affine.Triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq
+-/
 
+#print Affine.Triangle.mem_circumsphere_of_two_zsmul_oangle_eq /-
 /-- Given a triangle, and a fourth point such that twice the angle between two points of the
 triangle at that fourth point equals twice the third angle of the triangle, the fourth point
 lies in the circumsphere of the triangle. -/
@@ -385,6 +430,7 @@ theorem mem_circumsphere_of_two_zsmul_oangle_eq {t : Triangle ℝ P} {p : P} {i
     h₂']
   exact simplex.mem_circumsphere _ _
 #align affine.triangle.mem_circumsphere_of_two_zsmul_oangle_eq Affine.Triangle.mem_circumsphere_of_two_zsmul_oangle_eq
+-/
 
 end Triangle
 
@@ -397,6 +443,7 @@ variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ
 
 local notation "o" => Module.Oriented.positiveOrientation
 
+#print EuclideanGeometry.cospherical_of_two_zsmul_oangle_eq_of_not_collinear /-
 /-- Converse of "angles in same segment are equal" and "opposite angles of a cyclic quadrilateral
 add to π", for oriented angles mod π. -/
 theorem cospherical_of_two_zsmul_oangle_eq_of_not_collinear {p₁ p₂ p₃ p₄ : P}
@@ -416,7 +463,9 @@ theorem cospherical_of_two_zsmul_oangle_eq_of_not_collinear {p₁ p₂ p₃ p₄
       (show t₂.points 0 = t₁.points 0 from rfl) rfl h.symm]
   exact t₁.mem_circumsphere 1
 #align euclidean_geometry.cospherical_of_two_zsmul_oangle_eq_of_not_collinear EuclideanGeometry.cospherical_of_two_zsmul_oangle_eq_of_not_collinear
+-/
 
+#print EuclideanGeometry.concyclic_of_two_zsmul_oangle_eq_of_not_collinear /-
 /-- Converse of "angles in same segment are equal" and "opposite angles of a cyclic quadrilateral
 add to π", for oriented angles mod π, with a "concyclic" conclusion. -/
 theorem concyclic_of_two_zsmul_oangle_eq_of_not_collinear {p₁ p₂ p₃ p₄ : P}
@@ -424,7 +473,9 @@ theorem concyclic_of_two_zsmul_oangle_eq_of_not_collinear {p₁ p₂ p₃ p₄ :
     Concyclic ({p₁, p₂, p₃, p₄} : Set P) :=
   ⟨cospherical_of_two_zsmul_oangle_eq_of_not_collinear h hn, coplanar_of_fact_finrank_eq_two _⟩
 #align euclidean_geometry.concyclic_of_two_zsmul_oangle_eq_of_not_collinear EuclideanGeometry.concyclic_of_two_zsmul_oangle_eq_of_not_collinear
+-/
 
+#print EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq /-
 /-- Converse of "angles in same segment are equal" and "opposite angles of a cyclic quadrilateral
 add to π", for oriented angles mod π, with a "cospherical or collinear" conclusion. -/
 theorem cospherical_or_collinear_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P}
@@ -452,7 +503,9 @@ theorem cospherical_or_collinear_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P
         (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))) he]
   · exact Or.inl (cospherical_of_two_zsmul_oangle_eq_of_not_collinear h hc)
 #align euclidean_geometry.cospherical_or_collinear_of_two_zsmul_oangle_eq EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq
+-/
 
+#print EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eq /-
 /-- Converse of "angles in same segment are equal" and "opposite angles of a cyclic quadrilateral
 add to π", for oriented angles mod π, with a "concyclic or collinear" conclusion. -/
 theorem concyclic_or_collinear_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P}
@@ -463,6 +516,7 @@ theorem concyclic_or_collinear_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P}
   · exact Or.inl ⟨hc, coplanar_of_fact_finrank_eq_two _⟩
   · exact Or.inr hc
 #align euclidean_geometry.concyclic_or_collinear_of_two_zsmul_oangle_eq EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eq
+-/
 
 end EuclideanGeometry
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/893964fc28cefbcffc7cb784ed00a2895b4e65cf

@@ -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.sphere
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit cff8231f04dfa33fd8f2f45792eebd862ef30cad
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Geometry.Euclidean.Circumcenter
 /-!
 # Angles in circles and sphere.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves results about angles in circles and spheres.
 
 -/

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

@@ -79,9 +79,6 @@ 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
 
 namespace Sphere
@@ -272,9 +269,6 @@ open 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 circumcenter of a triangle may be expressed explicitly as a multiple (by half the inverse
@@ -398,9 +392,6 @@ 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
 
 /-- Converse of "angles in same segment are equal" and "opposite angles of a cyclic quadrilateral

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -51,7 +51,6 @@ theorem oangle_eq_two_zsmul_oangle_sub_of_norm_eq {x y z : V} (hxyne : x ≠ y)
     _ = (2 : ℤ) • o.oangle (x - y) (x - z) := by
       rw [o.oangle_sub_right (sub_ne_zero_of_ne hxyne) (sub_ne_zero_of_ne hxzne) hx]
     _ = (2 : ℤ) • o.oangle (y - x) (z - x) := by rw [← oangle_neg_neg, neg_sub, neg_sub]
-    
 #align orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq Orientation.oangle_eq_two_zsmul_oangle_sub_of_norm_eq
 
 /-- Angle at center of a circle equals twice angle at circumference, oriented vector angle

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

@@ -196,7 +196,7 @@ theorem inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center {s : Sp
       s.center :=
   by
   convert tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center hp₁ hp₃ hp₁p₃
-  convert(Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi _).symm
+  convert (Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi _).symm
   rw [add_comm,
     two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi hp₁ hp₂ hp₃ hp₁p₂.symm hp₂p₃ hp₁p₃]
 #align euclidean_geometry.sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center

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

@@ -38,7 +38,7 @@ theorem oangle_eq_two_zsmul_oangle_sub_of_norm_eq {x y z : V} (hxyne : x ≠ y)
   by
   have hy : y ≠ 0 := by
     rintro rfl
-    rw [norm_zero, norm_eq_zero] at hxy
+    rw [norm_zero, norm_eq_zero] at hxy 
     exact hxyne hxy
   have hx : x ≠ 0 := norm_ne_zero_iff.1 (hxy.symm ▸ norm_ne_zero_iff.2 hy)
   have hz : z ≠ 0 := norm_ne_zero_iff.1 (hxz ▸ norm_ne_zero_iff.2 hx)
@@ -92,7 +92,7 @@ theorem oangle_center_eq_two_zsmul_oangle {s : Sphere P} {p₁ p₂ p₃ : P} (h
     (hp₂ : p₂ ∈ s) (hp₃ : p₃ ∈ s) (hp₂p₁ : p₂ ≠ p₁) (hp₂p₃ : p₂ ≠ p₃) :
     ∡ p₁ s.center p₃ = (2 : ℤ) • ∡ p₁ p₂ p₃ :=
   by
-  rw [mem_sphere, @dist_eq_norm_vsub V] at hp₁ hp₂ hp₃
+  rw [mem_sphere, @dist_eq_norm_vsub V] at hp₁ hp₂ hp₃ 
   rw [oangle, oangle, o.oangle_eq_two_zsmul_oangle_sub_of_norm_eq_real _ _ hp₂ hp₁ hp₃] <;>
     simp [hp₂p₁, hp₂p₃]
 #align euclidean_geometry.sphere.oangle_center_eq_two_zsmul_oangle EuclideanGeometry.Sphere.oangle_center_eq_two_zsmul_oangle
@@ -104,7 +104,7 @@ theorem two_zsmul_oangle_eq {s : Sphere P} {p₁ p₂ p₃ p₄ : P} (hp₁ : p
     (hp₃ : p₃ ∈ s) (hp₄ : p₄ ∈ s) (hp₂p₁ : p₂ ≠ p₁) (hp₂p₄ : p₂ ≠ p₄) (hp₃p₁ : p₃ ≠ p₁)
     (hp₃p₄ : p₃ ≠ p₄) : (2 : ℤ) • ∡ p₁ p₂ p₄ = (2 : ℤ) • ∡ p₁ p₃ p₄ :=
   by
-  rw [mem_sphere, @dist_eq_norm_vsub V] at hp₁ hp₂ hp₃ hp₄
+  rw [mem_sphere, @dist_eq_norm_vsub V] at hp₁ hp₂ hp₃ hp₄ 
   rw [oangle, oangle, ← vsub_sub_vsub_cancel_right p₁ p₂ s.center, ←
       vsub_sub_vsub_cancel_right p₄ p₂ s.center,
       o.two_zsmul_oangle_sub_eq_two_zsmul_oangle_sub_of_norm_eq _ _ _ _ hp₂ hp₃ hp₁ hp₄] <;>
@@ -121,7 +121,7 @@ theorem Cospherical.two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P}
     (hp₃p₁ : p₃ ≠ p₁) (hp₃p₄ : p₃ ≠ p₄) : (2 : ℤ) • ∡ p₁ p₂ p₄ = (2 : ℤ) • ∡ p₁ p₃ p₄ :=
   by
   obtain ⟨s, hs⟩ := cospherical_iff_exists_sphere.1 h
-  simp_rw [Set.insert_subset, Set.singleton_subset_iff, sphere.mem_coe] at hs
+  simp_rw [Set.insert_subset, Set.singleton_subset_iff, sphere.mem_coe] at hs 
   exact sphere.two_zsmul_oangle_eq hs.1 hs.2.1 hs.2.2.1 hs.2.2.2 hp₂p₁ hp₂p₄ hp₃p₁ hp₃p₄
 #align euclidean_geometry.cospherical.two_zsmul_oangle_eq EuclideanGeometry.Cospherical.two_zsmul_oangle_eq
 
@@ -453,7 +453,7 @@ theorem cospherical_or_collinear_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P
     have hc' : Collinear ℝ ({p₁, p₃, p₄} : Set P) := by
       rwa [← collinear_iff_of_two_zsmul_oangle_eq h]
     refine' Or.inr _
-    rw [Set.insert_comm p₁ p₂] at hc
+    rw [Set.insert_comm p₁ p₂] at hc 
     rwa [Set.insert_comm p₁ p₂,
       hc'.collinear_insert_iff_of_ne (Set.mem_insert _ _)
         (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))) he]

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

@@ -23,7 +23,7 @@ noncomputable section
 
 open FiniteDimensional Complex
 
-open EuclideanGeometry Real RealInnerProductSpace ComplexConjugate
+open scoped EuclideanGeometry Real RealInnerProductSpace ComplexConjugate
 
 namespace Orientation
 

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

@@ -443,8 +443,7 @@ theorem cospherical_or_collinear_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P
     · rw [he,
         Set.insert_eq_self.2
           (Set.mem_insert_of_mem _ (Set.mem_insert_of_mem _ (Set.mem_singleton _)))]
-      by_cases hl : Collinear ℝ ({p₂, p₃, p₄} : Set P)
-      · exact Or.inr hl
+      by_cases hl : Collinear ℝ ({p₂, p₃, p₄} : Set P); · exact Or.inr hl
       rw [or_iff_left hl]
       let t : Affine.Triangle ℝ P := ⟨![p₂, p₃, p₄], affineIndependent_iff_not_collinear_set.2 hl⟩
       rw [cospherical_iff_exists_sphere]

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.sphere
-! leanprover-community/mathlib commit 6d0adfa76594f304b4650d098273d4366edeb61b
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -27,7 +27,7 @@ open EuclideanGeometry Real RealInnerProductSpace ComplexConjugate
 
 namespace Orientation
 
-variable {V : Type _} [InnerProductSpace ℝ V]
+variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
 
 variable [Fact (finrank ℝ V = 2)] (o : Orientation ℝ V (Fin 2))
 
@@ -77,9 +77,8 @@ end Orientation
 
 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
 
@@ -271,9 +270,8 @@ namespace Triangle
 
 open 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
 
@@ -398,9 +396,8 @@ end Affine
 
 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
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -197,7 +197,7 @@ theorem inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center {s : Sp
       s.center :=
   by
   convert tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center hp₁ hp₃ hp₁p₃
-  convert (Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi _).symm
+  convert(Real.Angle.tan_eq_inv_of_two_zsmul_add_two_zsmul_eq_pi _).symm
   rw [add_comm,
     two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi hp₁ hp₂ hp₃ hp₁p₂.symm hp₂p₃ hp₁p₃]
 #align euclidean_geometry.sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -429,11 +429,11 @@ theorem cospherical_of_two_zsmul_oangle_eq_of_not_collinear {p₁ p₂ p₃ p₄
 
 /-- Converse of "angles in same segment are equal" and "opposite angles of a cyclic quadrilateral
 add to π", for oriented angles mod π, with a "concyclic" conclusion. -/
-theorem concyclicOfTwoZsmulOangleEqOfNotCollinear {p₁ p₂ p₃ p₄ : P}
+theorem concyclic_of_two_zsmul_oangle_eq_of_not_collinear {p₁ p₂ p₃ p₄ : P}
     (h : (2 : ℤ) • ∡ p₁ p₂ p₄ = (2 : ℤ) • ∡ p₁ p₃ p₄) (hn : ¬Collinear ℝ ({p₁, p₂, p₄} : Set P)) :
     Concyclic ({p₁, p₂, p₃, p₄} : Set P) :=
   ⟨cospherical_of_two_zsmul_oangle_eq_of_not_collinear h hn, coplanar_of_fact_finrank_eq_two _⟩
-#align euclidean_geometry.concyclic_of_two_zsmul_oangle_eq_of_not_collinear EuclideanGeometry.concyclicOfTwoZsmulOangleEqOfNotCollinear
+#align euclidean_geometry.concyclic_of_two_zsmul_oangle_eq_of_not_collinear EuclideanGeometry.concyclic_of_two_zsmul_oangle_eq_of_not_collinear
 
 /-- Converse of "angles in same segment are equal" and "opposite angles of a cyclic quadrilateral
 add to π", for oriented angles mod π, with a "cospherical or collinear" conclusion. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -337,7 +337,7 @@ theorem circumsphere_eq_of_dist_of_oangle (t : Triangle ℝ P) {i₁ i₂ i₃ :
     (t.dist_div_sin_oangle_div_two_eq_circumradius h₁₂ h₁₃ h₂₃).symm
 #align affine.triangle.circumsphere_eq_of_dist_of_oangle Affine.Triangle.circumsphere_eq_of_dist_of_oangle
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr ⟨«expr +ᵥ »(«expr • »(«expr / »(«expr ⁻¹»((_ : exprℝ())), 2), _), _), «expr / »(«expr / »(_, _), 2)⟩]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ⟨«expr +ᵥ »(«expr • »(«expr / »(«expr ⁻¹»((_ : exprℝ())), 2), _), _), «expr / »(«expr / »(_, _), 2)⟩]] -/
 /-- If two triangles have two points the same, and twice the angle at the third point the same,
 they have the same circumsphere. -/
 theorem circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq {t₁ t₂ : Triangle ℝ P}
@@ -351,7 +351,7 @@ theorem circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq {t₁ t
   rw [t₁.circumsphere_eq_of_dist_of_oangle h₁₂ h₁₃ h₂₃,
     t₂.circumsphere_eq_of_dist_of_oangle h₁₂ h₁₃ h₂₃]
   trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr ⟨«expr +ᵥ »(«expr • »(«expr / »(«expr ⁻¹»((_ : exprℝ())), 2), _), _), «expr / »(«expr / »(_, _), 2)⟩]]"
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ⟨«expr +ᵥ »(«expr • »(«expr / »(«expr ⁻¹»((_ : exprℝ())), 2), _), _), «expr / »(«expr / »(_, _), 2)⟩]]"
   · exact Real.Angle.tan_eq_of_two_zsmul_eq h₂
   · rw [h₁, h₃]
   · rw [h₁, h₃]

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

A PR analogous to #12338: reformatting proofs following the multiple goals linter of #12339.

@@ -199,17 +199,18 @@ theorem dist_div_cos_oangle_center_div_two_eq_radius {s : Sphere P} {p₁ p₂ :
     div_mul_cancel₀ _ (two_ne_zero' ℝ), @dist_eq_norm_vsub' V, @dist_eq_norm_vsub' V,
     vadd_vsub_assoc, add_comm, o.oangle_add_right_smul_rotation_pi_div_two, Real.Angle.cos_coe,
     Real.cos_arctan]
-  norm_cast
-  rw [one_div, div_inv_eq_mul, ←
-    mul_self_inj (mul_nonneg (norm_nonneg _) (Real.sqrt_nonneg _)) (norm_nonneg _),
-    norm_add_sq_eq_norm_sq_add_norm_sq_real (o.inner_smul_rotation_pi_div_two_right _ _), ←
-    mul_assoc, mul_comm, mul_comm _ (√_), ← mul_assoc, ← mul_assoc,
-    Real.mul_self_sqrt (add_nonneg zero_le_one (sq_nonneg _)), norm_smul,
-    LinearIsometryEquiv.norm_map]
-  swap; · simpa using h.symm
-  conv_rhs =>
-    rw [← mul_assoc, mul_comm _ ‖Real.Angle.tan _‖, ← mul_assoc, Real.norm_eq_abs, abs_mul_abs_self]
-  ring
+  · norm_cast
+    rw [one_div, div_inv_eq_mul, ←
+      mul_self_inj (mul_nonneg (norm_nonneg _) (Real.sqrt_nonneg _)) (norm_nonneg _),
+      norm_add_sq_eq_norm_sq_add_norm_sq_real (o.inner_smul_rotation_pi_div_two_right _ _), ←
+      mul_assoc, mul_comm, mul_comm _ (√_), ← mul_assoc, ← mul_assoc,
+      Real.mul_self_sqrt (add_nonneg zero_le_one (sq_nonneg _)), norm_smul,
+      LinearIsometryEquiv.norm_map]
+    conv_rhs =>
+      rw [← mul_assoc, mul_comm _ ‖Real.Angle.tan _‖, ← mul_assoc, Real.norm_eq_abs,
+        abs_mul_abs_self]
+    ring
+  · simpa using h.symm
 #align euclidean_geometry.sphere.dist_div_cos_oangle_center_div_two_eq_radius EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius
 
 /-- Given two points on a circle, twice the radius of that circle may be expressed explicitly as

This adds the notation √r for Real.sqrt r. The precedence is such that √x⁻¹ is parsed as √(x⁻¹); not because this is particularly desirable, but because it's the default and the choice doesn't really matter.

This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing x.sqrt as that PR does.

While perhaps claiming √ for Real.sqrt is greedy; it:

• Is far more common thatn NNReal.sqrt and Nat.sqrt
• Is far more interesting to mathlib than sqrt on Float
• Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types.
• Will be replaced by a more general typeclass in a future PR.

Zulip

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -203,7 +203,7 @@ theorem dist_div_cos_oangle_center_div_two_eq_radius {s : Sphere P} {p₁ p₂ :
   rw [one_div, div_inv_eq_mul, ←
     mul_self_inj (mul_nonneg (norm_nonneg _) (Real.sqrt_nonneg _)) (norm_nonneg _),
     norm_add_sq_eq_norm_sq_add_norm_sq_real (o.inner_smul_rotation_pi_div_two_right _ _), ←
-    mul_assoc, mul_comm, mul_comm _ (Real.sqrt _), ← mul_assoc, ← mul_assoc,
+    mul_assoc, mul_comm, mul_comm _ (√_), ← mul_assoc, ← mul_assoc,
     Real.mul_self_sqrt (add_nonneg zero_le_one (sq_nonneg _)), norm_smul,
     LinearIsometryEquiv.norm_map]
   swap; · simpa using h.symm

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -137,7 +137,7 @@ theorem two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi {s : Sphere P} {p₁
     (hp₁ : p₁ ∈ s) (hp₂ : p₂ ∈ s) (hp₃ : p₃ ∈ s) (hp₂p₁ : p₂ ≠ p₁) (hp₂p₃ : p₂ ≠ p₃)
     (hp₁p₃ : p₁ ≠ p₃) : (2 : ℤ) • ∡ p₃ p₁ s.center + (2 : ℤ) • ∡ p₁ p₂ p₃ = π := by
   rw [← oangle_center_eq_two_zsmul_oangle hp₁ hp₂ hp₃ hp₂p₁ hp₂p₃,
-    oangle_eq_pi_sub_two_zsmul_oangle_center_right hp₁ hp₃ hp₁p₃, add_sub_cancel'_right]
+    oangle_eq_pi_sub_two_zsmul_oangle_center_right hp₁ hp₃ hp₁p₃, add_sub_cancel]
 #align euclidean_geometry.sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi EuclideanGeometry.Sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi
 
 /-- A base angle of an isosceles triangle with apex at the center of a circle is acute. -/
@@ -167,7 +167,7 @@ theorem tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center {s : Sphere
   rw [← hr, ← oangle_midpoint_rev_left, oangle, vadd_vsub_assoc]
   nth_rw 1 [show p₂ -ᵥ p₁ = (2 : ℝ) • (midpoint ℝ p₁ p₂ -ᵥ p₁) by simp]
   rw [map_smul, smul_smul, add_comm, o.tan_oangle_add_right_smul_rotation_pi_div_two,
-    mul_div_cancel _ (two_ne_zero' ℝ)]
+    mul_div_cancel_right₀ _ (two_ne_zero' ℝ)]
   simpa using h.symm
 #align euclidean_geometry.sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center
 
@@ -196,7 +196,7 @@ theorem dist_div_cos_oangle_center_div_two_eq_radius {s : Sphere P} {p₁ p₂ :
     tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center hp₁ hp₂ h, ←
     oangle_midpoint_rev_left, oangle, vadd_vsub_assoc,
     show p₂ -ᵥ p₁ = (2 : ℝ) • (midpoint ℝ p₁ p₂ -ᵥ p₁) by simp, map_smul, smul_smul,
-    div_mul_cancel _ (two_ne_zero' ℝ), @dist_eq_norm_vsub' V, @dist_eq_norm_vsub' V,
+    div_mul_cancel₀ _ (two_ne_zero' ℝ), @dist_eq_norm_vsub' V, @dist_eq_norm_vsub' V,
     vadd_vsub_assoc, add_comm, o.oangle_add_right_smul_rotation_pi_div_two, Real.Angle.cos_coe,
     Real.cos_arctan]
   norm_cast
@@ -218,7 +218,7 @@ the radius at one of those points. -/
 theorem dist_div_cos_oangle_center_eq_two_mul_radius {s : Sphere P} {p₁ p₂ : P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) (h : p₁ ≠ p₂) :
     dist p₁ p₂ / Real.Angle.cos (∡ p₂ p₁ s.center) = 2 * s.radius := by
-  rw [← dist_div_cos_oangle_center_div_two_eq_radius hp₁ hp₂ h, mul_div_cancel' _ (two_ne_zero' ℝ)]
+  rw [← dist_div_cos_oangle_center_div_two_eq_radius hp₁ hp₂ h, mul_div_cancel₀ _ (two_ne_zero' ℝ)]
 #align euclidean_geometry.sphere.dist_div_cos_oangle_center_eq_two_mul_radius EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius
 
 /-- Given three points on a circle, the radius of that circle may be expressed explicitly as half
@@ -241,7 +241,7 @@ theorem dist_div_sin_oangle_eq_two_mul_radius {s : Sphere P} {p₁ p₂ p₃ : P
     (hp₂ : p₂ ∈ s) (hp₃ : p₃ ∈ s) (hp₁p₂ : p₁ ≠ p₂) (hp₁p₃ : p₁ ≠ p₃) (hp₂p₃ : p₂ ≠ p₃) :
     dist p₁ p₃ / |Real.Angle.sin (∡ p₁ p₂ p₃)| = 2 * s.radius := by
   rw [← dist_div_sin_oangle_div_two_eq_radius hp₁ hp₂ hp₃ hp₁p₂ hp₁p₃ hp₂p₃,
-    mul_div_cancel' _ (two_ne_zero' ℝ)]
+    mul_div_cancel₀ _ (two_ne_zero' ℝ)]
 #align euclidean_geometry.sphere.dist_div_sin_oangle_eq_two_mul_radius EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius
 
 end Sphere

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -25,7 +25,6 @@ open scoped EuclideanGeometry Real RealInnerProductSpace ComplexConjugate
 namespace Orientation
 
 variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
-
 variable [Fact (finrank ℝ V = 2)] (o : Orientation ℝ V (Fin 2))
 
 /-- Angle at center of a circle equals twice angle at circumference, oriented vector angle

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

@@ -330,9 +330,9 @@ theorem mem_circumsphere_of_two_zsmul_oangle_eq {t : Triangle ℝ P} {p : P} {i
     (h : (2 : ℤ) • ∡ (t.points i₁) p (t.points i₃) =
       (2 : ℤ) • ∡ (t.points i₁) (t.points i₂) (t.points i₃)) : p ∈ t.circumsphere := by
   let t'p : Fin 3 → P := Function.update t.points i₂ p
-  have h₁ : t'p i₁ = t.points i₁ := by simp [h₁₂]
-  have h₂ : t'p i₂ = p := by simp
-  have h₃ : t'p i₃ = t.points i₃ := by simp [h₂₃.symm]
+  have h₁ : t'p i₁ = t.points i₁ := by simp [t'p, h₁₂]
+  have h₂ : t'p i₂ = p := by simp [t'p]
+  have h₃ : t'p i₃ = t.points i₃ := by simp [t'p, h₂₃.symm]
   have ha : AffineIndependent ℝ t'p := by
     rw [affineIndependent_iff_not_collinear_of_ne h₁₂ h₁₃ h₂₃, h₁, h₂, h₃,
       collinear_iff_of_two_zsmul_oangle_eq h, ←

This holds a proof not a Prop, so should be lowercase.

@@ -269,8 +269,8 @@ theorem inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter (
       o.rotation (π / 2 : ℝ) (t.points i₃ -ᵥ t.points i₁) +ᵥ
         midpoint ℝ (t.points i₁) (t.points i₃) = t.circumcenter :=
   Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center (t.mem_circumsphere _)
-    (t.mem_circumsphere _) (t.mem_circumsphere _) (t.Independent.injective.ne h₁₂)
-    (t.Independent.injective.ne h₁₃) (t.Independent.injective.ne h₂₃)
+    (t.mem_circumsphere _) (t.mem_circumsphere _) (t.independent.injective.ne h₁₂)
+    (t.independent.injective.ne h₁₃) (t.independent.injective.ne h₂₃)
 #align affine.triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter
 
 /-- The circumradius of a triangle may be expressed explicitly as half the length of a side
@@ -280,8 +280,8 @@ theorem dist_div_sin_oangle_div_two_eq_circumradius (t : Triangle ℝ P) {i₁ i
     (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) : dist (t.points i₁) (t.points i₃) /
       |Real.Angle.sin (∡ (t.points i₁) (t.points i₂) (t.points i₃))| / 2 = t.circumradius :=
   Sphere.dist_div_sin_oangle_div_two_eq_radius (t.mem_circumsphere _) (t.mem_circumsphere _)
-    (t.mem_circumsphere _) (t.Independent.injective.ne h₁₂) (t.Independent.injective.ne h₁₃)
-    (t.Independent.injective.ne h₂₃)
+    (t.mem_circumsphere _) (t.independent.injective.ne h₁₂) (t.independent.injective.ne h₁₃)
+    (t.independent.injective.ne h₂₃)
 #align affine.triangle.dist_div_sin_oangle_div_two_eq_circumradius Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius
 
 /-- Twice the circumradius of a triangle may be expressed explicitly as the length of a side
@@ -291,8 +291,8 @@ theorem dist_div_sin_oangle_eq_two_mul_circumradius (t : Triangle ℝ P) {i₁ i
     (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃) (h₂₃ : i₂ ≠ i₃) : dist (t.points i₁) (t.points i₃) /
       |Real.Angle.sin (∡ (t.points i₁) (t.points i₂) (t.points i₃))| = 2 * t.circumradius :=
   Sphere.dist_div_sin_oangle_eq_two_mul_radius (t.mem_circumsphere _) (t.mem_circumsphere _)
-    (t.mem_circumsphere _) (t.Independent.injective.ne h₁₂) (t.Independent.injective.ne h₁₃)
-    (t.Independent.injective.ne h₂₃)
+    (t.mem_circumsphere _) (t.independent.injective.ne h₁₂) (t.independent.injective.ne h₁₃)
+    (t.independent.injective.ne h₂₃)
 #align affine.triangle.dist_div_sin_oangle_eq_two_mul_circumradius Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius
 
 /-- The circumsphere of a triangle may be expressed explicitly in terms of two points and the
@@ -337,7 +337,7 @@ theorem mem_circumsphere_of_two_zsmul_oangle_eq {t : Triangle ℝ P} {p : P} {i
     rw [affineIndependent_iff_not_collinear_of_ne h₁₂ h₁₃ h₂₃, h₁, h₂, h₃,
       collinear_iff_of_two_zsmul_oangle_eq h, ←
       affineIndependent_iff_not_collinear_of_ne h₁₂ h₁₃ h₂₃]
-    exact t.Independent
+    exact t.independent
   let t' : Triangle ℝ P := ⟨t'p, ha⟩
   have h₁' : t'.points i₁ = t.points i₁ := h₁
   have h₂' : t'.points i₂ = p := h₂

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

This has nice performance benefits.

@@ -24,7 +24,7 @@ open scoped EuclideanGeometry Real RealInnerProductSpace ComplexConjugate
 
 namespace Orientation
 
-variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
+variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
 
 variable [Fact (finrank ℝ V = 2)] (o : Orientation ℝ V (Fin 2))
 
@@ -72,7 +72,7 @@ end Orientation
 
 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)]
 
 local notation "o" => Module.Oriented.positiveOrientation
@@ -255,7 +255,7 @@ namespace Triangle
 
 open 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)]
 
 local notation "o" => Module.Oriented.positiveOrientation
@@ -355,7 +355,7 @@ end Affine
 
 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)]
 
 local notation "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>

@@ -2,15 +2,12 @@
 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.sphere
-! 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.Geometry.Euclidean.Angle.Oriented.RightAngle
 import Mathlib.Geometry.Euclidean.Circumcenter
 
+#align_import geometry.euclidean.angle.sphere from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-!
 # Angles in circles and sphere.
 

Currently, (for both Set and Finset) insert_subset is an iff lemma stating that insert a s ⊆ t if and only if a ∈ t and s ⊆ t. For both types, this PR renames this lemma to insert_subset_iff, and adds an insert_subset lemma that gives the implication just in the reverse direction : namely theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t .

This both aligns the naming with union_subset and union_subset_iff, and removes the need for the awkward insert_subset.mpr ⟨_,_⟩ idiom. It touches a lot of files (too many to list), but in a trivial way.

@@ -113,7 +113,7 @@ theorem Cospherical.two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P}
     (h : Cospherical ({p₁, p₂, p₃, p₄} : Set P)) (hp₂p₁ : p₂ ≠ p₁) (hp₂p₄ : p₂ ≠ p₄)
     (hp₃p₁ : p₃ ≠ p₁) (hp₃p₄ : p₃ ≠ p₄) : (2 : ℤ) • ∡ p₁ p₂ p₄ = (2 : ℤ) • ∡ p₁ p₃ p₄ := by
   obtain ⟨s, hs⟩ := cospherical_iff_exists_sphere.1 h
-  simp_rw [Set.insert_subset, Set.singleton_subset_iff, Sphere.mem_coe] at hs
+  simp_rw [Set.insert_subset_iff, Set.singleton_subset_iff, Sphere.mem_coe] at hs
   exact Sphere.two_zsmul_oangle_eq hs.1 hs.2.1 hs.2.2.1 hs.2.2.2 hp₂p₁ hp₂p₄ hp₃p₁ hp₃p₄
 #align euclidean_geometry.cospherical.two_zsmul_oangle_eq EuclideanGeometry.Cospherical.two_zsmul_oangle_eq
 
@@ -374,7 +374,7 @@ theorem cospherical_of_two_zsmul_oangle_eq_of_not_collinear {p₁ p₂ p₃ p₄
   let t₂ : Affine.Triangle ℝ P := ⟨![p₁, p₃, p₄], affineIndependent_iff_not_collinear_set.2 hn'⟩
   rw [cospherical_iff_exists_sphere]
   refine' ⟨t₂.circumsphere, _⟩
-  simp_rw [Set.insert_subset, Set.singleton_subset_iff]
+  simp_rw [Set.insert_subset_iff, Set.singleton_subset_iff]
   refine' ⟨t₂.mem_circumsphere 0, _, t₂.mem_circumsphere 1, t₂.mem_circumsphere 2⟩
   rw [Affine.Triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq
     (by decide : (0 : Fin 3) ≠ 1) (by decide : (0 : Fin 3) ≠ 2) (by decide)
@@ -404,7 +404,7 @@ theorem cospherical_or_collinear_of_two_zsmul_oangle_eq {p₁ p₂ p₃ p₄ : P
       let t : Affine.Triangle ℝ P := ⟨![p₂, p₃, p₄], affineIndependent_iff_not_collinear_set.2 hl⟩
       rw [cospherical_iff_exists_sphere]
       refine' ⟨t.circumsphere, _⟩
-      simp_rw [Set.insert_subset, Set.singleton_subset_iff]
+      simp_rw [Set.insert_subset_iff, Set.singleton_subset_iff]
       exact ⟨t.mem_circumsphere 0, t.mem_circumsphere 1, t.mem_circumsphere 2⟩
     have hc' : Collinear ℝ ({p₁, p₃, p₄} : Set P) := by
       rwa [← collinear_iff_of_two_zsmul_oangle_eq h]