geometry.euclidean.sphere.power ⟷ Mathlib.Geometry.Euclidean.Sphere.Power

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

@@ -98,8 +98,8 @@ theorem mul_dist_eq_abs_sub_sq_dist {a b p q : P} (hp : ∃ k : ℝ, k ≠ 1 ∧
     rw [midpoint_vsub_left, ← right_vsub_midpoint, add_comm, vsub_add_vsub_cancel]
   iterate 4 rw [dist_eq_norm_vsub V]
   rw [← h1, ← h2, h, h]
-  rw [← h1, h] at hp 
-  rw [dist_eq_norm_vsub V a q, dist_eq_norm_vsub V b q, ← h3, h] at hq 
+  rw [← h1, h] at hp
+  rw [dist_eq_norm_vsub V a q, dist_eq_norm_vsub V b q, ← h3, h] at hq
   exact mul_norm_eq_abs_sub_sq_norm hp hq
 #align euclidean_geometry.mul_dist_eq_abs_sub_sq_dist EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist
 -/
@@ -114,8 +114,8 @@ theorem mul_dist_eq_mul_dist_of_cospherical {a b c d p : P} (h : Cospherical ({a
   by
   obtain ⟨q, r, h'⟩ := (cospherical_def {a, b, c, d}).mp h
   obtain ⟨ha, hb, hc, hd⟩ := h' a _, h' b _, h' c _, h' d _
-  · rw [← hd] at hc 
-    rw [← hb] at ha 
+  · rw [← hd] at hc
+    rw [← hb] at ha
     rw [mul_dist_eq_abs_sub_sq_dist hapb ha, hb, mul_dist_eq_abs_sub_sq_dist hcpd hc, hd]
   all_goals simp
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Manuel Candales. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Manuel Candales, Benjamin Davidson
 -/
-import Mathbin.Geometry.Euclidean.Angle.Unoriented.Affine
-import Mathbin.Geometry.Euclidean.Sphere.Basic
+import Geometry.Euclidean.Angle.Unoriented.Affine
+import Geometry.Euclidean.Sphere.Basic
 
 #align_import geometry.euclidean.sphere.power from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Manuel Candales. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Manuel Candales, Benjamin Davidson
-
-! This file was ported from Lean 3 source module geometry.euclidean.sphere.power
-! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Geometry.Euclidean.Angle.Unoriented.Affine
 import Mathbin.Geometry.Euclidean.Sphere.Basic
 
+#align_import geometry.euclidean.sphere.power from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
+
 /-!
 # Power of a point (intersecting chords and secants)
 

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

@@ -43,6 +43,7 @@ which are used to deduce corresponding results for Euclidean affine spaces.
 -/
 
 
+#print InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm /-
 theorem mul_norm_eq_abs_sub_sq_norm {x y z : V} (h₁ : ∃ k : ℝ, k ≠ 1 ∧ x + y = k • (x - y))
     (h₂ : ‖z - y‖ = ‖z + y‖) : ‖x - y‖ * ‖x + y‖ = |‖z + y‖ ^ 2 - ‖z - x‖ ^ 2| :=
   by
@@ -71,6 +72,7 @@ theorem mul_norm_eq_abs_sub_sq_norm {x y z : V} (h₁ : ∃ k : ℝ, k ≠ 1 ∧
     _ = |‖z + y‖ ^ 2 - ‖z - x‖ ^ 2| := by
       simp [norm_add_sq_real, norm_sub_sq_real, hzy, hzx, abs_sub_comm]
 #align inner_product_geometry.mul_norm_eq_abs_sub_sq_norm InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm
+-/
 
 end InnerProductGeometry
 
@@ -87,8 +89,7 @@ open InnerProductGeometry
 
 variable {P : Type _} [MetricSpace P] [NormedAddTorsor V P]
 
-include V
-
+#print EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist /-
 /-- If `P` is a point on the line `AB` and `Q` is equidistant from `A` and `B`, then
 `AP * BP = abs (BQ ^ 2 - PQ ^ 2)`. -/
 theorem mul_dist_eq_abs_sub_sq_dist {a b p q : P} (hp : ∃ k : ℝ, k ≠ 1 ∧ b -ᵥ p = k • (a -ᵥ p))
@@ -104,7 +105,9 @@ theorem mul_dist_eq_abs_sub_sq_dist {a b p q : P} (hp : ∃ k : ℝ, k ≠ 1 ∧
   rw [dist_eq_norm_vsub V a q, dist_eq_norm_vsub V b q, ← h3, h] at hq 
   exact mul_norm_eq_abs_sub_sq_norm hp hq
 #align euclidean_geometry.mul_dist_eq_abs_sub_sq_dist EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist
+-/
 
+#print EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical /-
 /-- If `A`, `B`, `C`, `D` are cospherical and `P` is on both lines `AB` and `CD`, then
 `AP * BP = CP * DP`. -/
 theorem mul_dist_eq_mul_dist_of_cospherical {a b c d p : P} (h : Cospherical ({a, b, c, d} : Set P))
@@ -119,7 +122,9 @@ theorem mul_dist_eq_mul_dist_of_cospherical {a b c d p : P} (h : Cospherical ({a
     rw [mul_dist_eq_abs_sub_sq_dist hapb ha, hb, mul_dist_eq_abs_sub_sq_dist hcpd hc, hd]
   all_goals simp
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical
+-/
 
+#print EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi /-
 /-- **Intersecting Chords Theorem**. -/
 theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi {a b c d p : P}
     (h : Cospherical ({a, b, c, d} : Set P)) (hapb : ∠ a p b = π) (hcpd : ∠ c p d = π) :
@@ -129,7 +134,9 @@ theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi {a b c d p : P}
   obtain ⟨-, k₂, _, hcd⟩ := angle_eq_pi_iff.mp hcpd
   exact mul_dist_eq_mul_dist_of_cospherical h ⟨k₁, by linarith, hab⟩ ⟨k₂, by linarith, hcd⟩
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi
+-/
 
+#print EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero /-
 /-- **Intersecting Secants Theorem**. -/
 theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero {a b c d p : P}
     (h : Cospherical ({a, b, c, d} : Set P)) (hab : a ≠ b) (hcd : c ≠ d) (hapb : ∠ a p b = 0)
@@ -141,6 +148,7 @@ theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero {a b c d p : P}
     simp_all only [Classical.not_not, one_smul]
   exacts [hab (vsub_left_cancel hab₁).symm, hcd (vsub_left_cancel hcd₁).symm]
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero
+-/
 
 end EuclideanGeometry
 

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

@@ -57,7 +57,6 @@ theorem mul_norm_eq_abs_sub_sq_norm {x y z : V} (h₁ : ∃ k : ℝ, k ≠ 1 ∧
       _ = k • x - k • y - (x + y) := by simp_rw [← sub_sub, sub_right_comm]
       _ = k • (x - y) - (x + y) := by rw [← smul_sub k x y]
       _ = 0 := sub_eq_zero.mpr hk.symm
-      
   have hzy : ⟪z, y⟫ = 0 := by
     rwa [inner_eq_zero_iff_angle_eq_pi_div_two, ← norm_add_eq_norm_sub_iff_angle_eq_pi_div_two,
       eq_comm]
@@ -71,7 +70,6 @@ theorem mul_norm_eq_abs_sub_sq_norm {x y z : V} (h₁ : ∃ k : ℝ, k ≠ 1 ∧
     _ = |‖x‖ ^ 2 - ‖y‖ ^ 2| := by simp [hxy, norm_smul, mul_pow, sq_abs]
     _ = |‖z + y‖ ^ 2 - ‖z - x‖ ^ 2| := by
       simp [norm_add_sq_real, norm_sub_sq_real, hzy, hzx, abs_sub_comm]
-    
 #align inner_product_geometry.mul_norm_eq_abs_sub_sq_norm InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm
 
 end InnerProductGeometry

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

@@ -102,8 +102,8 @@ theorem mul_dist_eq_abs_sub_sq_dist {a b p q : P} (hp : ∃ k : ℝ, k ≠ 1 ∧
     rw [midpoint_vsub_left, ← right_vsub_midpoint, add_comm, vsub_add_vsub_cancel]
   iterate 4 rw [dist_eq_norm_vsub V]
   rw [← h1, ← h2, h, h]
-  rw [← h1, h] at hp
-  rw [dist_eq_norm_vsub V a q, dist_eq_norm_vsub V b q, ← h3, h] at hq
+  rw [← h1, h] at hp 
+  rw [dist_eq_norm_vsub V a q, dist_eq_norm_vsub V b q, ← h3, h] at hq 
   exact mul_norm_eq_abs_sub_sq_norm hp hq
 #align euclidean_geometry.mul_dist_eq_abs_sub_sq_dist EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist
 
@@ -116,8 +116,8 @@ theorem mul_dist_eq_mul_dist_of_cospherical {a b c d p : P} (h : Cospherical ({a
   by
   obtain ⟨q, r, h'⟩ := (cospherical_def {a, b, c, d}).mp h
   obtain ⟨ha, hb, hc, hd⟩ := h' a _, h' b _, h' c _, h' d _
-  · rw [← hd] at hc
-    rw [← hb] at ha
+  · rw [← hd] at hc 
+    rw [← hb] at ha 
     rw [mul_dist_eq_abs_sub_sq_dist hapb ha, hb, mul_dist_eq_abs_sub_sq_dist hcpd hc, hd]
   all_goals simp
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical
@@ -141,7 +141,7 @@ theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero {a b c d p : P}
   obtain ⟨-, k₂, -, hcd₁⟩ := angle_eq_zero_iff.mp hcpd
   refine' mul_dist_eq_mul_dist_of_cospherical h ⟨k₁, _, hab₁⟩ ⟨k₂, _, hcd₁⟩ <;> by_contra hnot <;>
     simp_all only [Classical.not_not, one_smul]
-  exacts[hab (vsub_left_cancel hab₁).symm, hcd (vsub_left_cancel hcd₁).symm]
+  exacts [hab (vsub_left_cancel hab₁).symm, hcd (vsub_left_cancel hcd₁).symm]
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero
 
 end EuclideanGeometry

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Manuel Candales, Benjamin Davidson
 
 ! This file was ported from Lean 3 source module geometry.euclidean.sphere.power
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit f60c6087a7275b72d5db3c5a1d0e19e35a429c0a
 ! 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.Sphere.Basic
 /-!
 # Power of a point (intersecting chords and secants)
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves basic geometrical results about power of a point (intersecting chords and
 secants) in spheres in real inner product spaces and Euclidean affine spaces.
 

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

@@ -26,7 +26,7 @@ secants) in spheres in real inner product spaces and Euclidean affine spaces.
 
 open Real
 
-open EuclideanGeometry RealInnerProductSpace Real
+open scoped EuclideanGeometry RealInnerProductSpace Real
 
 variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
 

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

@@ -40,9 +40,6 @@ which are used to deduce corresponding results for Euclidean affine spaces.
 -/
 
 
-/- warning: inner_product_geometry.mul_norm_eq_abs_sub_sq_norm -> InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inner_product_geometry.mul_norm_eq_abs_sub_sq_norm InnerProductGeometry.mul_norm_eq_abs_sub_sq_normₓ'. -/
 theorem mul_norm_eq_abs_sub_sq_norm {x y z : V} (h₁ : ∃ k : ℝ, k ≠ 1 ∧ x + y = k • (x - y))
     (h₂ : ‖z - y‖ = ‖z + y‖) : ‖x - y‖ * ‖x + y‖ = |‖z + y‖ ^ 2 - ‖z - x‖ ^ 2| :=
   by
@@ -91,9 +88,6 @@ variable {P : Type _} [MetricSpace P] [NormedAddTorsor V P]
 
 include V
 
-/- warning: euclidean_geometry.mul_dist_eq_abs_sub_sq_dist -> EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.mul_dist_eq_abs_sub_sq_dist EuclideanGeometry.mul_dist_eq_abs_sub_sq_distₓ'. -/
 /-- If `P` is a point on the line `AB` and `Q` is equidistant from `A` and `B`, then
 `AP * BP = abs (BQ ^ 2 - PQ ^ 2)`. -/
 theorem mul_dist_eq_abs_sub_sq_dist {a b p q : P} (hp : ∃ k : ℝ, k ≠ 1 ∧ b -ᵥ p = k • (a -ᵥ p))
@@ -110,9 +104,6 @@ theorem mul_dist_eq_abs_sub_sq_dist {a b p q : P} (hp : ∃ k : ℝ, k ≠ 1 ∧
   exact mul_norm_eq_abs_sub_sq_norm hp hq
 #align euclidean_geometry.mul_dist_eq_abs_sub_sq_dist EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist
 
-/- warning: euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical -> EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical EuclideanGeometry.mul_dist_eq_mul_dist_of_cosphericalₓ'. -/
 /-- If `A`, `B`, `C`, `D` are cospherical and `P` is on both lines `AB` and `CD`, then
 `AP * BP = CP * DP`. -/
 theorem mul_dist_eq_mul_dist_of_cospherical {a b c d p : P} (h : Cospherical ({a, b, c, d} : Set P))
@@ -128,12 +119,6 @@ theorem mul_dist_eq_mul_dist_of_cospherical {a b c d p : P} (h : Cospherical ({a
   all_goals simp
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical
 
-/- warning: euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi -> EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi is a dubious translation:
-lean 3 declaration is
-  forall {V : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] {P : Type.{u2}} [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {a : P} {b : P} {c : P} {d : P} {p : P}, (EuclideanGeometry.Cospherical.{u2} P _inst_3 (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) a (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) b (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) c (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.hasSingleton.{u2} P) d))))) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 a p b) Real.pi) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 c p d) Real.pi) -> (Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) a p) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) b p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) c p) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) d p)))
-but is expected to have type
-  forall {V : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] {P : Type.{u2}} [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {a : P} {b : P} {c : P} {d : P} {p : P}, (EuclideanGeometry.Cospherical.{u2} P _inst_3 (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) a (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) b (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) c (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.instSingletonSet.{u2} P) d))))) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 a p b) Real.pi) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 c p d) Real.pi) -> (Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) a p) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) b p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) c p) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) d p)))
-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_piₓ'. -/
 /-- **Intersecting Chords Theorem**. -/
 theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi {a b c d p : P}
     (h : Cospherical ({a, b, c, d} : Set P)) (hapb : ∠ a p b = π) (hcpd : ∠ c p d = π) :
@@ -144,12 +129,6 @@ theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi {a b c d p : P}
   exact mul_dist_eq_mul_dist_of_cospherical h ⟨k₁, by linarith, hab⟩ ⟨k₂, by linarith, hcd⟩
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi
 
-/- warning: euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero -> EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero is a dubious translation:
-lean 3 declaration is
-  forall {V : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] {P : Type.{u2}} [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {a : P} {b : P} {c : P} {d : P} {p : P}, (EuclideanGeometry.Cospherical.{u2} P _inst_3 (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) a (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) b (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) c (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.hasSingleton.{u2} P) d))))) -> (Ne.{succ u2} P a b) -> (Ne.{succ u2} P c d) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 a p b) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 c p d) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) a p) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) b p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) c p) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) d p)))
-but is expected to have type
-  forall {V : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] {P : Type.{u2}} [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {a : P} {b : P} {c : P} {d : P} {p : P}, (EuclideanGeometry.Cospherical.{u2} P _inst_3 (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) a (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) b (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) c (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.instSingletonSet.{u2} P) d))))) -> (Ne.{succ u2} P a b) -> (Ne.{succ u2} P c d) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 a p b) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 c p d) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) a p) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) b p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) c p) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) d p)))
-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zeroₓ'. -/
 /-- **Intersecting Secants Theorem**. -/
 theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero {a b c d p : P}
     (h : Cospherical ({a, b, c, d} : Set P)) (hab : a ≠ b) (hcd : c ≠ d) (hapb : ∠ a p b = 0)

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

@@ -40,6 +40,9 @@ which are used to deduce corresponding results for Euclidean affine spaces.
 -/
 
 
+/- warning: inner_product_geometry.mul_norm_eq_abs_sub_sq_norm -> InnerProductGeometry.mul_norm_eq_abs_sub_sq_norm is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align inner_product_geometry.mul_norm_eq_abs_sub_sq_norm InnerProductGeometry.mul_norm_eq_abs_sub_sq_normₓ'. -/
 theorem mul_norm_eq_abs_sub_sq_norm {x y z : V} (h₁ : ∃ k : ℝ, k ≠ 1 ∧ x + y = k • (x - y))
     (h₂ : ‖z - y‖ = ‖z + y‖) : ‖x - y‖ * ‖x + y‖ = |‖z + y‖ ^ 2 - ‖z - x‖ ^ 2| :=
   by
@@ -88,6 +91,9 @@ variable {P : Type _} [MetricSpace P] [NormedAddTorsor V P]
 
 include V
 
+/- warning: euclidean_geometry.mul_dist_eq_abs_sub_sq_dist -> EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.mul_dist_eq_abs_sub_sq_dist EuclideanGeometry.mul_dist_eq_abs_sub_sq_distₓ'. -/
 /-- If `P` is a point on the line `AB` and `Q` is equidistant from `A` and `B`, then
 `AP * BP = abs (BQ ^ 2 - PQ ^ 2)`. -/
 theorem mul_dist_eq_abs_sub_sq_dist {a b p q : P} (hp : ∃ k : ℝ, k ≠ 1 ∧ b -ᵥ p = k • (a -ᵥ p))
@@ -104,6 +110,9 @@ theorem mul_dist_eq_abs_sub_sq_dist {a b p q : P} (hp : ∃ k : ℝ, k ≠ 1 ∧
   exact mul_norm_eq_abs_sub_sq_norm hp hq
 #align euclidean_geometry.mul_dist_eq_abs_sub_sq_dist EuclideanGeometry.mul_dist_eq_abs_sub_sq_dist
 
+/- warning: euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical -> EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical EuclideanGeometry.mul_dist_eq_mul_dist_of_cosphericalₓ'. -/
 /-- If `A`, `B`, `C`, `D` are cospherical and `P` is on both lines `AB` and `CD`, then
 `AP * BP = CP * DP`. -/
 theorem mul_dist_eq_mul_dist_of_cospherical {a b c d p : P} (h : Cospherical ({a, b, c, d} : Set P))
@@ -119,6 +128,12 @@ theorem mul_dist_eq_mul_dist_of_cospherical {a b c d p : P} (h : Cospherical ({a
   all_goals simp
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical
 
+/- warning: euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi -> EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] {P : Type.{u2}} [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {a : P} {b : P} {c : P} {d : P} {p : P}, (EuclideanGeometry.Cospherical.{u2} P _inst_3 (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) a (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) b (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) c (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.hasSingleton.{u2} P) d))))) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 a p b) Real.pi) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 c p d) Real.pi) -> (Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) a p) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) b p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) c p) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) d p)))
+but is expected to have type
+  forall {V : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] {P : Type.{u2}} [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {a : P} {b : P} {c : P} {d : P} {p : P}, (EuclideanGeometry.Cospherical.{u2} P _inst_3 (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) a (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) b (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) c (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.instSingletonSet.{u2} P) d))))) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 a p b) Real.pi) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 c p d) Real.pi) -> (Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) a p) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) b p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) c p) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) d p)))
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_piₓ'. -/
 /-- **Intersecting Chords Theorem**. -/
 theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi {a b c d p : P}
     (h : Cospherical ({a, b, c, d} : Set P)) (hapb : ∠ a p b = π) (hcpd : ∠ c p d = π) :
@@ -129,6 +144,12 @@ theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi {a b c d p : P}
   exact mul_dist_eq_mul_dist_of_cospherical h ⟨k₁, by linarith, hab⟩ ⟨k₂, by linarith, hcd⟩
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi
 
+/- warning: euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero -> EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] {P : Type.{u2}} [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {a : P} {b : P} {c : P} {d : P} {p : P}, (EuclideanGeometry.Cospherical.{u2} P _inst_3 (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) a (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) b (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.hasInsert.{u2} P) c (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.hasSingleton.{u2} P) d))))) -> (Ne.{succ u2} P a b) -> (Ne.{succ u2} P c d) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 a p b) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 c p d) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) a p) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) b p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) c p) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) d p)))
+but is expected to have type
+  forall {V : Type.{u1}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] {P : Type.{u2}} [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {a : P} {b : P} {c : P} {d : P} {p : P}, (EuclideanGeometry.Cospherical.{u2} P _inst_3 (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) a (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) b (Insert.insert.{u2, u2} P (Set.{u2} P) (Set.instInsertSet.{u2} P) c (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.instSingletonSet.{u2} P) d))))) -> (Ne.{succ u2} P a b) -> (Ne.{succ u2} P c d) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 a p b) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (EuclideanGeometry.angle.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 c p d) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) a p) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) b p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) c p) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) d p)))
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zeroₓ'. -/
 /-- **Intersecting Secants Theorem**. -/
 theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero {a b c d p : P}
     (h : Cospherical ({a, b, c, d} : Set P)) (hab : a ≠ b) (hcd : c ≠ d) (hapb : ∠ a p b = 0)

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: Manuel Candales, Benjamin Davidson
 
 ! This file was ported from Lean 3 source module geometry.euclidean.sphere.power
-! leanprover-community/mathlib commit eea141bc9cf205beebfd46e2068c7c01ee8db4f6
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -28,7 +28,7 @@ open Real
 
 open EuclideanGeometry RealInnerProductSpace Real
 
-variable {V : Type _} [InnerProductSpace ℝ V]
+variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
 
 namespace InnerProductGeometry
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

@@ -3,45 +3,24 @@ Copyright (c) 2021 Manuel Candales. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Manuel Candales, Benjamin Davidson
 
-! This file was ported from Lean 3 source module geometry.euclidean.sphere
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
+! This file was ported from Lean 3 source module geometry.euclidean.sphere.power
+! leanprover-community/mathlib commit eea141bc9cf205beebfd46e2068c7c01ee8db4f6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Geometry.Euclidean.Basic
-import Mathbin.Geometry.Euclidean.Triangle
+import Mathbin.Geometry.Euclidean.Angle.Unoriented.Affine
+import Mathbin.Geometry.Euclidean.Sphere.Basic
 
 /-!
-# Spheres
+# Power of a point (intersecting chords and secants)
 
-This file proves basic geometrical results about distances and angles
-in spheres in real inner product spaces and Euclidean affine spaces.
+This file proves basic geometrical results about power of a point (intersecting chords and
+secants) in spheres in real inner product spaces and Euclidean affine spaces.
 
 ## Main theorems
 
 * `mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi`: Intersecting Chords Theorem (Freek No. 55).
 * `mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero`: Intersecting Secants Theorem.
-* `mul_dist_add_mul_dist_eq_mul_dist_of_cospherical`: Ptolemy’s Theorem (Freek No. 95).
-
-TODO: The current statement of Ptolemy’s theorem works around the lack of a "cyclic polygon" concept
-in mathlib, which is what the theorem statement would naturally use (or two such concepts, since
-both a strict version, where all vertices must be distinct, and a weak version, where consecutive
-vertices may be equal, would be useful; Ptolemy's theorem should then use the weak one).
-
-An API needs to be built around that concept, which would include:
-- strict cyclic implies weak cyclic,
-- weak cyclic and consecutive points distinct implies strict cyclic,
-- weak/strict cyclic implies weak/strict cyclic for any subsequence,
-- any three points on a sphere are weakly or strictly cyclic according to whether they are distinct,
-- any number of points on a sphere intersected with a two-dimensional affine subspace are cyclic in
-  some order,
-- a list of points is cyclic if and only if its reversal is,
-- a list of points is cyclic if and only if any cyclic permutation is, while other permutations
-  are not when the points are distinct,
-- a point P where the diagonals of a cyclic polygon cross exists (and is unique) with weak/strict
-  betweenness depending on weak/strict cyclicity,
-- four points on a sphere with such a point P are cyclic in the appropriate order,
-and so on.
 -/
 
 
@@ -162,30 +141,5 @@ theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero {a b c d p : P}
   exacts[hab (vsub_left_cancel hab₁).symm, hcd (vsub_left_cancel hcd₁).symm]
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero
 
-/-- **Ptolemy’s Theorem**. -/
-theorem mul_dist_add_mul_dist_eq_mul_dist_of_cospherical {a b c d p : P}
-    (h : Cospherical ({a, b, c, d} : Set P)) (hapc : ∠ a p c = π) (hbpd : ∠ b p d = π) :
-    dist a b * dist c d + dist b c * dist d a = dist a c * dist b d :=
-  by
-  have h' : cospherical ({a, c, b, d} : Set P) := by rwa [Set.insert_comm c b {d}]
-  have hmul := mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi h' hapc hbpd
-  have hbp := left_dist_ne_zero_of_angle_eq_pi hbpd
-  have h₁ : dist c d = dist c p / dist b p * dist a b :=
-    by
-    rw [dist_mul_of_eq_angle_of_dist_mul b p a c p d, dist_comm a b]
-    · rw [angle_eq_angle_of_angle_eq_pi_of_angle_eq_pi hbpd hapc, angle_comm]
-    all_goals field_simp [mul_comm, hmul]
-  have h₂ : dist d a = dist a p / dist b p * dist b c :=
-    by
-    rw [dist_mul_of_eq_angle_of_dist_mul c p b d p a, dist_comm c b]
-    · rwa [angle_comm, angle_eq_angle_of_angle_eq_pi_of_angle_eq_pi]
-      rwa [angle_comm]
-    all_goals field_simp [mul_comm, hmul]
-  have h₃ : dist d p = dist a p * dist c p / dist b p := by field_simp [mul_comm, hmul]
-  have h₄ : ∀ x y : ℝ, x * (y * x) = x * x * y := fun x y => by rw [mul_left_comm, mul_comm]
-  field_simp [h₁, h₂, dist_eq_add_dist_of_angle_eq_pi hbpd, h₃, hbp, dist_comm a b, h₄, ← sq,
-    dist_sq_mul_dist_add_dist_sq_mul_dist b, hapc]
-#align euclidean_geometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical
-
 end EuclideanGeometry
 

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -52,7 +52,7 @@ theorem mul_norm_eq_abs_sub_sq_norm {x y z : V} (h₁ : ∃ k : ℝ, k ≠ 1 ∧
   have hzy : ⟪z, y⟫ = 0 := by
     rwa [inner_eq_zero_iff_angle_eq_pi_div_two, ← norm_add_eq_norm_sub_iff_angle_eq_pi_div_two,
       eq_comm]
-  have hzx : ⟪z, x⟫ = 0 := by rw [hxy, inner_smul_right, hzy, MulZeroClass.mul_zero]
+  have hzx : ⟪z, x⟫ = 0 := by rw [hxy, inner_smul_right, hzy, mul_zero]
   calc
     ‖x - y‖ * ‖x + y‖ = ‖(r - 1) • y‖ * ‖(r + 1) • y‖ := by simp [sub_smul, add_smul, hxy]
     _ = ‖r - 1‖ * ‖y‖ * (‖r + 1‖ * ‖y‖) := by simp_rw [norm_smul]

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

This has nice performance benefits.

@@ -25,7 +25,7 @@ open Real
 
 open EuclideanGeometry RealInnerProductSpace Real
 
-variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
+variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
 
 namespace InnerProductGeometry
 
@@ -77,7 +77,7 @@ This section develops some results on spheres in Euclidean affine spaces.
 
 open InnerProductGeometry
 
-variable {P : Type _} [MetricSpace P] [NormedAddTorsor V P]
+variable {P : Type*} [MetricSpace P] [NormedAddTorsor V P]
 
 /-- If `P` is a point on the line `AB` and `Q` is equidistant from `A` and `B`, then
 `AP * BP = abs (BQ ^ 2 - PQ ^ 2)`. -/

• 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) 2021 Manuel Candales. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Manuel Candales, Benjamin Davidson
-
-! This file was ported from Lean 3 source module geometry.euclidean.sphere.power
-! 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.Unoriented.Affine
 import Mathlib.Geometry.Euclidean.Sphere.Basic
 
+#align_import geometry.euclidean.sphere.power from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-!
 # Power of a point (intersecting chords and secants)
 

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -129,7 +129,7 @@ theorem mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero {a b c d p : P}
   obtain ⟨-, k₂, -, hcd₁⟩ := angle_eq_zero_iff.mp hcpd
   refine' mul_dist_eq_mul_dist_of_cospherical h ⟨k₁, _, hab₁⟩ ⟨k₂, _, hcd₁⟩ <;> by_contra hnot <;>
     simp_all only [Classical.not_not, one_smul]
-  exacts[hab (vsub_left_cancel hab₁).symm, hcd (vsub_left_cancel hcd₁).symm]
+  exacts [hab (vsub_left_cancel hab₁).symm, hcd (vsub_left_cancel hcd₁).symm]
 #align euclidean_geometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero
 
 end EuclideanGeometry