geometry.euclidean.sphere.second_inter ⟷ Mathlib.Geometry.Euclidean.Sphere.SecondInter

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

@@ -122,8 +122,8 @@ theorem Sphere.secondInter_smul (s : Sphere P) (p : P) (v : V) {r : ℝ} (hr : r
   by
   simp_rw [sphere.second_inter, real_inner_smul_left, inner_smul_right, smul_smul,
     div_mul_eq_div_div]
-  rw [mul_comm, ← mul_div_assoc, ← mul_div_assoc, mul_div_cancel_left _ hr, mul_comm, mul_assoc,
-    mul_div_cancel_left _ hr, mul_comm]
+  rw [mul_comm, ← mul_div_assoc, ← mul_div_assoc, mul_div_cancel_left₀ _ hr, mul_comm, mul_assoc,
+    mul_div_cancel_left₀ _ hr, mul_comm]
 #align euclidean_geometry.sphere.second_inter_smul EuclideanGeometry.Sphere.secondInter_smul
 -/
 
@@ -145,7 +145,7 @@ theorem Sphere.secondInter_secondInter (s : Sphere P) (p : P) (v : V) :
   by_cases hv : v = 0; · simp [hv]
   have hv' : ⟪v, v⟫ ≠ 0 := inner_self_ne_zero.2 hv
   simp only [sphere.second_inter, vadd_vsub_assoc, vadd_vadd, inner_add_right, inner_smul_right,
-    div_mul_cancel _ hv']
+    div_mul_cancel₀ _ hv']
   rw [← @vsub_eq_zero_iff_eq V, vadd_vsub, ← add_smul, ← add_div]
   convert zero_smul ℝ _
   convert zero_div _

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

@@ -87,7 +87,7 @@ theorem Sphere.secondInter_eq_self_iff {s : Sphere P} {p : P} {v : V} :
   · by_cases hv : v = 0; · simp [hv]
     rwa [sphere.second_inter, eq_comm, eq_vadd_iff_vsub_eq, vsub_self, eq_comm, smul_eq_zero,
       or_iff_left hv, div_eq_zero_iff, inner_self_eq_zero, or_iff_left hv, mul_eq_zero,
-      or_iff_right (by norm_num : (-2 : ℝ) ≠ 0)] at hp 
+      or_iff_right (by norm_num : (-2 : ℝ) ≠ 0)] at hp
   · rw [sphere.second_inter, hp, MulZeroClass.mul_zero, zero_div, zero_smul, zero_vadd]
 #align euclidean_geometry.sphere.second_inter_eq_self_iff EuclideanGeometry.Sphere.secondInter_eq_self_iff
 -/
@@ -102,14 +102,14 @@ theorem Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem {s : Spher
   · rcases h with (h | h)
     · rwa [h]
     · rwa [h, sphere.second_inter_mem]
-  · rw [AffineSubspace.mem_mk'_iff_vsub_mem, Submodule.mem_span_singleton] at hp' 
+  · rw [AffineSubspace.mem_mk'_iff_vsub_mem, Submodule.mem_span_singleton] at hp'
     rcases hp' with ⟨r, hr⟩
-    rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr 
+    rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr
     subst hr
     by_cases hv : v = 0; · simp [hv]
     rw [sphere.second_inter]
-    rw [mem_sphere] at h hp 
-    rw [← hp, dist_smul_vadd_eq_dist _ _ hv] at h 
+    rw [mem_sphere] at h hp
+    rw [← hp, dist_smul_vadd_eq_dist _ _ hv] at h
     rcases h with (h | h) <;> simp [h]
 #align euclidean_geometry.sphere.eq_or_eq_second_inter_of_mem_mk'_span_singleton_iff_mem EuclideanGeometry.Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem
 -/
@@ -198,7 +198,7 @@ theorem Sphere.wbtw_secondInter {s : Sphere P} {p p' : P} (hp : p ∈ s)
       ((sphere.second_inter_mem _).2 hp) _
   intro he
   rw [eq_comm, sphere.second_inter_eq_self_iff, ← neg_neg (p' -ᵥ p), inner_neg_left,
-    neg_vsub_eq_vsub_rev, neg_eq_zero, eq_comm] at he 
+    neg_vsub_eq_vsub_rev, neg_eq_zero, eq_comm] at he
   exact ((inner_pos_or_eq_of_dist_le_radius hp hp').resolve_right (Ne.symm h)).Ne he
 #align euclidean_geometry.sphere.wbtw_second_inter EuclideanGeometry.Sphere.wbtw_secondInter
 -/
@@ -211,9 +211,9 @@ theorem Sphere.sbtw_secondInter {s : Sphere P} {p p' : P} (hp : p ∈ s)
     (hp' : dist p' s.center < s.radius) : Sbtw ℝ p p' (s.secondInter p (p' -ᵥ p)) :=
   by
   refine' ⟨sphere.wbtw_second_inter hp hp'.le, _, _⟩
-  · rintro rfl; rw [mem_sphere] at hp ; simpa [hp] using hp'
+  · rintro rfl; rw [mem_sphere] at hp; simpa [hp] using hp'
   · rintro h
-    rw [h, mem_sphere.1 ((sphere.second_inter_mem _).2 hp)] at hp' 
+    rw [h, mem_sphere.1 ((sphere.second_inter_mem _).2 hp)] at hp'
     exact lt_irrefl _ hp'
 #align euclidean_geometry.sphere.sbtw_second_inter EuclideanGeometry.Sphere.sbtw_secondInter
 -/

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

@@ -3,7 +3,7 @@ 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.Sphere.Basic
+import Geometry.Euclidean.Sphere.Basic
 
 #align_import geometry.euclidean.sphere.second_inter from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
 

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

@@ -2,14 +2,11 @@
 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.sphere.second_inter
-! 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.Sphere.Basic
 
+#align_import geometry.euclidean.sphere.second_inter from "leanprover-community/mathlib"@"f60c6087a7275b72d5db3c5a1d0e19e35a429c0a"
+
 /-!
 # Second intersection of a sphere and a line
 

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

@@ -36,8 +36,6 @@ namespace EuclideanGeometry
 variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
-include V
-
 #print EuclideanGeometry.Sphere.secondInter /-
 /-- The second intersection of a sphere with a line through a point on that sphere; that point
 if it is the only point of intersection of the line with the sphere. The intended use of this
@@ -72,14 +70,17 @@ theorem Sphere.secondInter_mem {s : Sphere P} {p : P} (v : V) : s.secondInter p
 
 variable (V)
 
+#print EuclideanGeometry.Sphere.secondInter_zero /-
 /-- If the vector is zero, `second_inter` gives the original point. -/
 @[simp]
 theorem Sphere.secondInter_zero (s : Sphere P) (p : P) : s.secondInter p (0 : V) = p := by
   simp [sphere.second_inter]
 #align euclidean_geometry.sphere.second_inter_zero EuclideanGeometry.Sphere.secondInter_zero
+-/
 
 variable {V}
 
+#print EuclideanGeometry.Sphere.secondInter_eq_self_iff /-
 /-- The point given by `second_inter` equals the original point if and only if the line is
 orthogonal to the radius vector. -/
 theorem Sphere.secondInter_eq_self_iff {s : Sphere P} {p : P} {v : V} :
@@ -92,6 +93,7 @@ theorem Sphere.secondInter_eq_self_iff {s : Sphere P} {p : P} {v : V} :
       or_iff_right (by norm_num : (-2 : ℝ) ≠ 0)] at hp 
   · rw [sphere.second_inter, hp, MulZeroClass.mul_zero, zero_div, zero_smul, zero_vadd]
 #align euclidean_geometry.sphere.second_inter_eq_self_iff EuclideanGeometry.Sphere.secondInter_eq_self_iff
+-/
 
 #print EuclideanGeometry.Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem /-
 /-- A point on a line through a point on a sphere equals that point or `second_inter`. -/
@@ -115,6 +117,7 @@ theorem Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem {s : Spher
 #align euclidean_geometry.sphere.eq_or_eq_second_inter_of_mem_mk'_span_singleton_iff_mem EuclideanGeometry.Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem
 -/
 
+#print EuclideanGeometry.Sphere.secondInter_smul /-
 /-- `second_inter` is unchanged by multiplying the vector by a nonzero real. -/
 @[simp]
 theorem Sphere.secondInter_smul (s : Sphere P) (p : P) (v : V) {r : ℝ} (hr : r ≠ 0) :
@@ -125,13 +128,16 @@ theorem Sphere.secondInter_smul (s : Sphere P) (p : P) (v : V) {r : ℝ} (hr : r
   rw [mul_comm, ← mul_div_assoc, ← mul_div_assoc, mul_div_cancel_left _ hr, mul_comm, mul_assoc,
     mul_div_cancel_left _ hr, mul_comm]
 #align euclidean_geometry.sphere.second_inter_smul EuclideanGeometry.Sphere.secondInter_smul
+-/
 
+#print EuclideanGeometry.Sphere.secondInter_neg /-
 /-- `second_inter` is unchanged by negating the vector. -/
 @[simp]
 theorem Sphere.secondInter_neg (s : Sphere P) (p : P) (v : V) :
     s.secondInter p (-v) = s.secondInter p v := by
   rw [← neg_one_smul ℝ v, s.second_inter_smul p v (by norm_num : (-1 : ℝ) ≠ 0)]
 #align euclidean_geometry.sphere.second_inter_neg EuclideanGeometry.Sphere.secondInter_neg
+-/
 
 #print EuclideanGeometry.Sphere.secondInter_secondInter /-
 /-- Applying `second_inter` twice returns the original point. -/
@@ -150,6 +156,7 @@ theorem Sphere.secondInter_secondInter (s : Sphere P) (p : P) (v : V) :
 #align euclidean_geometry.sphere.second_inter_second_inter EuclideanGeometry.Sphere.secondInter_secondInter
 -/
 
+#print EuclideanGeometry.Sphere.secondInter_eq_lineMap /-
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, the result of `second_inter` may be expressed using `line_map`. -/
 theorem Sphere.secondInter_eq_lineMap (s : Sphere P) (p p' : P) :
@@ -157,6 +164,7 @@ theorem Sphere.secondInter_eq_lineMap (s : Sphere P) (p p' : P) :
       AffineMap.lineMap p p' (-2 * ⟪p' -ᵥ p, p -ᵥ s.center⟫ / ⟪p' -ᵥ p, p' -ᵥ p⟫) :=
   rfl
 #align euclidean_geometry.sphere.second_inter_eq_line_map EuclideanGeometry.Sphere.secondInter_eq_lineMap
+-/
 
 #print EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan /-
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
@@ -180,6 +188,7 @@ theorem Sphere.secondInter_collinear (s : Sphere P) (p p' : P) :
 #align euclidean_geometry.sphere.second_inter_collinear EuclideanGeometry.Sphere.secondInter_collinear
 -/
 
+#print EuclideanGeometry.Sphere.wbtw_secondInter /-
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, and the second point is not outside the sphere, the second point is weakly
 between the first point and the result of `second_inter`. -/
@@ -195,7 +204,9 @@ theorem Sphere.wbtw_secondInter {s : Sphere P} {p p' : P} (hp : p ∈ s)
     neg_vsub_eq_vsub_rev, neg_eq_zero, eq_comm] at he 
   exact ((inner_pos_or_eq_of_dist_le_radius hp hp').resolve_right (Ne.symm h)).Ne he
 #align euclidean_geometry.sphere.wbtw_second_inter EuclideanGeometry.Sphere.wbtw_secondInter
+-/
 
+#print EuclideanGeometry.Sphere.sbtw_secondInter /-
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, and the second point is inside the sphere, the second point is strictly between
 the first point and the result of `second_inter`. -/
@@ -208,6 +219,7 @@ theorem Sphere.sbtw_secondInter {s : Sphere P} {p p' : P} (hp : p ∈ s)
     rw [h, mem_sphere.1 ((sphere.second_inter_mem _).2 hp)] at hp' 
     exact lt_irrefl _ hp'
 #align euclidean_geometry.sphere.sbtw_second_inter EuclideanGeometry.Sphere.sbtw_secondInter
+-/
 
 end EuclideanGeometry
 

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

@@ -89,7 +89,7 @@ theorem Sphere.secondInter_eq_self_iff {s : Sphere P} {p : P} {v : V} :
   · by_cases hv : v = 0; · simp [hv]
     rwa [sphere.second_inter, eq_comm, eq_vadd_iff_vsub_eq, vsub_self, eq_comm, smul_eq_zero,
       or_iff_left hv, div_eq_zero_iff, inner_self_eq_zero, or_iff_left hv, mul_eq_zero,
-      or_iff_right (by norm_num : (-2 : ℝ) ≠ 0)] at hp
+      or_iff_right (by norm_num : (-2 : ℝ) ≠ 0)] at hp 
   · rw [sphere.second_inter, hp, MulZeroClass.mul_zero, zero_div, zero_smul, zero_vadd]
 #align euclidean_geometry.sphere.second_inter_eq_self_iff EuclideanGeometry.Sphere.secondInter_eq_self_iff
 
@@ -103,14 +103,14 @@ theorem Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem {s : Spher
   · rcases h with (h | h)
     · rwa [h]
     · rwa [h, sphere.second_inter_mem]
-  · rw [AffineSubspace.mem_mk'_iff_vsub_mem, Submodule.mem_span_singleton] at hp'
+  · rw [AffineSubspace.mem_mk'_iff_vsub_mem, Submodule.mem_span_singleton] at hp' 
     rcases hp' with ⟨r, hr⟩
-    rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr
+    rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr 
     subst hr
     by_cases hv : v = 0; · simp [hv]
     rw [sphere.second_inter]
-    rw [mem_sphere] at h hp
-    rw [← hp, dist_smul_vadd_eq_dist _ _ hv] at h
+    rw [mem_sphere] at h hp 
+    rw [← hp, dist_smul_vadd_eq_dist _ _ hv] at h 
     rcases h with (h | h) <;> simp [h]
 #align euclidean_geometry.sphere.eq_or_eq_second_inter_of_mem_mk'_span_singleton_iff_mem EuclideanGeometry.Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem
 -/
@@ -192,7 +192,7 @@ theorem Sphere.wbtw_secondInter {s : Sphere P} {p p' : P} (hp : p ∈ s)
       ((sphere.second_inter_mem _).2 hp) _
   intro he
   rw [eq_comm, sphere.second_inter_eq_self_iff, ← neg_neg (p' -ᵥ p), inner_neg_left,
-    neg_vsub_eq_vsub_rev, neg_eq_zero, eq_comm] at he
+    neg_vsub_eq_vsub_rev, neg_eq_zero, eq_comm] at he 
   exact ((inner_pos_or_eq_of_dist_le_radius hp hp').resolve_right (Ne.symm h)).Ne he
 #align euclidean_geometry.sphere.wbtw_second_inter EuclideanGeometry.Sphere.wbtw_secondInter
 
@@ -203,9 +203,9 @@ theorem Sphere.sbtw_secondInter {s : Sphere P} {p p' : P} (hp : p ∈ s)
     (hp' : dist p' s.center < s.radius) : Sbtw ℝ p p' (s.secondInter p (p' -ᵥ p)) :=
   by
   refine' ⟨sphere.wbtw_second_inter hp hp'.le, _, _⟩
-  · rintro rfl; rw [mem_sphere] at hp; simpa [hp] using hp'
+  · rintro rfl; rw [mem_sphere] at hp ; simpa [hp] using hp'
   · rintro h
-    rw [h, mem_sphere.1 ((sphere.second_inter_mem _).2 hp)] at hp'
+    rw [h, mem_sphere.1 ((sphere.second_inter_mem _).2 hp)] at hp' 
     exact lt_irrefl _ hp'
 #align euclidean_geometry.sphere.sbtw_second_inter EuclideanGeometry.Sphere.sbtw_secondInter
 

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: Joseph Myers
 
 ! This file was ported from Lean 3 source module geometry.euclidean.sphere.second_inter
-! 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.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Geometry.Euclidean.Sphere.Basic
 /-!
 # Second intersection of a sphere and a line
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines and proves basic results about the second intersection of a sphere with a line
 through a point on that sphere.
 

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

@@ -26,7 +26,7 @@ through a point on that sphere.
 
 noncomputable section
 
-open RealInnerProductSpace
+open scoped RealInnerProductSpace
 
 namespace EuclideanGeometry
 

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

@@ -69,12 +69,6 @@ theorem Sphere.secondInter_mem {s : Sphere P} {p : P} (v : V) : s.secondInter p
 
 variable (V)
 
-/- warning: euclidean_geometry.sphere.second_inter_zero -> EuclideanGeometry.Sphere.secondInter_zero is a dubious translation:
-lean 3 declaration is
-  forall (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] (s : EuclideanGeometry.Sphere.{u2} P _inst_3) (p : P), Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (OfNat.ofNat.{u1} V 0 (OfNat.mk.{u1} V 0 (Zero.zero.{u1} V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (NormedAddGroup.toAddGroup.{u1} V (NormedAddCommGroup.toNormedAddGroup.{u1} V _inst_1)))))))))) p
-but is expected to have type
-  forall (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] (s : EuclideanGeometry.Sphere.{u2} P _inst_3) (p : P), Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (OfNat.ofNat.{u1} V 0 (Zero.toOfNat0.{u1} V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_1))))))))) p
-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_zero EuclideanGeometry.Sphere.secondInter_zeroₓ'. -/
 /-- If the vector is zero, `second_inter` gives the original point. -/
 @[simp]
 theorem Sphere.secondInter_zero (s : Sphere P) (p : P) : s.secondInter p (0 : V) = p := by
@@ -83,12 +77,6 @@ theorem Sphere.secondInter_zero (s : Sphere P) (p : P) : s.secondInter p (0 : V)
 
 variable {V}
 
-/- warning: euclidean_geometry.sphere.second_inter_eq_self_iff -> EuclideanGeometry.Sphere.secondInter_eq_self_iff is a dubious translation:
-lean 3 declaration is
-  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {v : V}, Iff (Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p v) p) (Eq.{1} Real (Inner.inner.{0, u1} Real V (InnerProductSpace.toHasInner.{0, u1} Real V Real.isROrC _inst_1 _inst_2) v (VSub.vsub.{u1, u2} V P (AddTorsor.toHasVsub.{u1, u2} V P (NormedAddGroup.toAddGroup.{u1} V (NormedAddCommGroup.toNormedAddGroup.{u1} V _inst_1)) (NormedAddTorsor.toAddTorsor'.{u1, u2} V P _inst_1 _inst_3 _inst_4)) p (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {v : V}, Iff (Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p v) p) (Eq.{1} Real (Inner.inner.{0, u1} Real V (InnerProductSpace.toInner.{0, u1} Real V Real.isROrC _inst_1 _inst_2) v (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (SeminormedAddGroup.toAddGroup.{u1} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} V (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1))) (NormedAddTorsor.toAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3) _inst_4)) p (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_eq_self_iff EuclideanGeometry.Sphere.secondInter_eq_self_iffₓ'. -/
 /-- The point given by `second_inter` equals the original point if and only if the line is
 orthogonal to the radius vector. -/
 theorem Sphere.secondInter_eq_self_iff {s : Sphere P} {p : P} {v : V} :
@@ -124,9 +112,6 @@ theorem Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem {s : Spher
 #align euclidean_geometry.sphere.eq_or_eq_second_inter_of_mem_mk'_span_singleton_iff_mem EuclideanGeometry.Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem
 -/
 
-/- warning: euclidean_geometry.sphere.second_inter_smul -> EuclideanGeometry.Sphere.secondInter_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_smul EuclideanGeometry.Sphere.secondInter_smulₓ'. -/
 /-- `second_inter` is unchanged by multiplying the vector by a nonzero real. -/
 @[simp]
 theorem Sphere.secondInter_smul (s : Sphere P) (p : P) (v : V) {r : ℝ} (hr : r ≠ 0) :
@@ -138,12 +123,6 @@ theorem Sphere.secondInter_smul (s : Sphere P) (p : P) (v : V) {r : ℝ} (hr : r
     mul_div_cancel_left _ hr, mul_comm]
 #align euclidean_geometry.sphere.second_inter_smul EuclideanGeometry.Sphere.secondInter_smul
 
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-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_neg EuclideanGeometry.Sphere.secondInter_negₓ'. -/
 /-- `second_inter` is unchanged by negating the vector. -/
 @[simp]
 theorem Sphere.secondInter_neg (s : Sphere P) (p : P) (v : V) :
@@ -168,12 +147,6 @@ theorem Sphere.secondInter_secondInter (s : Sphere P) (p : P) (v : V) :
 #align euclidean_geometry.sphere.second_inter_second_inter EuclideanGeometry.Sphere.secondInter_secondInter
 -/
 
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-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_eq_line_map EuclideanGeometry.Sphere.secondInter_eq_lineMapₓ'. -/
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, the result of `second_inter` may be expressed using `line_map`. -/
 theorem Sphere.secondInter_eq_lineMap (s : Sphere P) (p p' : P) :
@@ -204,12 +177,6 @@ theorem Sphere.secondInter_collinear (s : Sphere P) (p p' : P) :
 #align euclidean_geometry.sphere.second_inter_collinear EuclideanGeometry.Sphere.secondInter_collinear
 -/
 
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-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.wbtw_second_inter EuclideanGeometry.Sphere.wbtw_secondInterₓ'. -/
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, and the second point is not outside the sphere, the second point is weakly
 between the first point and the result of `second_inter`. -/
@@ -226,12 +193,6 @@ theorem Sphere.wbtw_secondInter {s : Sphere P} {p p' : P} (hp : p ∈ s)
   exact ((inner_pos_or_eq_of_dist_le_radius hp hp').resolve_right (Ne.symm h)).Ne he
 #align euclidean_geometry.sphere.wbtw_second_inter EuclideanGeometry.Sphere.wbtw_secondInter
 
-/- warning: euclidean_geometry.sphere.sbtw_second_inter -> EuclideanGeometry.Sphere.sbtw_secondInter is a dubious translation:
-lean 3 declaration is
-  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {p' : P}, (Membership.Mem.{u2, u2} P (EuclideanGeometry.Sphere.{u2} P _inst_3) (EuclideanGeometry.Sphere.hasMem.{u2} P _inst_3) p s) -> (LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) p' (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s)) (EuclideanGeometry.Sphere.radius.{u2} P _inst_3 s)) -> (Sbtw.{0, u1, u2} Real V P Real.orderedRing (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_1) (NormedSpace.toModule.{0, u1} Real V Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (InnerProductSpace.toNormedSpace.{0, u1} Real V Real.isROrC _inst_1 _inst_2)) (NormedAddTorsor.toAddTorsor'.{u1, u2} V P _inst_1 _inst_3 _inst_4) p p' (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (VSub.vsub.{u1, u2} V P (AddTorsor.toHasVsub.{u1, u2} V P (NormedAddGroup.toAddGroup.{u1} V (NormedAddCommGroup.toNormedAddGroup.{u1} V _inst_1)) (NormedAddTorsor.toAddTorsor'.{u1, u2} V P _inst_1 _inst_3 _inst_4)) p' p)))
-but is expected to have type
-  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {p' : P}, (Membership.mem.{u2, u2} P (EuclideanGeometry.Sphere.{u2} P _inst_3) (EuclideanGeometry.instMembershipSphere.{u2} P _inst_3) p s) -> (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) p' (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s)) (EuclideanGeometry.Sphere.radius.{u2} P _inst_3 s)) -> (Sbtw.{0, u1, u2} Real V P Real.orderedRing (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_1) (NormedSpace.toModule.{0, u1} Real V Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (InnerProductSpace.toNormedSpace.{0, u1} Real V Real.isROrC _inst_1 _inst_2)) (NormedAddTorsor.toAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3) _inst_4) p p' (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (SeminormedAddGroup.toAddGroup.{u1} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} V (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1))) (NormedAddTorsor.toAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3) _inst_4)) p' p)))
-Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.sbtw_second_inter EuclideanGeometry.Sphere.sbtw_secondInterₓ'. -/
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, and the second point is inside the sphere, the second point is strictly between
 the first point and the result of `second_inter`. -/

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

@@ -95,8 +95,7 @@ theorem Sphere.secondInter_eq_self_iff {s : Sphere P} {p : P} {v : V} :
     s.secondInter p v = p ↔ ⟪v, p -ᵥ s.center⟫ = 0 :=
   by
   refine' ⟨fun hp => _, fun hp => _⟩
-  · by_cases hv : v = 0
-    · simp [hv]
+  · by_cases hv : v = 0; · simp [hv]
     rwa [sphere.second_inter, eq_comm, eq_vadd_iff_vsub_eq, vsub_self, eq_comm, smul_eq_zero,
       or_iff_left hv, div_eq_zero_iff, inner_self_eq_zero, or_iff_left hv, mul_eq_zero,
       or_iff_right (by norm_num : (-2 : ℝ) ≠ 0)] at hp
@@ -117,8 +116,7 @@ theorem Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem {s : Spher
     rcases hp' with ⟨r, hr⟩
     rw [eq_comm, ← eq_vadd_iff_vsub_eq] at hr
     subst hr
-    by_cases hv : v = 0
-    · simp [hv]
+    by_cases hv : v = 0; · simp [hv]
     rw [sphere.second_inter]
     rw [mem_sphere] at h hp
     rw [← hp, dist_smul_vadd_eq_dist _ _ hv] at h
@@ -241,9 +239,7 @@ theorem Sphere.sbtw_secondInter {s : Sphere P} {p p' : P} (hp : p ∈ s)
     (hp' : dist p' s.center < s.radius) : Sbtw ℝ p p' (s.secondInter p (p' -ᵥ p)) :=
   by
   refine' ⟨sphere.wbtw_second_inter hp hp'.le, _, _⟩
-  · rintro rfl
-    rw [mem_sphere] at hp
-    simpa [hp] using hp'
+  · rintro rfl; rw [mem_sphere] at hp; simpa [hp] using hp'
   · rintro h
     rw [h, mem_sphere.1 ((sphere.second_inter_mem _).2 hp)] at hp'
     exact lt_irrefl _ hp'

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

@@ -35,6 +35,7 @@ variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ
 
 include V
 
+#print EuclideanGeometry.Sphere.secondInter /-
 /-- The second intersection of a sphere with a line through a point on that sphere; that point
 if it is the only point of intersection of the line with the sphere. The intended use of this
 definition is when `p ∈ s`; the definition does not use `s.radius`, so in general it returns
@@ -42,7 +43,9 @@ the second intersection with the sphere through `p` and with center `s.center`.
 def Sphere.secondInter (s : Sphere P) (p : P) (v : V) : P :=
   (-2 * ⟪v, p -ᵥ s.center⟫ / ⟪v, v⟫) • v +ᵥ p
 #align euclidean_geometry.sphere.second_inter EuclideanGeometry.Sphere.secondInter
+-/
 
+#print EuclideanGeometry.Sphere.secondInter_dist /-
 /-- The distance between `second_inter` and the center equals the distance between the original
 point and the center. -/
 @[simp]
@@ -54,15 +57,24 @@ theorem Sphere.secondInter_dist (s : Sphere P) (p : P) (v : V) :
   rw [dist_smul_vadd_eq_dist _ _ hv]
   exact Or.inr rfl
 #align euclidean_geometry.sphere.second_inter_dist EuclideanGeometry.Sphere.secondInter_dist
+-/
 
+#print EuclideanGeometry.Sphere.secondInter_mem /-
 /-- The point given by `second_inter` lies on the sphere. -/
 @[simp]
 theorem Sphere.secondInter_mem {s : Sphere P} {p : P} (v : V) : s.secondInter p v ∈ s ↔ p ∈ s := by
   simp_rw [mem_sphere, sphere.second_inter_dist]
 #align euclidean_geometry.sphere.second_inter_mem EuclideanGeometry.Sphere.secondInter_mem
+-/
 
 variable (V)
 
+/- warning: euclidean_geometry.sphere.second_inter_zero -> EuclideanGeometry.Sphere.secondInter_zero is a dubious translation:
+lean 3 declaration is
+  forall (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] (s : EuclideanGeometry.Sphere.{u2} P _inst_3) (p : P), Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (OfNat.ofNat.{u1} V 0 (OfNat.mk.{u1} V 0 (Zero.zero.{u1} V (AddZeroClass.toHasZero.{u1} V (AddMonoid.toAddZeroClass.{u1} V (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (NormedAddGroup.toAddGroup.{u1} V (NormedAddCommGroup.toNormedAddGroup.{u1} V _inst_1)))))))))) p
+but is expected to have type
+  forall (V : Type.{u1}) {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] (s : EuclideanGeometry.Sphere.{u2} P _inst_3) (p : P), Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (OfNat.ofNat.{u1} V 0 (Zero.toOfNat0.{u1} V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_1))))))))) p
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_zero EuclideanGeometry.Sphere.secondInter_zeroₓ'. -/
 /-- If the vector is zero, `second_inter` gives the original point. -/
 @[simp]
 theorem Sphere.secondInter_zero (s : Sphere P) (p : P) : s.secondInter p (0 : V) = p := by
@@ -71,6 +83,12 @@ theorem Sphere.secondInter_zero (s : Sphere P) (p : P) : s.secondInter p (0 : V)
 
 variable {V}
 
+/- warning: euclidean_geometry.sphere.second_inter_eq_self_iff -> EuclideanGeometry.Sphere.secondInter_eq_self_iff is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {v : V}, Iff (Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p v) p) (Eq.{1} Real (Inner.inner.{0, u1} Real V (InnerProductSpace.toHasInner.{0, u1} Real V Real.isROrC _inst_1 _inst_2) v (VSub.vsub.{u1, u2} V P (AddTorsor.toHasVsub.{u1, u2} V P (NormedAddGroup.toAddGroup.{u1} V (NormedAddCommGroup.toNormedAddGroup.{u1} V _inst_1)) (NormedAddTorsor.toAddTorsor'.{u1, u2} V P _inst_1 _inst_3 _inst_4)) p (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {v : V}, Iff (Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p v) p) (Eq.{1} Real (Inner.inner.{0, u1} Real V (InnerProductSpace.toInner.{0, u1} Real V Real.isROrC _inst_1 _inst_2) v (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (SeminormedAddGroup.toAddGroup.{u1} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} V (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1))) (NormedAddTorsor.toAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3) _inst_4)) p (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_eq_self_iff EuclideanGeometry.Sphere.secondInter_eq_self_iffₓ'. -/
 /-- The point given by `second_inter` equals the original point if and only if the line is
 orthogonal to the radius vector. -/
 theorem Sphere.secondInter_eq_self_iff {s : Sphere P} {p : P} {v : V} :
@@ -85,6 +103,7 @@ theorem Sphere.secondInter_eq_self_iff {s : Sphere P} {p : P} {v : V} :
   · rw [sphere.second_inter, hp, MulZeroClass.mul_zero, zero_div, zero_smul, zero_vadd]
 #align euclidean_geometry.sphere.second_inter_eq_self_iff EuclideanGeometry.Sphere.secondInter_eq_self_iff
 
+#print EuclideanGeometry.Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem /-
 /-- A point on a line through a point on a sphere equals that point or `second_inter`. -/
 theorem Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem {s : Sphere P} {p : P}
     (hp : p ∈ s) {v : V} {p' : P} (hp' : p' ∈ AffineSubspace.mk' p (ℝ ∙ v)) :
@@ -105,7 +124,11 @@ theorem Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem {s : Spher
     rw [← hp, dist_smul_vadd_eq_dist _ _ hv] at h
     rcases h with (h | h) <;> simp [h]
 #align euclidean_geometry.sphere.eq_or_eq_second_inter_of_mem_mk'_span_singleton_iff_mem EuclideanGeometry.Sphere.eq_or_eq_secondInter_of_mem_mk'_span_singleton_iff_mem
+-/
 
+/- warning: euclidean_geometry.sphere.second_inter_smul -> EuclideanGeometry.Sphere.secondInter_smul is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_smul EuclideanGeometry.Sphere.secondInter_smulₓ'. -/
 /-- `second_inter` is unchanged by multiplying the vector by a nonzero real. -/
 @[simp]
 theorem Sphere.secondInter_smul (s : Sphere P) (p : P) (v : V) {r : ℝ} (hr : r ≠ 0) :
@@ -117,6 +140,12 @@ theorem Sphere.secondInter_smul (s : Sphere P) (p : P) (v : V) {r : ℝ} (hr : r
     mul_div_cancel_left _ hr, mul_comm]
 #align euclidean_geometry.sphere.second_inter_smul EuclideanGeometry.Sphere.secondInter_smul
 
+/- warning: euclidean_geometry.sphere.second_inter_neg -> EuclideanGeometry.Sphere.secondInter_neg is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] (s : EuclideanGeometry.Sphere.{u2} P _inst_3) (p : P) (v : V), Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (Neg.neg.{u1} V (SubNegMonoid.toHasNeg.{u1} V (AddGroup.toSubNegMonoid.{u1} V (NormedAddGroup.toAddGroup.{u1} V (NormedAddCommGroup.toNormedAddGroup.{u1} V _inst_1)))) v)) (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p v)
+but is expected to have type
+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] (s : EuclideanGeometry.Sphere.{u2} P _inst_3) (p : P) (v : V), Eq.{succ u2} P (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (Neg.neg.{u1} V (NegZeroClass.toNeg.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_1)))))) v)) (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p v)
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_neg EuclideanGeometry.Sphere.secondInter_negₓ'. -/
 /-- `second_inter` is unchanged by negating the vector. -/
 @[simp]
 theorem Sphere.secondInter_neg (s : Sphere P) (p : P) (v : V) :
@@ -124,6 +153,7 @@ theorem Sphere.secondInter_neg (s : Sphere P) (p : P) (v : V) :
   rw [← neg_one_smul ℝ v, s.second_inter_smul p v (by norm_num : (-1 : ℝ) ≠ 0)]
 #align euclidean_geometry.sphere.second_inter_neg EuclideanGeometry.Sphere.secondInter_neg
 
+#print EuclideanGeometry.Sphere.secondInter_secondInter /-
 /-- Applying `second_inter` twice returns the original point. -/
 @[simp]
 theorem Sphere.secondInter_secondInter (s : Sphere P) (p : P) (v : V) :
@@ -138,7 +168,14 @@ theorem Sphere.secondInter_secondInter (s : Sphere P) (p : P) (v : V) :
   convert zero_div _
   ring
 #align euclidean_geometry.sphere.second_inter_second_inter EuclideanGeometry.Sphere.secondInter_secondInter
+-/
 
+/- warning: euclidean_geometry.sphere.second_inter_eq_line_map -> EuclideanGeometry.Sphere.secondInter_eq_lineMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3) _inst_4)) p' p))))
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.second_inter_eq_line_map EuclideanGeometry.Sphere.secondInter_eq_lineMapₓ'. -/
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, the result of `second_inter` may be expressed using `line_map`. -/
 theorem Sphere.secondInter_eq_lineMap (s : Sphere P) (p p' : P) :
@@ -147,13 +184,16 @@ theorem Sphere.secondInter_eq_lineMap (s : Sphere P) (p p' : P) :
   rfl
 #align euclidean_geometry.sphere.second_inter_eq_line_map EuclideanGeometry.Sphere.secondInter_eq_lineMap
 
+#print EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan /-
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, the result lies in the span of the two points. -/
 theorem Sphere.secondInter_vsub_mem_affineSpan (s : Sphere P) (p₁ p₂ : P) :
     s.secondInter p₁ (p₂ -ᵥ p₁) ∈ line[ℝ, p₁, p₂] :=
   smul_vsub_vadd_mem_affineSpan_pair _ _ _
 #align euclidean_geometry.sphere.second_inter_vsub_mem_affine_span EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan
+-/
 
+#print EuclideanGeometry.Sphere.secondInter_collinear /-
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, the three points are collinear. -/
 theorem Sphere.secondInter_collinear (s : Sphere P) (p p' : P) :
@@ -164,7 +204,14 @@ theorem Sphere.secondInter_collinear (s : Sphere P) (p p' : P) :
     (collinear_insert_iff_of_mem_affineSpan (s.second_inter_vsub_mem_affine_span _ _)).2
       (collinear_pair ℝ _ _)
 #align euclidean_geometry.sphere.second_inter_collinear EuclideanGeometry.Sphere.secondInter_collinear
+-/
 
+/- warning: euclidean_geometry.sphere.wbtw_second_inter -> EuclideanGeometry.Sphere.wbtw_secondInter is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {p' : P}, (Membership.Mem.{u2, u2} P (EuclideanGeometry.Sphere.{u2} P _inst_3) (EuclideanGeometry.Sphere.hasMem.{u2} P _inst_3) p s) -> (LE.le.{0} Real Real.hasLe (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) p' (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s)) (EuclideanGeometry.Sphere.radius.{u2} P _inst_3 s)) -> (Wbtw.{0, u1, u2} Real V P Real.orderedRing (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_1) (NormedSpace.toModule.{0, u1} Real V Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (InnerProductSpace.toNormedSpace.{0, u1} Real V Real.isROrC _inst_1 _inst_2)) (NormedAddTorsor.toAddTorsor'.{u1, u2} V P _inst_1 _inst_3 _inst_4) p p' (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (VSub.vsub.{u1, u2} V P (AddTorsor.toHasVsub.{u1, u2} V P (NormedAddGroup.toAddGroup.{u1} V (NormedAddCommGroup.toNormedAddGroup.{u1} V _inst_1)) (NormedAddTorsor.toAddTorsor'.{u1, u2} V P _inst_1 _inst_3 _inst_4)) p' p)))
+but is expected to have type
+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {p' : P}, (Membership.mem.{u2, u2} P (EuclideanGeometry.Sphere.{u2} P _inst_3) (EuclideanGeometry.instMembershipSphere.{u2} P _inst_3) p s) -> (LE.le.{0} Real Real.instLEReal (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) p' (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s)) (EuclideanGeometry.Sphere.radius.{u2} P _inst_3 s)) -> (Wbtw.{0, u1, u2} Real V P Real.orderedRing (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_1) (NormedSpace.toModule.{0, u1} Real V Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (InnerProductSpace.toNormedSpace.{0, u1} Real V Real.isROrC _inst_1 _inst_2)) (NormedAddTorsor.toAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3) _inst_4) p p' (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (SeminormedAddGroup.toAddGroup.{u1} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} V (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1))) (NormedAddTorsor.toAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3) _inst_4)) p' p)))
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.wbtw_second_inter EuclideanGeometry.Sphere.wbtw_secondInterₓ'. -/
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, and the second point is not outside the sphere, the second point is weakly
 between the first point and the result of `second_inter`. -/
@@ -181,6 +228,12 @@ theorem Sphere.wbtw_secondInter {s : Sphere P} {p p' : P} (hp : p ∈ s)
   exact ((inner_pos_or_eq_of_dist_le_radius hp hp').resolve_right (Ne.symm h)).Ne he
 #align euclidean_geometry.sphere.wbtw_second_inter EuclideanGeometry.Sphere.wbtw_secondInter
 
+/- warning: euclidean_geometry.sphere.sbtw_second_inter -> EuclideanGeometry.Sphere.sbtw_secondInter is a dubious translation:
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+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {p' : P}, (Membership.Mem.{u2, u2} P (EuclideanGeometry.Sphere.{u2} P _inst_3) (EuclideanGeometry.Sphere.hasMem.{u2} P _inst_3) p s) -> (LT.lt.{0} Real Real.hasLt (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) p' (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s)) (EuclideanGeometry.Sphere.radius.{u2} P _inst_3 s)) -> (Sbtw.{0, u1, u2} Real V P Real.orderedRing (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_1) (NormedSpace.toModule.{0, u1} Real V Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (InnerProductSpace.toNormedSpace.{0, u1} Real V Real.isROrC _inst_1 _inst_2)) (NormedAddTorsor.toAddTorsor'.{u1, u2} V P _inst_1 _inst_3 _inst_4) p p' (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (VSub.vsub.{u1, u2} V P (AddTorsor.toHasVsub.{u1, u2} V P (NormedAddGroup.toAddGroup.{u1} V (NormedAddCommGroup.toNormedAddGroup.{u1} V _inst_1)) (NormedAddTorsor.toAddTorsor'.{u1, u2} V P _inst_1 _inst_3 _inst_4)) p' p)))
+but is expected to have type
+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedAddCommGroup.{u1} V] [_inst_2 : InnerProductSpace.{0, u1} Real V Real.isROrC _inst_1] [_inst_3 : MetricSpace.{u2} P] [_inst_4 : NormedAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)] {s : EuclideanGeometry.Sphere.{u2} P _inst_3} {p : P} {p' : P}, (Membership.mem.{u2, u2} P (EuclideanGeometry.Sphere.{u2} P _inst_3) (EuclideanGeometry.instMembershipSphere.{u2} P _inst_3) p s) -> (LT.lt.{0} Real Real.instLTReal (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3)) p' (EuclideanGeometry.Sphere.center.{u2} P _inst_3 s)) (EuclideanGeometry.Sphere.radius.{u2} P _inst_3 s)) -> (Sbtw.{0, u1, u2} Real V P Real.orderedRing (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_1) (NormedSpace.toModule.{0, u1} Real V Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (InnerProductSpace.toNormedSpace.{0, u1} Real V Real.isROrC _inst_1 _inst_2)) (NormedAddTorsor.toAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3) _inst_4) p p' (EuclideanGeometry.Sphere.secondInter.{u1, u2} V P _inst_1 _inst_2 _inst_3 _inst_4 s p (VSub.vsub.{u1, u2} V P (AddTorsor.toVSub.{u1, u2} V P (SeminormedAddGroup.toAddGroup.{u1} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} V (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1))) (NormedAddTorsor.toAddTorsor.{u1, u2} V P (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_1) (MetricSpace.toPseudoMetricSpace.{u2} P _inst_3) _inst_4)) p' p)))
+Case conversion may be inaccurate. Consider using '#align euclidean_geometry.sphere.sbtw_second_inter EuclideanGeometry.Sphere.sbtw_secondInterₓ'. -/
 /-- If the vector passed to `second_inter` is given by a subtraction involving the point in
 `second_inter`, and the second point is inside the sphere, the second point is strictly between
 the first point and the result of `second_inter`. -/

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.sphere.second_inter
-! 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.
 -/
@@ -30,7 +30,8 @@ open RealInnerProductSpace
 
 namespace EuclideanGeometry
 
-variable {V : Type _} {P : Type _} [InnerProductSpace ℝ V] [MetricSpace P] [NormedAddTorsor V P]
+variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
+  [NormedAddTorsor V P]
 
 include V
 

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

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 | |

@@ -104,8 +104,8 @@ theorem Sphere.secondInter_smul (s : Sphere P) (p : P) (v : V) {r : ℝ} (hr : r
     s.secondInter p (r • v) = s.secondInter p v := by
   simp_rw [Sphere.secondInter, real_inner_smul_left, inner_smul_right, smul_smul,
     div_mul_eq_div_div]
-  rw [mul_comm, ← mul_div_assoc, ← mul_div_assoc, mul_div_cancel_left _ hr, mul_comm, mul_assoc,
-    mul_div_cancel_left _ hr, mul_comm]
+  rw [mul_comm, ← mul_div_assoc, ← mul_div_assoc, mul_div_cancel_left₀ _ hr, mul_comm, mul_assoc,
+    mul_div_cancel_left₀ _ hr, mul_comm]
 #align euclidean_geometry.sphere.second_inter_smul EuclideanGeometry.Sphere.secondInter_smul
 
 /-- `secondInter` is unchanged by negating the vector. -/
@@ -122,7 +122,7 @@ theorem Sphere.secondInter_secondInter (s : Sphere P) (p : P) (v : V) :
   by_cases hv : v = 0; · simp [hv]
   have hv' : ⟪v, v⟫ ≠ 0 := inner_self_ne_zero.2 hv
   simp only [Sphere.secondInter, vadd_vsub_assoc, vadd_vadd, inner_add_right, inner_smul_right,
-    div_mul_cancel _ hv']
+    div_mul_cancel₀ _ hv']
   rw [← @vsub_eq_zero_iff_eq V, vadd_vsub, ← add_smul, ← add_div]
   convert zero_smul ℝ (M := V) _
   convert zero_div (G₀ := ℝ) _

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).

@@ -75,7 +75,7 @@ theorem Sphere.secondInter_eq_self_iff {s : Sphere P} {p : P} {v : V} :
     rwa [Sphere.secondInter, eq_comm, eq_vadd_iff_vsub_eq, vsub_self, eq_comm, smul_eq_zero,
       or_iff_left hv, div_eq_zero_iff, inner_self_eq_zero, or_iff_left hv, mul_eq_zero,
       or_iff_right (by norm_num : (-2 : ℝ) ≠ 0)] at hp
-  · rw [Sphere.secondInter, hp, MulZeroClass.mul_zero, zero_div, zero_smul, zero_vadd]
+  · rw [Sphere.secondInter, hp, mul_zero, zero_div, zero_smul, zero_vadd]
 #align euclidean_geometry.sphere.second_inter_eq_self_iff EuclideanGeometry.Sphere.secondInter_eq_self_iff
 
 /-- A point on a line through a point on a sphere equals that point or `secondInter`. -/

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

This has nice performance benefits.

@@ -27,7 +27,7 @@ open RealInnerProductSpace
 
 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]
 
 /-- The second intersection of a sphere with a line through a point on that sphere; that point

• depends on: #5966

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

@@ -2,14 +2,11 @@
 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.sphere.second_inter
-! 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.Sphere.Basic
 
+#align_import geometry.euclidean.sphere.second_inter from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-!
 # Second intersection of a sphere and a line
 

Co-authored-by: Chris Hughes <chrishughes24@gmail.com>