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

@@ -504,7 +504,7 @@ theorem angle_eq_arcsin_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
     inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0
+  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arcsin_of_inner_eq_zero h h0]
 #align euclidean_geometry.angle_eq_arcsin_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two
@@ -530,7 +530,7 @@ theorem angle_pos_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
     inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [← @vsub_ne_zero V, eq_comm, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+  rw [← @vsub_ne_zero V, eq_comm, ← @vsub_eq_zero_iff_eq V, or_comm] at h0
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_pos_of_inner_eq_zero h h0
 #align euclidean_geometry.angle_pos_of_angle_eq_pi_div_two EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two
@@ -580,7 +580,7 @@ theorem sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
     inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0
+  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, sin_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.sin_angle_of_angle_eq_pi_div_two EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two
@@ -632,7 +632,7 @@ theorem tan_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
     inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, tan_angle_add_mul_norm_of_inner_eq_zero h h0]
 #align euclidean_geometry.tan_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two
@@ -646,7 +646,7 @@ theorem dist_div_cos_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
     inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm] at h0
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_cos_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_cos_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two
@@ -660,7 +660,7 @@ theorem dist_div_sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
     inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_sin_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_sin_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two
@@ -674,7 +674,7 @@ theorem dist_div_tan_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
     inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_tan_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_tan_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two

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

@@ -110,7 +110,7 @@ theorem angle_add_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
   rw [angle_add_eq_arccos_of_inner_eq_zero h,
     Real.arccos_eq_arcsin (div_nonneg (norm_nonneg _) (norm_nonneg _)), div_pow, one_sub_div hxy]
   nth_rw 1 [pow_two]
-  rw [norm_add_sq_eq_norm_sq_add_norm_sq_real h, pow_two, add_sub_cancel', ← pow_two, ← div_pow,
+  rw [norm_add_sq_eq_norm_sq_add_norm_sq_real h, pow_two, add_sub_cancel_left, ← pow_two, ← div_pow,
     Real.sqrt_sq (div_nonneg (norm_nonneg _) (norm_nonneg _))]
 #align inner_product_geometry.angle_add_eq_arcsin_of_inner_eq_zero InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zero
 -/
@@ -220,7 +220,7 @@ theorem cos_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     rw [hxy, MulZeroClass.zero_mul, eq_comm,
       add_eq_zero_iff' (hMul_self_nonneg ‖x‖) (hMul_self_nonneg ‖y‖), mul_self_eq_zero] at h'
     simp [h'.1]
-  · exact div_mul_cancel _ hxy
+  · exact div_mul_cancel₀ _ hxy
 #align inner_product_geometry.cos_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero
 -/
 
@@ -232,7 +232,7 @@ theorem sin_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   by
   by_cases h0 : x = 0 ∧ y = 0; · simp [h0]
   rw [not_and_or] at h0
-  rw [sin_angle_add_of_inner_eq_zero h h0, div_mul_cancel]
+  rw [sin_angle_add_of_inner_eq_zero h h0, div_mul_cancel₀]
   rw [← mul_self_ne_zero, norm_add_sq_eq_norm_sq_add_norm_sq_real h]
   refine' (ne_of_lt _).symm
   rcases h0 with (h0 | h0)

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

@@ -218,7 +218,7 @@ theorem cos_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   by_cases hxy : ‖x + y‖ = 0
   · have h' := norm_add_sq_eq_norm_sq_add_norm_sq_real h
     rw [hxy, MulZeroClass.zero_mul, eq_comm,
-      add_eq_zero_iff' (hMul_self_nonneg ‖x‖) (hMul_self_nonneg ‖y‖), mul_self_eq_zero] at h' 
+      add_eq_zero_iff' (hMul_self_nonneg ‖x‖) (hMul_self_nonneg ‖y‖), mul_self_eq_zero] at h'
     simp [h'.1]
   · exact div_mul_cancel _ hxy
 #align inner_product_geometry.cos_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero
@@ -231,7 +231,7 @@ theorem sin_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.sin (angle x (x + y)) * ‖x + y‖ = ‖y‖ :=
   by
   by_cases h0 : x = 0 ∧ y = 0; · simp [h0]
-  rw [not_and_or] at h0 
+  rw [not_and_or] at h0
   rw [sin_angle_add_of_inner_eq_zero h h0, div_mul_cancel]
   rw [← mul_self_ne_zero, norm_add_sq_eq_norm_sq_add_norm_sq_real h]
   refine' (ne_of_lt _).symm
@@ -299,7 +299,7 @@ theorem norm_div_tan_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
 theorem angle_sub_eq_arccos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     angle x (x - y) = Real.arccos (‖x‖ / ‖x - y‖) :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
   rw [sub_eq_add_neg, angle_add_eq_arccos_of_inner_eq_zero h]
 #align inner_product_geometry.angle_sub_eq_arccos_of_inner_eq_zero InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero
 -/
@@ -309,8 +309,8 @@ theorem angle_sub_eq_arccos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
 theorem angle_sub_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y ≠ 0) :
     angle x (x - y) = Real.arcsin (‖y‖ / ‖x - y‖) :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
-  nth_rw 2 [← neg_ne_zero] at h0 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
+  nth_rw 2 [← neg_ne_zero] at h0
   rw [sub_eq_add_neg, angle_add_eq_arcsin_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.angle_sub_eq_arcsin_of_inner_eq_zero InnerProductGeometry.angle_sub_eq_arcsin_of_inner_eq_zero
 -/
@@ -320,7 +320,7 @@ theorem angle_sub_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
 theorem angle_sub_eq_arctan_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0) :
     angle x (x - y) = Real.arctan (‖y‖ / ‖x‖) :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
   rw [sub_eq_add_neg, angle_add_eq_arctan_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.angle_sub_eq_arctan_of_inner_eq_zero InnerProductGeometry.angle_sub_eq_arctan_of_inner_eq_zero
 -/
@@ -330,8 +330,8 @@ theorem angle_sub_eq_arctan_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
 vectors. -/
 theorem angle_sub_pos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
     0 < angle x (x - y) := by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
-  rw [← neg_ne_zero] at h0 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_ne_zero] at h0
   rw [sub_eq_add_neg]
   exact angle_add_pos_of_inner_eq_zero h h0
 #align inner_product_geometry.angle_sub_pos_of_inner_eq_zero InnerProductGeometry.angle_sub_pos_of_inner_eq_zero
@@ -342,7 +342,7 @@ theorem angle_sub_pos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x =
 theorem angle_sub_le_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     angle x (x - y) ≤ π / 2 :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
   rw [sub_eq_add_neg]
   exact angle_add_le_pi_div_two_of_inner_eq_zero h
 #align inner_product_geometry.angle_sub_le_pi_div_two_of_inner_eq_zero InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero
@@ -354,7 +354,7 @@ vectors. -/
 theorem angle_sub_lt_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0) :
     angle x (x - y) < π / 2 :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
   rw [sub_eq_add_neg]
   exact angle_add_lt_pi_div_two_of_inner_eq_zero h h0
 #align inner_product_geometry.angle_sub_lt_pi_div_two_of_inner_eq_zero InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero
@@ -366,7 +366,7 @@ vectors. -/
 theorem cos_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.cos (angle x (x - y)) = ‖x‖ / ‖x - y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
   rw [sub_eq_add_neg, cos_angle_add_of_inner_eq_zero h]
 #align inner_product_geometry.cos_angle_sub_of_inner_eq_zero InnerProductGeometry.cos_angle_sub_of_inner_eq_zero
 -/
@@ -377,8 +377,8 @@ vectors. -/
 theorem sin_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y ≠ 0) :
     Real.sin (angle x (x - y)) = ‖y‖ / ‖x - y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
-  nth_rw 2 [← neg_ne_zero] at h0 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
+  nth_rw 2 [← neg_ne_zero] at h0
   rw [sub_eq_add_neg, sin_angle_add_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.sin_angle_sub_of_inner_eq_zero InnerProductGeometry.sin_angle_sub_of_inner_eq_zero
 -/
@@ -389,7 +389,7 @@ vectors. -/
 theorem tan_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.tan (angle x (x - y)) = ‖y‖ / ‖x‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
   rw [sub_eq_add_neg, tan_angle_add_of_inner_eq_zero h, norm_neg]
 #align inner_product_geometry.tan_angle_sub_of_inner_eq_zero InnerProductGeometry.tan_angle_sub_of_inner_eq_zero
 -/
@@ -400,7 +400,7 @@ adjacent side, version subtracting vectors. -/
 theorem cos_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.cos (angle x (x - y)) * ‖x - y‖ = ‖x‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
   rw [sub_eq_add_neg, cos_angle_add_mul_norm_of_inner_eq_zero h]
 #align inner_product_geometry.cos_angle_sub_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_sub_mul_norm_of_inner_eq_zero
 -/
@@ -411,7 +411,7 @@ opposite side, version subtracting vectors. -/
 theorem sin_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.sin (angle x (x - y)) * ‖x - y‖ = ‖y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
   rw [sub_eq_add_neg, sin_angle_add_mul_norm_of_inner_eq_zero h, norm_neg]
 #align inner_product_geometry.sin_angle_sub_mul_norm_of_inner_eq_zero InnerProductGeometry.sin_angle_sub_mul_norm_of_inner_eq_zero
 -/
@@ -422,8 +422,8 @@ the opposite side, version subtracting vectors. -/
 theorem tan_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y = 0) :
     Real.tan (angle x (x - y)) * ‖x‖ = ‖y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
-  rw [← neg_eq_zero] at h0 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero] at h0
   rw [sub_eq_add_neg, tan_angle_add_mul_norm_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.tan_angle_sub_mul_norm_of_inner_eq_zero InnerProductGeometry.tan_angle_sub_mul_norm_of_inner_eq_zero
 -/
@@ -434,8 +434,8 @@ hypotenuse, version subtracting vectors. -/
 theorem norm_div_cos_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y = 0) :
     ‖x‖ / Real.cos (angle x (x - y)) = ‖x - y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
-  rw [← neg_eq_zero] at h0 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero] at h0
   rw [sub_eq_add_neg, norm_div_cos_angle_add_of_inner_eq_zero h h0]
 #align inner_product_geometry.norm_div_cos_angle_sub_of_inner_eq_zero InnerProductGeometry.norm_div_cos_angle_sub_of_inner_eq_zero
 -/
@@ -446,8 +446,8 @@ hypotenuse, version subtracting vectors. -/
 theorem norm_div_sin_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
     ‖y‖ / Real.sin (angle x (x - y)) = ‖x - y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
-  rw [← neg_ne_zero] at h0 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_ne_zero] at h0
   rw [sub_eq_add_neg, ← norm_neg, norm_div_sin_angle_add_of_inner_eq_zero h h0]
 #align inner_product_geometry.norm_div_sin_angle_sub_of_inner_eq_zero InnerProductGeometry.norm_div_sin_angle_sub_of_inner_eq_zero
 -/
@@ -458,8 +458,8 @@ adjacent side, version subtracting vectors. -/
 theorem norm_div_tan_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
     ‖y‖ / Real.tan (angle x (x - y)) = ‖x‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h 
-  rw [← neg_ne_zero] at h0 
+  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_ne_zero] at h0
   rw [sub_eq_add_neg, ← norm_neg, norm_div_tan_angle_add_of_inner_eq_zero h h0]
 #align inner_product_geometry.norm_div_tan_angle_sub_of_inner_eq_zero InnerProductGeometry.norm_div_tan_angle_sub_of_inner_eq_zero
 -/
@@ -491,7 +491,7 @@ theorem angle_eq_arccos_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
     ∠ p₂ p₃ p₁ = Real.arccos (dist p₃ p₂ / dist p₁ p₃) :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arccos_of_inner_eq_zero h]
 #align euclidean_geometry.angle_eq_arccos_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arccos_of_angle_eq_pi_div_two
@@ -503,8 +503,8 @@ theorem angle_eq_arcsin_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
     (h0 : p₁ ≠ p₂ ∨ p₃ ≠ p₂) : ∠ p₂ p₃ p₁ = Real.arcsin (dist p₁ p₂ / dist p₁ p₃) :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
-  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arcsin_of_inner_eq_zero h h0]
 #align euclidean_geometry.angle_eq_arcsin_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two
@@ -516,8 +516,8 @@ theorem angle_eq_arctan_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
     (h0 : p₃ ≠ p₂) : ∠ p₂ p₃ p₁ = Real.arctan (dist p₁ p₂ / dist p₃ p₂) :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
-  rw [ne_comm, ← @vsub_ne_zero V] at h0 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+  rw [ne_comm, ← @vsub_ne_zero V] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arctan_of_inner_eq_zero h h0]
 #align euclidean_geometry.angle_eq_arctan_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_two
@@ -529,8 +529,8 @@ theorem angle_pos_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
     (h0 : p₁ ≠ p₂ ∨ p₃ = p₂) : 0 < ∠ p₂ p₃ p₁ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
-  rw [← @vsub_ne_zero V, eq_comm, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+  rw [← @vsub_ne_zero V, eq_comm, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_pos_of_inner_eq_zero h h0
 #align euclidean_geometry.angle_pos_of_angle_eq_pi_div_two EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two
@@ -542,7 +542,7 @@ theorem angle_le_pi_div_two_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     ∠ p₂ p₃ p₁ ≤ π / 2 :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_le_pi_div_two_of_inner_eq_zero h
 #align euclidean_geometry.angle_le_pi_div_two_of_angle_eq_pi_div_two EuclideanGeometry.angle_le_pi_div_two_of_angle_eq_pi_div_two
@@ -554,8 +554,8 @@ theorem angle_lt_pi_div_two_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₃ ≠ p₂) : ∠ p₂ p₃ p₁ < π / 2 :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
-  rw [ne_comm, ← @vsub_ne_zero V] at h0 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+  rw [ne_comm, ← @vsub_ne_zero V] at h0
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_lt_pi_div_two_of_inner_eq_zero h h0
 #align euclidean_geometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two
@@ -567,7 +567,7 @@ theorem cos_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
     Real.cos (∠ p₂ p₃ p₁) = dist p₃ p₂ / dist p₁ p₃ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, cos_angle_add_of_inner_eq_zero h]
 #align euclidean_geometry.cos_angle_of_angle_eq_pi_div_two EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two
@@ -579,8 +579,8 @@ theorem sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
     (h0 : p₁ ≠ p₂ ∨ p₃ ≠ p₂) : Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₁ p₃ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
-  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, sin_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.sin_angle_of_angle_eq_pi_div_two EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two
@@ -592,7 +592,7 @@ theorem tan_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
     Real.tan (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₃ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, tan_angle_add_of_inner_eq_zero h]
 #align euclidean_geometry.tan_angle_of_angle_eq_pi_div_two EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two
@@ -605,7 +605,7 @@ theorem cos_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     Real.cos (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₃ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, cos_angle_add_mul_norm_of_inner_eq_zero h]
 #align euclidean_geometry.cos_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two
@@ -618,7 +618,7 @@ theorem sin_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     Real.sin (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₁ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, sin_angle_add_mul_norm_of_inner_eq_zero h]
 #align euclidean_geometry.sin_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two
@@ -631,8 +631,8 @@ theorem tan_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₁ = p₂ ∨ p₃ ≠ p₂) : Real.tan (∠ p₂ p₃ p₁) * dist p₃ p₂ = dist p₁ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
-  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, tan_angle_add_mul_norm_of_inner_eq_zero h h0]
 #align euclidean_geometry.tan_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two
@@ -645,8 +645,8 @@ theorem dist_div_cos_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₁ = p₂ ∨ p₃ ≠ p₂) : dist p₃ p₂ / Real.cos (∠ p₂ p₃ p₁) = dist p₁ p₃ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
-  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_cos_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_cos_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two
@@ -659,8 +659,8 @@ theorem dist_div_sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₁ ≠ p₂ ∨ p₃ = p₂) : dist p₁ p₂ / Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₃ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
-  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_sin_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_sin_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two
@@ -673,8 +673,8 @@ theorem dist_div_tan_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₁ ≠ p₂ ∨ p₃ = p₂) : dist p₁ p₂ / Real.tan (∠ p₂ p₃ p₁) = dist p₃ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
-  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_tan_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_tan_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two

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

@@ -103,10 +103,10 @@ theorem angle_add_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
     rcases h0 with (h0 | h0)
     ·
       exact
-        Left.add_pos_of_pos_of_nonneg (mul_self_pos.2 (norm_ne_zero_iff.2 h0)) (mul_self_nonneg _)
+        Left.add_pos_of_pos_of_nonneg (mul_self_pos.2 (norm_ne_zero_iff.2 h0)) (hMul_self_nonneg _)
     ·
       exact
-        Left.add_pos_of_nonneg_of_pos (mul_self_nonneg _) (mul_self_pos.2 (norm_ne_zero_iff.2 h0))
+        Left.add_pos_of_nonneg_of_pos (hMul_self_nonneg _) (mul_self_pos.2 (norm_ne_zero_iff.2 h0))
   rw [angle_add_eq_arccos_of_inner_eq_zero h,
     Real.arccos_eq_arcsin (div_nonneg (norm_nonneg _) (norm_nonneg _)), div_pow, one_sub_div hxy]
   nth_rw 1 [pow_two]
@@ -139,7 +139,7 @@ theorem angle_add_pos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x =
   rw [div_lt_one
       (Real.sqrt_pos.2
         (Left.add_pos_of_pos_of_nonneg (mul_self_pos.2 (norm_ne_zero_iff.2 hx))
-          (mul_self_nonneg _))),
+          (hMul_self_nonneg _))),
     Real.lt_sqrt (norm_nonneg _), pow_two]
   simpa [hx] using h0
 #align inner_product_geometry.angle_add_pos_of_inner_eq_zero InnerProductGeometry.angle_add_pos_of_inner_eq_zero
@@ -166,7 +166,7 @@ theorem angle_add_lt_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0)
     div_pos (norm_pos_iff.2 h0)
       (Real.sqrt_pos.2
         (Left.add_pos_of_pos_of_nonneg (mul_self_pos.2 (norm_ne_zero_iff.2 h0))
-          (mul_self_nonneg _)))
+          (hMul_self_nonneg _)))
 #align inner_product_geometry.angle_add_lt_pi_div_two_of_inner_eq_zero InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero
 -/
 
@@ -180,7 +180,7 @@ theorem cos_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
       (div_le_one_of_le _ (norm_nonneg _))]
   rw [mul_self_le_mul_self_iff (norm_nonneg _) (norm_nonneg _),
     norm_add_sq_eq_norm_sq_add_norm_sq_real h]
-  exact le_add_of_nonneg_right (mul_self_nonneg _)
+  exact le_add_of_nonneg_right (hMul_self_nonneg _)
 #align inner_product_geometry.cos_angle_add_of_inner_eq_zero InnerProductGeometry.cos_angle_add_of_inner_eq_zero
 -/
 
@@ -194,7 +194,7 @@ theorem sin_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x 
       (div_le_one_of_le _ (norm_nonneg _))]
   rw [mul_self_le_mul_self_iff (norm_nonneg _) (norm_nonneg _),
     norm_add_sq_eq_norm_sq_add_norm_sq_real h]
-  exact le_add_of_nonneg_left (mul_self_nonneg _)
+  exact le_add_of_nonneg_left (hMul_self_nonneg _)
 #align inner_product_geometry.sin_angle_add_of_inner_eq_zero InnerProductGeometry.sin_angle_add_of_inner_eq_zero
 -/
 
@@ -218,7 +218,7 @@ theorem cos_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   by_cases hxy : ‖x + y‖ = 0
   · have h' := norm_add_sq_eq_norm_sq_add_norm_sq_real h
     rw [hxy, MulZeroClass.zero_mul, eq_comm,
-      add_eq_zero_iff' (mul_self_nonneg ‖x‖) (mul_self_nonneg ‖y‖), mul_self_eq_zero] at h' 
+      add_eq_zero_iff' (hMul_self_nonneg ‖x‖) (hMul_self_nonneg ‖y‖), mul_self_eq_zero] at h' 
     simp [h'.1]
   · exact div_mul_cancel _ hxy
 #align inner_product_geometry.cos_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero
@@ -236,8 +236,12 @@ theorem sin_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   rw [← mul_self_ne_zero, norm_add_sq_eq_norm_sq_add_norm_sq_real h]
   refine' (ne_of_lt _).symm
   rcases h0 with (h0 | h0)
-  · exact Left.add_pos_of_pos_of_nonneg (mul_self_pos.2 (norm_ne_zero_iff.2 h0)) (mul_self_nonneg _)
-  · exact Left.add_pos_of_nonneg_of_pos (mul_self_nonneg _) (mul_self_pos.2 (norm_ne_zero_iff.2 h0))
+  ·
+    exact
+      Left.add_pos_of_pos_of_nonneg (mul_self_pos.2 (norm_ne_zero_iff.2 h0)) (hMul_self_nonneg _)
+  ·
+    exact
+      Left.add_pos_of_nonneg_of_pos (hMul_self_nonneg _) (mul_self_pos.2 (norm_ne_zero_iff.2 h0))
 #align inner_product_geometry.sin_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zero
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 -/
-import Mathbin.Analysis.SpecialFunctions.Trigonometric.Arctan
-import Mathbin.Geometry.Euclidean.Angle.Unoriented.Affine
+import Analysis.SpecialFunctions.Trigonometric.Arctan
+import Geometry.Euclidean.Angle.Unoriented.Affine
 
 #align_import geometry.euclidean.angle.unoriented.right_angle from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module geometry.euclidean.angle.unoriented.right_angle
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Trigonometric.Arctan
 import Mathbin.Geometry.Euclidean.Angle.Unoriented.Affine
 
+#align_import geometry.euclidean.angle.unoriented.right_angle from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # Right-angled triangles
 

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

@@ -47,6 +47,7 @@ namespace InnerProductGeometry
 
 variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
 
+#print InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two /-
 /-- Pythagorean theorem, if-and-only-if vector angle form. -/
 theorem norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two (x y : V) :
     ‖x + y‖ * ‖x + y‖ = ‖x‖ * ‖x‖ + ‖y‖ * ‖y‖ ↔ angle x y = π / 2 :=
@@ -54,13 +55,17 @@ theorem norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two (x y : V) :
   rw [norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero]
   exact inner_eq_zero_iff_angle_eq_pi_div_two x y
 #align inner_product_geometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two
+-/
 
+#print InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq' /-
 /-- Pythagorean theorem, vector angle form. -/
 theorem norm_add_sq_eq_norm_sq_add_norm_sq' (x y : V) (h : angle x y = π / 2) :
     ‖x + y‖ * ‖x + y‖ = ‖x‖ * ‖x‖ + ‖y‖ * ‖y‖ :=
   (norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two x y).2 h
 #align inner_product_geometry.norm_add_sq_eq_norm_sq_add_norm_sq' InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq'
+-/
 
+#print InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two /-
 /-- Pythagorean theorem, subtracting vectors, if-and-only-if vector angle form. -/
 theorem norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two (x y : V) :
     ‖x - y‖ * ‖x - y‖ = ‖x‖ * ‖x‖ + ‖y‖ * ‖y‖ ↔ angle x y = π / 2 :=
@@ -68,13 +73,17 @@ theorem norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two (x y : V) :
   rw [norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero]
   exact inner_eq_zero_iff_angle_eq_pi_div_two x y
 #align inner_product_geometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two
+-/
 
+#print InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq' /-
 /-- Pythagorean theorem, subtracting vectors, vector angle form. -/
 theorem norm_sub_sq_eq_norm_sq_add_norm_sq' (x y : V) (h : angle x y = π / 2) :
     ‖x - y‖ * ‖x - y‖ = ‖x‖ * ‖x‖ + ‖y‖ * ‖y‖ :=
   (norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two x y).2 h
 #align inner_product_geometry.norm_sub_sq_eq_norm_sq_add_norm_sq' InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq'
+-/
 
+#print InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zero /-
 /-- An angle in a right-angled triangle expressed using `arccos`. -/
 theorem angle_add_eq_arccos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     angle x (x + y) = Real.arccos (‖x‖ / ‖x + y‖) :=
@@ -83,7 +92,9 @@ theorem angle_add_eq_arccos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   by_cases hx : ‖x‖ = 0; · simp [hx]
   rw [div_mul_eq_div_div, mul_self_div_self]
 #align inner_product_geometry.angle_add_eq_arccos_of_inner_eq_zero InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zero /-
 /-- An angle in a right-angled triangle expressed using `arcsin`. -/
 theorem angle_add_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y ≠ 0) :
     angle x (x + y) = Real.arcsin (‖y‖ / ‖x + y‖) :=
@@ -105,7 +116,9 @@ theorem angle_add_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
   rw [norm_add_sq_eq_norm_sq_add_norm_sq_real h, pow_two, add_sub_cancel', ← pow_two, ← div_pow,
     Real.sqrt_sq (div_nonneg (norm_nonneg _) (norm_nonneg _))]
 #align inner_product_geometry.angle_add_eq_arcsin_of_inner_eq_zero InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zero /-
 /-- An angle in a right-angled triangle expressed using `arctan`. -/
 theorem angle_add_eq_arctan_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0) :
     angle x (x + y) = Real.arctan (‖y‖ / ‖x‖) :=
@@ -116,7 +129,9 @@ theorem angle_add_eq_arctan_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
   rw [← Real.sqrt_mul (sq_nonneg _), div_pow, pow_two, pow_two, mul_add, mul_one, mul_div,
     mul_comm (‖x‖ * ‖x‖), ← mul_div, div_self (mul_self_pos.2 (norm_ne_zero_iff.2 h0)).ne', mul_one]
 #align inner_product_geometry.angle_add_eq_arctan_of_inner_eq_zero InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_add_pos_of_inner_eq_zero /-
 /-- An angle in a non-degenerate right-angled triangle is positive. -/
 theorem angle_add_pos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
     0 < angle x (x + y) :=
@@ -131,7 +146,9 @@ theorem angle_add_pos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x =
     Real.lt_sqrt (norm_nonneg _), pow_two]
   simpa [hx] using h0
 #align inner_product_geometry.angle_add_pos_of_inner_eq_zero InnerProductGeometry.angle_add_pos_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero /-
 /-- An angle in a right-angled triangle is at most `π / 2`. -/
 theorem angle_add_le_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     angle x (x + y) ≤ π / 2 :=
@@ -139,7 +156,9 @@ theorem angle_add_le_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0)
   rw [angle_add_eq_arccos_of_inner_eq_zero h, Real.arccos_le_pi_div_two]
   exact div_nonneg (norm_nonneg _) (norm_nonneg _)
 #align inner_product_geometry.angle_add_le_pi_div_two_of_inner_eq_zero InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero /-
 /-- An angle in a non-degenerate right-angled triangle is less than `π / 2`. -/
 theorem angle_add_lt_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0) :
     angle x (x + y) < π / 2 :=
@@ -152,7 +171,9 @@ theorem angle_add_lt_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0)
         (Left.add_pos_of_pos_of_nonneg (mul_self_pos.2 (norm_ne_zero_iff.2 h0))
           (mul_self_nonneg _)))
 #align inner_product_geometry.angle_add_lt_pi_div_two_of_inner_eq_zero InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.cos_angle_add_of_inner_eq_zero /-
 /-- The cosine of an angle in a right-angled triangle as a ratio of sides. -/
 theorem cos_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.cos (angle x (x + y)) = ‖x‖ / ‖x + y‖ :=
@@ -164,7 +185,9 @@ theorem cos_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     norm_add_sq_eq_norm_sq_add_norm_sq_real h]
   exact le_add_of_nonneg_right (mul_self_nonneg _)
 #align inner_product_geometry.cos_angle_add_of_inner_eq_zero InnerProductGeometry.cos_angle_add_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.sin_angle_add_of_inner_eq_zero /-
 /-- The sine of an angle in a right-angled triangle as a ratio of sides. -/
 theorem sin_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y ≠ 0) :
     Real.sin (angle x (x + y)) = ‖y‖ / ‖x + y‖ :=
@@ -176,7 +199,9 @@ theorem sin_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x 
     norm_add_sq_eq_norm_sq_add_norm_sq_real h]
   exact le_add_of_nonneg_left (mul_self_nonneg _)
 #align inner_product_geometry.sin_angle_add_of_inner_eq_zero InnerProductGeometry.sin_angle_add_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.tan_angle_add_of_inner_eq_zero /-
 /-- The tangent of an angle in a right-angled triangle as a ratio of sides. -/
 theorem tan_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.tan (angle x (x + y)) = ‖y‖ / ‖x‖ :=
@@ -184,7 +209,9 @@ theorem tan_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   by_cases h0 : x = 0; · simp [h0]
   rw [angle_add_eq_arctan_of_inner_eq_zero h h0, Real.tan_arctan]
 #align inner_product_geometry.tan_angle_add_of_inner_eq_zero InnerProductGeometry.tan_angle_add_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero /-
 /-- The cosine of an angle in a right-angled triangle multiplied by the hypotenuse equals the
 adjacent side. -/
 theorem cos_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
@@ -198,7 +225,9 @@ theorem cos_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     simp [h'.1]
   · exact div_mul_cancel _ hxy
 #align inner_product_geometry.cos_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zero /-
 /-- The sine of an angle in a right-angled triangle multiplied by the hypotenuse equals the
 opposite side. -/
 theorem sin_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
@@ -213,7 +242,9 @@ theorem sin_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   · exact Left.add_pos_of_pos_of_nonneg (mul_self_pos.2 (norm_ne_zero_iff.2 h0)) (mul_self_nonneg _)
   · exact Left.add_pos_of_nonneg_of_pos (mul_self_nonneg _) (mul_self_pos.2 (norm_ne_zero_iff.2 h0))
 #align inner_product_geometry.sin_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zero /-
 /-- The tangent of an angle in a right-angled triangle multiplied by the adjacent side equals
 the opposite side. -/
 theorem tan_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y = 0) :
@@ -222,7 +253,9 @@ theorem tan_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
   rw [tan_angle_add_of_inner_eq_zero h]
   rcases h0 with (h0 | h0) <;> simp [h0]
 #align inner_product_geometry.tan_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.norm_div_cos_angle_add_of_inner_eq_zero /-
 /-- A side of a right-angled triangle divided by the cosine of the adjacent angle equals the
 hypotenuse. -/
 theorem norm_div_cos_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y = 0) :
@@ -233,7 +266,9 @@ theorem norm_div_cos_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
   · rw [div_div_eq_mul_div, mul_comm, div_eq_mul_inv, mul_inv_cancel_right₀ (norm_ne_zero_iff.2 h0)]
   · simp [h0]
 #align inner_product_geometry.norm_div_cos_angle_add_of_inner_eq_zero InnerProductGeometry.norm_div_cos_angle_add_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.norm_div_sin_angle_add_of_inner_eq_zero /-
 /-- A side of a right-angled triangle divided by the sine of the opposite angle equals the
 hypotenuse. -/
 theorem norm_div_sin_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
@@ -243,7 +278,9 @@ theorem norm_div_sin_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
   rw [sin_angle_add_of_inner_eq_zero h (Or.inr h0), div_div_eq_mul_div, mul_comm, div_eq_mul_inv,
     mul_inv_cancel_right₀ (norm_ne_zero_iff.2 h0)]
 #align inner_product_geometry.norm_div_sin_angle_add_of_inner_eq_zero InnerProductGeometry.norm_div_sin_angle_add_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.norm_div_tan_angle_add_of_inner_eq_zero /-
 /-- A side of a right-angled triangle divided by the tangent of the opposite angle equals the
 adjacent side. -/
 theorem norm_div_tan_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
@@ -254,7 +291,9 @@ theorem norm_div_tan_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
   · simp [h0]
   · rw [div_div_eq_mul_div, mul_comm, div_eq_mul_inv, mul_inv_cancel_right₀ (norm_ne_zero_iff.2 h0)]
 #align inner_product_geometry.norm_div_tan_angle_add_of_inner_eq_zero InnerProductGeometry.norm_div_tan_angle_add_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero /-
 /-- An angle in a right-angled triangle expressed using `arccos`, version subtracting vectors. -/
 theorem angle_sub_eq_arccos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     angle x (x - y) = Real.arccos (‖x‖ / ‖x - y‖) :=
@@ -262,7 +301,9 @@ theorem angle_sub_eq_arccos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, angle_add_eq_arccos_of_inner_eq_zero h]
 #align inner_product_geometry.angle_sub_eq_arccos_of_inner_eq_zero InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_sub_eq_arcsin_of_inner_eq_zero /-
 /-- An angle in a right-angled triangle expressed using `arcsin`, version subtracting vectors. -/
 theorem angle_sub_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y ≠ 0) :
     angle x (x - y) = Real.arcsin (‖y‖ / ‖x - y‖) :=
@@ -271,7 +312,9 @@ theorem angle_sub_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
   nth_rw 2 [← neg_ne_zero] at h0 
   rw [sub_eq_add_neg, angle_add_eq_arcsin_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.angle_sub_eq_arcsin_of_inner_eq_zero InnerProductGeometry.angle_sub_eq_arcsin_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_sub_eq_arctan_of_inner_eq_zero /-
 /-- An angle in a right-angled triangle expressed using `arctan`, version subtracting vectors. -/
 theorem angle_sub_eq_arctan_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0) :
     angle x (x - y) = Real.arctan (‖y‖ / ‖x‖) :=
@@ -279,7 +322,9 @@ theorem angle_sub_eq_arctan_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
   rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, angle_add_eq_arctan_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.angle_sub_eq_arctan_of_inner_eq_zero InnerProductGeometry.angle_sub_eq_arctan_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_sub_pos_of_inner_eq_zero /-
 /-- An angle in a non-degenerate right-angled triangle is positive, version subtracting
 vectors. -/
 theorem angle_sub_pos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
@@ -289,7 +334,9 @@ theorem angle_sub_pos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x =
   rw [sub_eq_add_neg]
   exact angle_add_pos_of_inner_eq_zero h h0
 #align inner_product_geometry.angle_sub_pos_of_inner_eq_zero InnerProductGeometry.angle_sub_pos_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero /-
 /-- An angle in a right-angled triangle is at most `π / 2`, version subtracting vectors. -/
 theorem angle_sub_le_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     angle x (x - y) ≤ π / 2 :=
@@ -298,7 +345,9 @@ theorem angle_sub_le_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0)
   rw [sub_eq_add_neg]
   exact angle_add_le_pi_div_two_of_inner_eq_zero h
 #align inner_product_geometry.angle_sub_le_pi_div_two_of_inner_eq_zero InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero /-
 /-- An angle in a non-degenerate right-angled triangle is less than `π / 2`, version subtracting
 vectors. -/
 theorem angle_sub_lt_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0) :
@@ -308,7 +357,9 @@ theorem angle_sub_lt_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0)
   rw [sub_eq_add_neg]
   exact angle_add_lt_pi_div_two_of_inner_eq_zero h h0
 #align inner_product_geometry.angle_sub_lt_pi_div_two_of_inner_eq_zero InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.cos_angle_sub_of_inner_eq_zero /-
 /-- The cosine of an angle in a right-angled triangle as a ratio of sides, version subtracting
 vectors. -/
 theorem cos_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
@@ -317,7 +368,9 @@ theorem cos_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, cos_angle_add_of_inner_eq_zero h]
 #align inner_product_geometry.cos_angle_sub_of_inner_eq_zero InnerProductGeometry.cos_angle_sub_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.sin_angle_sub_of_inner_eq_zero /-
 /-- The sine of an angle in a right-angled triangle as a ratio of sides, version subtracting
 vectors. -/
 theorem sin_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y ≠ 0) :
@@ -327,7 +380,9 @@ theorem sin_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x 
   nth_rw 2 [← neg_ne_zero] at h0 
   rw [sub_eq_add_neg, sin_angle_add_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.sin_angle_sub_of_inner_eq_zero InnerProductGeometry.sin_angle_sub_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.tan_angle_sub_of_inner_eq_zero /-
 /-- The tangent of an angle in a right-angled triangle as a ratio of sides, version subtracting
 vectors. -/
 theorem tan_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
@@ -336,7 +391,9 @@ theorem tan_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, tan_angle_add_of_inner_eq_zero h, norm_neg]
 #align inner_product_geometry.tan_angle_sub_of_inner_eq_zero InnerProductGeometry.tan_angle_sub_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.cos_angle_sub_mul_norm_of_inner_eq_zero /-
 /-- The cosine of an angle in a right-angled triangle multiplied by the hypotenuse equals the
 adjacent side, version subtracting vectors. -/
 theorem cos_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
@@ -345,7 +402,9 @@ theorem cos_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, cos_angle_add_mul_norm_of_inner_eq_zero h]
 #align inner_product_geometry.cos_angle_sub_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_sub_mul_norm_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.sin_angle_sub_mul_norm_of_inner_eq_zero /-
 /-- The sine of an angle in a right-angled triangle multiplied by the hypotenuse equals the
 opposite side, version subtracting vectors. -/
 theorem sin_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
@@ -354,7 +413,9 @@ theorem sin_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, sin_angle_add_mul_norm_of_inner_eq_zero h, norm_neg]
 #align inner_product_geometry.sin_angle_sub_mul_norm_of_inner_eq_zero InnerProductGeometry.sin_angle_sub_mul_norm_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.tan_angle_sub_mul_norm_of_inner_eq_zero /-
 /-- The tangent of an angle in a right-angled triangle multiplied by the adjacent side equals
 the opposite side, version subtracting vectors. -/
 theorem tan_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y = 0) :
@@ -364,7 +425,9 @@ theorem tan_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
   rw [← neg_eq_zero] at h0 
   rw [sub_eq_add_neg, tan_angle_add_mul_norm_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.tan_angle_sub_mul_norm_of_inner_eq_zero InnerProductGeometry.tan_angle_sub_mul_norm_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.norm_div_cos_angle_sub_of_inner_eq_zero /-
 /-- A side of a right-angled triangle divided by the cosine of the adjacent angle equals the
 hypotenuse, version subtracting vectors. -/
 theorem norm_div_cos_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y = 0) :
@@ -374,7 +437,9 @@ theorem norm_div_cos_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
   rw [← neg_eq_zero] at h0 
   rw [sub_eq_add_neg, norm_div_cos_angle_add_of_inner_eq_zero h h0]
 #align inner_product_geometry.norm_div_cos_angle_sub_of_inner_eq_zero InnerProductGeometry.norm_div_cos_angle_sub_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.norm_div_sin_angle_sub_of_inner_eq_zero /-
 /-- A side of a right-angled triangle divided by the sine of the opposite angle equals the
 hypotenuse, version subtracting vectors. -/
 theorem norm_div_sin_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
@@ -384,7 +449,9 @@ theorem norm_div_sin_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
   rw [← neg_ne_zero] at h0 
   rw [sub_eq_add_neg, ← norm_neg, norm_div_sin_angle_add_of_inner_eq_zero h h0]
 #align inner_product_geometry.norm_div_sin_angle_sub_of_inner_eq_zero InnerProductGeometry.norm_div_sin_angle_sub_of_inner_eq_zero
+-/
 
+#print InnerProductGeometry.norm_div_tan_angle_sub_of_inner_eq_zero /-
 /-- A side of a right-angled triangle divided by the tangent of the opposite angle equals the
 adjacent side, version subtracting vectors. -/
 theorem norm_div_tan_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
@@ -394,6 +461,7 @@ theorem norm_div_tan_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
   rw [← neg_ne_zero] at h0 
   rw [sub_eq_add_neg, ← norm_neg, norm_div_tan_angle_add_of_inner_eq_zero h h0]
 #align inner_product_geometry.norm_div_tan_angle_sub_of_inner_eq_zero InnerProductGeometry.norm_div_tan_angle_sub_of_inner_eq_zero
+-/
 
 end InnerProductGeometry
 
@@ -404,8 +472,7 @@ open InnerProductGeometry
 variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
-include V
-
+#print EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two /-
 /-- **Pythagorean theorem**, if-and-only-if angle-at-point form. -/
 theorem dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two (p1 p2 p3 : P) :
     dist p1 p3 * dist p1 p3 = dist p1 p2 * dist p1 p2 + dist p3 p2 * dist p3 p2 ↔
@@ -415,7 +482,9 @@ theorem dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two (p1 p2 p3 : P) :
     dist_eq_norm_vsub V p2 p3, ← norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two,
     vsub_sub_vsub_cancel_right p1, ← neg_vsub_eq_vsub_rev p2 p3, norm_neg]
 #align euclidean_geometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.angle_eq_arccos_of_angle_eq_pi_div_two /-
 /-- An angle in a right-angled triangle expressed using `arccos`. -/
 theorem angle_eq_arccos_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2) :
     ∠ p₂ p₃ p₁ = Real.arccos (dist p₃ p₂ / dist p₁ p₃) :=
@@ -425,7 +494,9 @@ theorem angle_eq_arccos_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arccos_of_inner_eq_zero h]
 #align euclidean_geometry.angle_eq_arccos_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arccos_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two /-
 /-- An angle in a right-angled triangle expressed using `arcsin`. -/
 theorem angle_eq_arcsin_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2)
     (h0 : p₁ ≠ p₂ ∨ p₃ ≠ p₂) : ∠ p₂ p₃ p₁ = Real.arcsin (dist p₁ p₂ / dist p₁ p₃) :=
@@ -436,7 +507,9 @@ theorem angle_eq_arcsin_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arcsin_of_inner_eq_zero h h0]
 #align euclidean_geometry.angle_eq_arcsin_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_two /-
 /-- An angle in a right-angled triangle expressed using `arctan`. -/
 theorem angle_eq_arctan_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2)
     (h0 : p₃ ≠ p₂) : ∠ p₂ p₃ p₁ = Real.arctan (dist p₁ p₂ / dist p₃ p₂) :=
@@ -447,7 +520,9 @@ theorem angle_eq_arctan_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arctan_of_inner_eq_zero h h0]
 #align euclidean_geometry.angle_eq_arctan_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two /-
 /-- An angle in a non-degenerate right-angled triangle is positive. -/
 theorem angle_pos_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2)
     (h0 : p₁ ≠ p₂ ∨ p₃ = p₂) : 0 < ∠ p₂ p₃ p₁ :=
@@ -458,7 +533,9 @@ theorem angle_pos_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_pos_of_inner_eq_zero h h0
 #align euclidean_geometry.angle_pos_of_angle_eq_pi_div_two EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.angle_le_pi_div_two_of_angle_eq_pi_div_two /-
 /-- An angle in a right-angled triangle is at most `π / 2`. -/
 theorem angle_le_pi_div_two_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2) :
     ∠ p₂ p₃ p₁ ≤ π / 2 :=
@@ -468,7 +545,9 @@ theorem angle_le_pi_div_two_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_le_pi_div_two_of_inner_eq_zero h
 #align euclidean_geometry.angle_le_pi_div_two_of_angle_eq_pi_div_two EuclideanGeometry.angle_le_pi_div_two_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two /-
 /-- An angle in a non-degenerate right-angled triangle is less than `π / 2`. -/
 theorem angle_lt_pi_div_two_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2)
     (h0 : p₃ ≠ p₂) : ∠ p₂ p₃ p₁ < π / 2 :=
@@ -479,7 +558,9 @@ theorem angle_lt_pi_div_two_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_lt_pi_div_two_of_inner_eq_zero h h0
 #align euclidean_geometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two /-
 /-- The cosine of an angle in a right-angled triangle as a ratio of sides. -/
 theorem cos_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2) :
     Real.cos (∠ p₂ p₃ p₁) = dist p₃ p₂ / dist p₁ p₃ :=
@@ -489,7 +570,9 @@ theorem cos_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, cos_angle_add_of_inner_eq_zero h]
 #align euclidean_geometry.cos_angle_of_angle_eq_pi_div_two EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two /-
 /-- The sine of an angle in a right-angled triangle as a ratio of sides. -/
 theorem sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2)
     (h0 : p₁ ≠ p₂ ∨ p₃ ≠ p₂) : Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₁ p₃ :=
@@ -500,7 +583,9 @@ theorem sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, sin_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.sin_angle_of_angle_eq_pi_div_two EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two /-
 /-- The tangent of an angle in a right-angled triangle as a ratio of sides. -/
 theorem tan_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2) :
     Real.tan (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₃ p₂ :=
@@ -510,7 +595,9 @@ theorem tan_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, tan_angle_add_of_inner_eq_zero h]
 #align euclidean_geometry.tan_angle_of_angle_eq_pi_div_two EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two /-
 /-- The cosine of an angle in a right-angled triangle multiplied by the hypotenuse equals the
 adjacent side. -/
 theorem cos_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2) :
@@ -521,7 +608,9 @@ theorem cos_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, cos_angle_add_mul_norm_of_inner_eq_zero h]
 #align euclidean_geometry.cos_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two /-
 /-- The sine of an angle in a right-angled triangle multiplied by the hypotenuse equals the
 opposite side. -/
 theorem sin_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2) :
@@ -532,7 +621,9 @@ theorem sin_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, sin_angle_add_mul_norm_of_inner_eq_zero h]
 #align euclidean_geometry.sin_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two /-
 /-- The tangent of an angle in a right-angled triangle multiplied by the adjacent side equals
 the opposite side. -/
 theorem tan_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2)
@@ -544,7 +635,9 @@ theorem tan_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, tan_angle_add_mul_norm_of_inner_eq_zero h h0]
 #align euclidean_geometry.tan_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two /-
 /-- A side of a right-angled triangle divided by the cosine of the adjacent angle equals the
 hypotenuse. -/
 theorem dist_div_cos_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2)
@@ -556,7 +649,9 @@ theorem dist_div_cos_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_cos_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_cos_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two /-
 /-- A side of a right-angled triangle divided by the sine of the opposite angle equals the
 hypotenuse. -/
 theorem dist_div_sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2)
@@ -568,7 +663,9 @@ theorem dist_div_sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_sin_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_sin_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two
+-/
 
+#print EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two /-
 /-- A side of a right-angled triangle divided by the tangent of the opposite angle equals the
 adjacent side. -/
 theorem dist_div_tan_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂ p₃ = π / 2)
@@ -580,6 +677,7 @@ theorem dist_div_tan_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_tan_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_tan_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two
+-/
 
 end EuclideanGeometry
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module geometry.euclidean.angle.unoriented.right_angle
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! 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.Angle.Unoriented.Affine
 /-!
 # Right-angled triangles
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves basic geometrical results about distances and angles in (possibly degenerate)
 right-angled triangles in real inner product spaces and Euclidean affine spaces.
 

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

@@ -191,7 +191,7 @@ theorem cos_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   by_cases hxy : ‖x + y‖ = 0
   · have h' := norm_add_sq_eq_norm_sq_add_norm_sq_real h
     rw [hxy, MulZeroClass.zero_mul, eq_comm,
-      add_eq_zero_iff' (mul_self_nonneg ‖x‖) (mul_self_nonneg ‖y‖), mul_self_eq_zero] at h'
+      add_eq_zero_iff' (mul_self_nonneg ‖x‖) (mul_self_nonneg ‖y‖), mul_self_eq_zero] at h' 
     simp [h'.1]
   · exact div_mul_cancel _ hxy
 #align inner_product_geometry.cos_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero
@@ -202,7 +202,7 @@ theorem sin_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.sin (angle x (x + y)) * ‖x + y‖ = ‖y‖ :=
   by
   by_cases h0 : x = 0 ∧ y = 0; · simp [h0]
-  rw [not_and_or] at h0
+  rw [not_and_or] at h0 
   rw [sin_angle_add_of_inner_eq_zero h h0, div_mul_cancel]
   rw [← mul_self_ne_zero, norm_add_sq_eq_norm_sq_add_norm_sq_real h]
   refine' (ne_of_lt _).symm
@@ -256,7 +256,7 @@ theorem norm_div_tan_angle_add_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (
 theorem angle_sub_eq_arccos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     angle x (x - y) = Real.arccos (‖x‖ / ‖x - y‖) :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, angle_add_eq_arccos_of_inner_eq_zero h]
 #align inner_product_geometry.angle_sub_eq_arccos_of_inner_eq_zero InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero
 
@@ -264,8 +264,8 @@ theorem angle_sub_eq_arccos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
 theorem angle_sub_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y ≠ 0) :
     angle x (x - y) = Real.arcsin (‖y‖ / ‖x - y‖) :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
-  nth_rw 2 [← neg_ne_zero] at h0
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  nth_rw 2 [← neg_ne_zero] at h0 
   rw [sub_eq_add_neg, angle_add_eq_arcsin_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.angle_sub_eq_arcsin_of_inner_eq_zero InnerProductGeometry.angle_sub_eq_arcsin_of_inner_eq_zero
 
@@ -273,7 +273,7 @@ theorem angle_sub_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
 theorem angle_sub_eq_arctan_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0) :
     angle x (x - y) = Real.arctan (‖y‖ / ‖x‖) :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, angle_add_eq_arctan_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.angle_sub_eq_arctan_of_inner_eq_zero InnerProductGeometry.angle_sub_eq_arctan_of_inner_eq_zero
 
@@ -281,8 +281,8 @@ theorem angle_sub_eq_arctan_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
 vectors. -/
 theorem angle_sub_pos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
     0 < angle x (x - y) := by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
-  rw [← neg_ne_zero] at h0
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_ne_zero] at h0 
   rw [sub_eq_add_neg]
   exact angle_add_pos_of_inner_eq_zero h h0
 #align inner_product_geometry.angle_sub_pos_of_inner_eq_zero InnerProductGeometry.angle_sub_pos_of_inner_eq_zero
@@ -291,7 +291,7 @@ theorem angle_sub_pos_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x =
 theorem angle_sub_le_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     angle x (x - y) ≤ π / 2 :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg]
   exact angle_add_le_pi_div_two_of_inner_eq_zero h
 #align inner_product_geometry.angle_sub_le_pi_div_two_of_inner_eq_zero InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero
@@ -301,7 +301,7 @@ vectors. -/
 theorem angle_sub_lt_pi_div_two_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0) :
     angle x (x - y) < π / 2 :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg]
   exact angle_add_lt_pi_div_two_of_inner_eq_zero h h0
 #align inner_product_geometry.angle_sub_lt_pi_div_two_of_inner_eq_zero InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero
@@ -311,7 +311,7 @@ vectors. -/
 theorem cos_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.cos (angle x (x - y)) = ‖x‖ / ‖x - y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, cos_angle_add_of_inner_eq_zero h]
 #align inner_product_geometry.cos_angle_sub_of_inner_eq_zero InnerProductGeometry.cos_angle_sub_of_inner_eq_zero
 
@@ -320,8 +320,8 @@ vectors. -/
 theorem sin_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y ≠ 0) :
     Real.sin (angle x (x - y)) = ‖y‖ / ‖x - y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
-  nth_rw 2 [← neg_ne_zero] at h0
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  nth_rw 2 [← neg_ne_zero] at h0 
   rw [sub_eq_add_neg, sin_angle_add_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.sin_angle_sub_of_inner_eq_zero InnerProductGeometry.sin_angle_sub_of_inner_eq_zero
 
@@ -330,7 +330,7 @@ vectors. -/
 theorem tan_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.tan (angle x (x - y)) = ‖y‖ / ‖x‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, tan_angle_add_of_inner_eq_zero h, norm_neg]
 #align inner_product_geometry.tan_angle_sub_of_inner_eq_zero InnerProductGeometry.tan_angle_sub_of_inner_eq_zero
 
@@ -339,7 +339,7 @@ adjacent side, version subtracting vectors. -/
 theorem cos_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.cos (angle x (x - y)) * ‖x - y‖ = ‖x‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, cos_angle_add_mul_norm_of_inner_eq_zero h]
 #align inner_product_geometry.cos_angle_sub_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_sub_mul_norm_of_inner_eq_zero
 
@@ -348,7 +348,7 @@ opposite side, version subtracting vectors. -/
 theorem sin_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.sin (angle x (x - y)) * ‖x - y‖ = ‖y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
   rw [sub_eq_add_neg, sin_angle_add_mul_norm_of_inner_eq_zero h, norm_neg]
 #align inner_product_geometry.sin_angle_sub_mul_norm_of_inner_eq_zero InnerProductGeometry.sin_angle_sub_mul_norm_of_inner_eq_zero
 
@@ -357,8 +357,8 @@ the opposite side, version subtracting vectors. -/
 theorem tan_angle_sub_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y = 0) :
     Real.tan (angle x (x - y)) * ‖x‖ = ‖y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
-  rw [← neg_eq_zero] at h0
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero] at h0 
   rw [sub_eq_add_neg, tan_angle_add_mul_norm_of_inner_eq_zero h h0, norm_neg]
 #align inner_product_geometry.tan_angle_sub_mul_norm_of_inner_eq_zero InnerProductGeometry.tan_angle_sub_mul_norm_of_inner_eq_zero
 
@@ -367,8 +367,8 @@ hypotenuse, version subtracting vectors. -/
 theorem norm_div_cos_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x ≠ 0 ∨ y = 0) :
     ‖x‖ / Real.cos (angle x (x - y)) = ‖x - y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
-  rw [← neg_eq_zero] at h0
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_eq_zero] at h0 
   rw [sub_eq_add_neg, norm_div_cos_angle_add_of_inner_eq_zero h h0]
 #align inner_product_geometry.norm_div_cos_angle_sub_of_inner_eq_zero InnerProductGeometry.norm_div_cos_angle_sub_of_inner_eq_zero
 
@@ -377,8 +377,8 @@ hypotenuse, version subtracting vectors. -/
 theorem norm_div_sin_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
     ‖y‖ / Real.sin (angle x (x - y)) = ‖x - y‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
-  rw [← neg_ne_zero] at h0
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_ne_zero] at h0 
   rw [sub_eq_add_neg, ← norm_neg, norm_div_sin_angle_add_of_inner_eq_zero h h0]
 #align inner_product_geometry.norm_div_sin_angle_sub_of_inner_eq_zero InnerProductGeometry.norm_div_sin_angle_sub_of_inner_eq_zero
 
@@ -387,8 +387,8 @@ adjacent side, version subtracting vectors. -/
 theorem norm_div_tan_angle_sub_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0 : x = 0 ∨ y ≠ 0) :
     ‖y‖ / Real.tan (angle x (x - y)) = ‖x‖ :=
   by
-  rw [← neg_eq_zero, ← inner_neg_right] at h
-  rw [← neg_ne_zero] at h0
+  rw [← neg_eq_zero, ← inner_neg_right] at h 
+  rw [← neg_ne_zero] at h0 
   rw [sub_eq_add_neg, ← norm_neg, norm_div_tan_angle_add_of_inner_eq_zero h h0]
 #align inner_product_geometry.norm_div_tan_angle_sub_of_inner_eq_zero InnerProductGeometry.norm_div_tan_angle_sub_of_inner_eq_zero
 
@@ -418,7 +418,7 @@ theorem angle_eq_arccos_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
     ∠ p₂ p₃ p₁ = Real.arccos (dist p₃ p₂ / dist p₁ p₃) :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arccos_of_inner_eq_zero h]
 #align euclidean_geometry.angle_eq_arccos_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arccos_of_angle_eq_pi_div_two
@@ -428,8 +428,8 @@ theorem angle_eq_arcsin_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
     (h0 : p₁ ≠ p₂ ∨ p₃ ≠ p₂) : ∠ p₂ p₃ p₁ = Real.arcsin (dist p₁ p₂ / dist p₁ p₃) :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0 
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arcsin_of_inner_eq_zero h h0]
 #align euclidean_geometry.angle_eq_arcsin_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two
@@ -439,8 +439,8 @@ theorem angle_eq_arctan_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p
     (h0 : p₃ ≠ p₂) : ∠ p₂ p₃ p₁ = Real.arctan (dist p₁ p₂ / dist p₃ p₂) :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [ne_comm, ← @vsub_ne_zero V] at h0
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+  rw [ne_comm, ← @vsub_ne_zero V] at h0 
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, angle_add_eq_arctan_of_inner_eq_zero h h0]
 #align euclidean_geometry.angle_eq_arctan_of_angle_eq_pi_div_two EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_two
@@ -450,8 +450,8 @@ theorem angle_pos_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
     (h0 : p₁ ≠ p₂ ∨ p₃ = p₂) : 0 < ∠ p₂ p₃ p₁ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [← @vsub_ne_zero V, eq_comm, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+  rw [← @vsub_ne_zero V, eq_comm, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_pos_of_inner_eq_zero h h0
 #align euclidean_geometry.angle_pos_of_angle_eq_pi_div_two EuclideanGeometry.angle_pos_of_angle_eq_pi_div_two
@@ -461,7 +461,7 @@ theorem angle_le_pi_div_two_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     ∠ p₂ p₃ p₁ ≤ π / 2 :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_le_pi_div_two_of_inner_eq_zero h
 #align euclidean_geometry.angle_le_pi_div_two_of_angle_eq_pi_div_two EuclideanGeometry.angle_le_pi_div_two_of_angle_eq_pi_div_two
@@ -471,8 +471,8 @@ theorem angle_lt_pi_div_two_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₃ ≠ p₂) : ∠ p₂ p₃ p₁ < π / 2 :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [ne_comm, ← @vsub_ne_zero V] at h0
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+  rw [ne_comm, ← @vsub_ne_zero V] at h0 
   rw [angle, ← vsub_add_vsub_cancel p₁ p₂ p₃, add_comm]
   exact angle_add_lt_pi_div_two_of_inner_eq_zero h h0
 #align euclidean_geometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_two
@@ -482,7 +482,7 @@ theorem cos_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
     Real.cos (∠ p₂ p₃ p₁) = dist p₃ p₂ / dist p₁ p₃ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, cos_angle_add_of_inner_eq_zero h]
 #align euclidean_geometry.cos_angle_of_angle_eq_pi_div_two EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two
@@ -492,8 +492,8 @@ theorem sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
     (h0 : p₁ ≠ p₂ ∨ p₃ ≠ p₂) : Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₁ p₃ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+  rw [← @vsub_ne_zero V, @ne_comm _ p₃, ← @vsub_ne_zero V _ _ _ p₂, or_comm'] at h0 
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, sin_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.sin_angle_of_angle_eq_pi_div_two EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two
@@ -503,7 +503,7 @@ theorem tan_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠ p₁ p₂
     Real.tan (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₃ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, tan_angle_add_of_inner_eq_zero h]
 #align euclidean_geometry.tan_angle_of_angle_eq_pi_div_two EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two
@@ -514,7 +514,7 @@ theorem cos_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     Real.cos (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₃ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, cos_angle_add_mul_norm_of_inner_eq_zero h]
 #align euclidean_geometry.cos_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two
@@ -525,7 +525,7 @@ theorem sin_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     Real.sin (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₁ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, sin_angle_add_mul_norm_of_inner_eq_zero h]
 #align euclidean_geometry.sin_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two
@@ -536,8 +536,8 @@ theorem tan_angle_mul_dist_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₁ = p₂ ∨ p₃ ≠ p₂) : Real.tan (∠ p₂ p₃ p₁) * dist p₃ p₂ = dist p₁ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, tan_angle_add_mul_norm_of_inner_eq_zero h h0]
 #align euclidean_geometry.tan_angle_mul_dist_of_angle_eq_pi_div_two EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two
@@ -548,8 +548,8 @@ theorem dist_div_cos_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₁ = p₂ ∨ p₃ ≠ p₂) : dist p₃ p₂ / Real.cos (∠ p₂ p₃ p₁) = dist p₁ p₃ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+  rw [ne_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
   rw [angle, dist_eq_norm_vsub' V p₃ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_cos_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_cos_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two
@@ -560,8 +560,8 @@ theorem dist_div_sin_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₁ ≠ p₂ ∨ p₃ = p₂) : dist p₁ p₂ / Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₃ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_sin_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_sin_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two
@@ -572,8 +572,8 @@ theorem dist_div_tan_angle_of_angle_eq_pi_div_two {p₁ p₂ p₃ : P} (h : ∠
     (h0 : p₁ ≠ p₂ ∨ p₃ = p₂) : dist p₁ p₂ / Real.tan (∠ p₂ p₃ p₁) = dist p₃ p₂ :=
   by
   rw [angle, ← inner_eq_zero_iff_angle_eq_pi_div_two, real_inner_comm, ← neg_eq_zero, ←
-    inner_neg_left, neg_vsub_eq_vsub_rev] at h
-  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0
+    inner_neg_left, neg_vsub_eq_vsub_rev] at h 
+  rw [eq_comm, ← @vsub_ne_zero V, ← @vsub_eq_zero_iff_eq V, or_comm'] at h0 
   rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub' V p₃ p₂, ← vsub_add_vsub_cancel p₁ p₂ p₃,
     add_comm, norm_div_tan_angle_add_of_inner_eq_zero h h0]
 #align euclidean_geometry.dist_div_tan_angle_of_angle_eq_pi_div_two EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two

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

@@ -32,13 +32,13 @@ triangle unnecessarily.
 
 noncomputable section
 
-open BigOperators
+open scoped BigOperators
 
-open EuclideanGeometry
+open scoped EuclideanGeometry
 
-open Real
+open scoped Real
 
-open RealInnerProductSpace
+open scoped RealInnerProductSpace
 
 namespace InnerProductGeometry
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module geometry.euclidean.angle.unoriented.right_angle
-! leanprover-community/mathlib commit 0efabe73557d6f5070d7ec68cab671a8a786ae7b
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -42,7 +42,7 @@ open RealInnerProductSpace
 
 namespace InnerProductGeometry
 
-variable {V : Type _} [InnerProductSpace ℝ V]
+variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
 
 /-- Pythagorean theorem, if-and-only-if vector angle form. -/
 theorem norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two (x y : V) :
@@ -398,7 +398,8 @@ namespace EuclideanGeometry
 
 open InnerProductGeometry
 
-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/3180fab693e2cee3bff62675571264cb8778b212

@@ -190,8 +190,8 @@ theorem cos_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   rw [cos_angle_add_of_inner_eq_zero h]
   by_cases hxy : ‖x + y‖ = 0
   · have h' := norm_add_sq_eq_norm_sq_add_norm_sq_real h
-    rw [hxy, zero_mul, eq_comm, add_eq_zero_iff' (mul_self_nonneg ‖x‖) (mul_self_nonneg ‖y‖),
-      mul_self_eq_zero] at h'
+    rw [hxy, MulZeroClass.zero_mul, eq_comm,
+      add_eq_zero_iff' (mul_self_nonneg ‖x‖) (mul_self_nonneg ‖y‖), mul_self_eq_zero] at h'
     simp [h'.1]
   · exact div_mul_cancel _ hxy
 #align inner_product_geometry.cos_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero

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

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 | |

@@ -89,7 +89,7 @@ theorem angle_add_eq_arcsin_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) (h0
   rw [angle_add_eq_arccos_of_inner_eq_zero h,
     Real.arccos_eq_arcsin (div_nonneg (norm_nonneg _) (norm_nonneg _)), div_pow, one_sub_div hxy]
   nth_rw 1 [pow_two]
-  rw [norm_add_sq_eq_norm_sq_add_norm_sq_real h, pow_two, add_sub_cancel', ← pow_two, ← div_pow,
+  rw [norm_add_sq_eq_norm_sq_add_norm_sq_real h, pow_two, add_sub_cancel_left, ← pow_two, ← div_pow,
     Real.sqrt_sq (div_nonneg (norm_nonneg _) (norm_nonneg _))]
 #align inner_product_geometry.angle_add_eq_arcsin_of_inner_eq_zero InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zero
 
@@ -169,7 +169,7 @@ theorem cos_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     rw [hxy, zero_mul, eq_comm,
       add_eq_zero_iff' (mul_self_nonneg ‖x‖) (mul_self_nonneg ‖y‖), mul_self_eq_zero] at h'
     simp [h'.1]
-  · exact div_mul_cancel _ hxy
+  · exact div_mul_cancel₀ _ hxy
 #align inner_product_geometry.cos_angle_add_mul_norm_of_inner_eq_zero InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero
 
 /-- The sine of an angle in a right-angled triangle multiplied by the hypotenuse equals the
@@ -178,7 +178,7 @@ theorem sin_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
     Real.sin (angle x (x + y)) * ‖x + y‖ = ‖y‖ := by
   by_cases h0 : x = 0 ∧ y = 0; · simp [h0]
   rw [not_and_or] at h0
-  rw [sin_angle_add_of_inner_eq_zero h h0, div_mul_cancel]
+  rw [sin_angle_add_of_inner_eq_zero h h0, div_mul_cancel₀]
   rw [← mul_self_ne_zero, norm_add_sq_eq_norm_sq_add_norm_sq_real h]
   refine' (ne_of_lt _).symm
   rcases h0 with (h0 | h0)

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -29,8 +29,6 @@ triangle unnecessarily.
 
 noncomputable section
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 open scoped BigOperators
 
 open scoped 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).

@@ -168,7 +168,7 @@ theorem cos_angle_add_mul_norm_of_inner_eq_zero {x y : V} (h : ⟪x, y⟫ = 0) :
   rw [cos_angle_add_of_inner_eq_zero h]
   by_cases hxy : ‖x + y‖ = 0
   · have h' := norm_add_sq_eq_norm_sq_add_norm_sq_real h
-    rw [hxy, MulZeroClass.zero_mul, eq_comm,
+    rw [hxy, zero_mul, eq_comm,
       add_eq_zero_iff' (mul_self_nonneg ‖x‖) (mul_self_nonneg ‖y‖), mul_self_eq_zero] at h'
     simp [h'.1]
   · exact div_mul_cancel _ hxy

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

This has nice performance benefits.

@@ -41,7 +41,7 @@ open scoped RealInnerProductSpace
 
 namespace InnerProductGeometry
 
-variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
+variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V]
 
 /-- Pythagorean theorem, if-and-only-if vector angle form. -/
 theorem norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two (x y : V) :
@@ -357,7 +357,7 @@ namespace EuclideanGeometry
 
 open InnerProductGeometry
 
-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]
 
 /-- **Pythagorean theorem**, if-and-only-if angle-at-point form. -/

@@ -29,7 +29,7 @@ triangle unnecessarily.
 
 noncomputable section
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 open scoped BigOperators
 

• 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) 2020 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module geometry.euclidean.angle.unoriented.right_angle
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan
 import Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine
 
+#align_import geometry.euclidean.angle.unoriented.right_angle from "leanprover-community/mathlib"@"46b633fd842bef9469441c0209906f6dddd2b4f5"
+
 /-!
 # Right-angled triangles