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

@@ -358,7 +358,7 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
     by
     rw [Submodule.mem_iInf]
     exact fun i => (Submodule.mem_inf.1 (h' i i.property)).1
-  rw [Submodule.iInf_orthogonal, ← Submodule.span_iUnion] at hi 
+  rw [Submodule.iInf_orthogonal, ← Submodule.span_iUnion] at hi
   have hu :
     (⋃ i : { i // i₁ ≠ i }, ({s.points i₁ -ᵥ s.points i} : Set V)) =
       (· -ᵥ ·) (s.points i₁) '' (s.points '' (Set.univ \ {i₁})) :=
@@ -371,7 +371,7 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
       use i, ⟨Set.mem_univ _, i.property.symm⟩
     · rintro ⟨i, ⟨hiu, hi⟩, rfl⟩
       use⟨i, hi.symm⟩, rfl
-  rw [hu, ← vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_univ _), Set.image_univ] at hi 
+  rw [hu, ← vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_univ _), Set.image_univ] at hi
   have hv : p -ᵥ s.monge_point ∈ vectorSpan ℝ (Set.range s.points) :=
     by
     let s₁ : Finset (Fin (n + 3)) := univ.erase i₁
@@ -479,14 +479,14 @@ theorem affineSpan_pair_eq_altitude_iff {n : ℕ} (s : Simplex ℝ P (n + 1)) (i
   · intro h
     constructor
     · intro heq
-      rw [HEq, Set.pair_eq_singleton, vectorSpan_singleton] at h 
+      rw [HEq, Set.pair_eq_singleton, vectorSpan_singleton] at h
       have hd : finrank ℝ (s.altitude i).direction = 0 := by rw [← h, finrank_bot]
       simpa using hd
     · rw [← Submodule.mem_inf, _root_.inf_comm, ← direction_altitude, ← h]
       exact
         vsub_mem_vectorSpan ℝ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
   · rintro ⟨hne, h⟩
-    rw [← Submodule.mem_inf, _root_.inf_comm, ← direction_altitude] at h 
+    rw [← Submodule.mem_inf, _root_.inf_comm, ← direction_altitude] at h
     rw [vectorSpan_eq_span_vsub_set_left_ne ℝ (Set.mem_insert _ _),
       Set.insert_diff_of_mem _ (Set.mem_singleton _),
       Set.diff_singleton_eq_self fun h => hne (Set.mem_singleton_iff.1 h), Set.image_singleton]
@@ -585,8 +585,8 @@ theorem eq_orthocenter_of_forall_mem_altitude {t : Triangle ℝ P} {i₁ i₂ :
     (h₁₂ : i₁ ≠ i₂) (h₁ : p ∈ t.altitude i₁) (h₂ : p ∈ t.altitude i₂) : p = t.orthocenter :=
   by
   obtain ⟨i₃, h₂₃, h₁₃⟩ : ∃ i₃, i₂ ≠ i₃ ∧ i₁ ≠ i₃ := by clear h₁ h₂; decide!
-  rw [t.altitude_eq_monge_plane h₁₃ h₁₂ h₂₃.symm] at h₁ 
-  rw [t.altitude_eq_monge_plane h₂₃ h₁₂.symm h₁₃.symm] at h₂ 
+  rw [t.altitude_eq_monge_plane h₁₃ h₁₂ h₂₃.symm] at h₁
+  rw [t.altitude_eq_monge_plane h₂₃ h₁₂.symm h₁₃.symm] at h₂
   rw [orthocenter_eq_monge_point]
   have ha : ∀ i, i₃ ≠ i → p ∈ t.monge_plane i₃ i :=
     by
@@ -768,12 +768,12 @@ theorem exists_of_range_subset_orthocentricSystem {t : Triangle ℝ P}
     rcases h i₃ h₁₃ with ⟨j₃, h₃⟩
     have hj₂₃ : j₂ ≠ j₃ := by
       intro he
-      rw [he, h₃] at h₂ 
+      rw [he, h₃] at h₂
       exact h₂₃.symm (hpi h₂)
     exact ⟨i₁, i₂, i₃, j₂, j₃, h₁₂, h₁₃, h₂₃, h₁₂₃, h₁, hj₂₃, h₂, h₃⟩
   · right
     have hs := Set.subset_diff_singleton hps h
-    rw [Set.insert_diff_self_of_not_mem ho] at hs 
+    rw [Set.insert_diff_self_of_not_mem ho] at hs
     refine' Set.eq_of_subset_of_card_le hs _
     rw [Set.card_range_of_injective hpi, Set.card_range_of_injective t.independent.injective]
 #align euclidean_geometry.exists_of_range_subset_orthocentric_system EuclideanGeometry.exists_of_range_subset_orthocentricSystem
@@ -810,7 +810,7 @@ theorem exists_dist_eq_circumradius_of_subset_insert_orthocenter {t : Triangle 
       exact t.dist_circumcenter_eq_circumradius _
   · use t.circumcenter, t.circumcenter_mem_affine_span
     intro p₁ hp₁
-    rw [hs] at hp₁ 
+    rw [hs] at hp₁
     rcases hp₁ with ⟨i, rfl⟩
     exact t.dist_circumcenter_eq_circumradius _
 #align euclidean_geometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter EuclideanGeometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter
@@ -822,7 +822,7 @@ theorem OrthocentricSystem.affineIndependent {s : Set P} (ho : OrthocentricSyste
     (hps : Set.range p ⊆ s) (hpi : Function.Injective p) : AffineIndependent ℝ p :=
   by
   rcases ho with ⟨t, hto, hst⟩
-  rw [hst] at hps 
+  rw [hst] at hps
   rcases exists_dist_eq_circumradius_of_subset_insert_orthocenter hto hps hpi with ⟨c, hcs, hc⟩
   exact cospherical.affine_independent ⟨c, t.circumradius, hc⟩ Set.Subset.rfl hpi
 #align euclidean_geometry.orthocentric_system.affine_independent EuclideanGeometry.OrthocentricSystem.affineIndependent
@@ -859,16 +859,16 @@ theorem OrthocentricSystem.exists_circumradius_eq {s : Set P} (ho : Orthocentric
   use t.circumradius
   intro t₂ ht₂
   have ht₂s := ht₂
-  rw [hts] at ht₂ 
+  rw [hts] at ht₂
   rcases exists_dist_eq_circumradius_of_subset_insert_orthocenter hto ht₂
       t₂.independent.injective with
     ⟨c, hc, h⟩
-  rw [Set.forall_range_iff] at h 
+  rw [Set.forall_mem_range] at h
   have hs : Set.range t.points ⊆ s := by
     rw [hts]
     exact Set.subset_insert _ _
   rw [affine_span_of_orthocentric_system ⟨t, hto, hts⟩ hs t.independent.injective, ←
-    affine_span_of_orthocentric_system ⟨t, hto, hts⟩ ht₂s t₂.independent.injective] at hc 
+    affine_span_of_orthocentric_system ⟨t, hto, hts⟩ ht₂s t₂.independent.injective] at hc
   exact (t₂.eq_circumradius_of_dist_eq hc h).symm
 #align euclidean_geometry.orthocentric_system.exists_circumradius_eq EuclideanGeometry.OrthocentricSystem.exists_circumradius_eq
 -/
@@ -881,7 +881,7 @@ theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricS
     s = insert t.orthocenter (Set.range t.points) :=
   by
   rcases ho with ⟨t₀, ht₀o, ht₀s⟩
-  rw [ht₀s] at ht 
+  rw [ht₀s] at ht
   rcases exists_of_range_subset_orthocentric_system ht₀o ht t.independent.injective with
     (⟨i₁, i₂, i₃, j₂, j₃, h₁₂, h₁₃, h₂₃, h₁₂₃, h₁, hj₂₃, h₂, h₃⟩ | hs)
   · obtain ⟨j₁, hj₁₂, hj₁₃, hj₁₂₃⟩ :

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

@@ -3,7 +3,7 @@ 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.Geometry.Euclidean.Circumcenter
+import Geometry.Euclidean.Circumcenter
 
 #align_import geometry.euclidean.monge_point from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -309,7 +309,7 @@ theorem mongePlane_comm {n : ℕ} (s : Simplex ℝ P (n + 2)) (i₁ i₂ : Fin (
   · ext
     simp_rw [Submodule.mem_span_singleton]
     constructor
-    all_goals rintro ⟨r, rfl⟩; use -r; rw [neg_smul, ← smul_neg, neg_vsub_eq_vsub_rev]
+    all_goals rintro ⟨r, rfl⟩; use-r; rw [neg_smul, ← smul_neg, neg_vsub_eq_vsub_rev]
 #align affine.simplex.monge_plane_comm Affine.Simplex.mongePlane_comm
 -/
 
@@ -370,7 +370,7 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
     · rintro ⟨i, rfl⟩
       use i, ⟨Set.mem_univ _, i.property.symm⟩
     · rintro ⟨i, ⟨hiu, hi⟩, rfl⟩
-      use ⟨i, hi.symm⟩, rfl
+      use⟨i, hi.symm⟩, rfl
   rw [hu, ← vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_univ _), Set.image_univ] at hi 
   have hv : p -ᵥ s.monge_point ∈ vectorSpan ℝ (Set.range s.points) :=
     by

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

@@ -2,14 +2,11 @@
 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.monge_point
-! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Geometry.Euclidean.Circumcenter
 
+#align_import geometry.euclidean.monge_point from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
+
 /-!
 # Monge point and orthocenter
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -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.monge_point
-! leanprover-community/mathlib commit 1a4df69ca1a9a0e5e26bfe12e2b92814216016d0
+! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Geometry.Euclidean.Circumcenter
 /-!
 # Monge point and orthocenter
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the orthocenter of a triangle, via its n-dimensional
 generalization, the Monge point of a simplex.
 

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

@@ -69,6 +69,7 @@ open Finset AffineSubspace EuclideanGeometry PointsWithCircumcenterIndex
 variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
+#print Affine.Simplex.mongePoint /-
 /-- The Monge point of a simplex (in 2 or more dimensions) is a
 generalization of the orthocenter of a triangle.  It is defined to be
 the intersection of the Monge planes, where a Monge plane is the
@@ -86,7 +87,9 @@ def mongePoint {n : ℕ} (s : Simplex ℝ P n) : P :=
       ((univ : Finset (Fin (n + 1))).centroid ℝ s.points -ᵥ s.circumcenter) +ᵥ
     s.circumcenter
 #align affine.simplex.monge_point Affine.Simplex.mongePoint
+-/
 
+#print Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter /-
 /-- The position of the Monge point in relation to the circumcenter
 and centroid. -/
 theorem mongePoint_eq_smul_vsub_vadd_circumcenter {n : ℕ} (s : Simplex ℝ P n) :
@@ -96,28 +99,36 @@ theorem mongePoint_eq_smul_vsub_vadd_circumcenter {n : ℕ} (s : Simplex ℝ P n
         s.circumcenter :=
   rfl
 #align affine.simplex.monge_point_eq_smul_vsub_vadd_circumcenter Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter
+-/
 
+#print Affine.Simplex.mongePoint_mem_affineSpan /-
 /-- The Monge point lies in the affine span. -/
 theorem mongePoint_mem_affineSpan {n : ℕ} (s : Simplex ℝ P n) :
     s.mongePoint ∈ affineSpan ℝ (Set.range s.points) :=
   smul_vsub_vadd_mem _ _ (centroid_mem_affineSpan_of_card_eq_add_one ℝ _ (card_fin (n + 1)))
     s.circumcenter_mem_affineSpan s.circumcenter_mem_affineSpan
 #align affine.simplex.monge_point_mem_affine_span Affine.Simplex.mongePoint_mem_affineSpan
+-/
 
+#print Affine.Simplex.mongePoint_eq_of_range_eq /-
 /-- Two simplices with the same points have the same Monge point. -/
 theorem mongePoint_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex ℝ P n}
     (h : Set.range s₁.points = Set.range s₂.points) : s₁.mongePoint = s₂.mongePoint := by
   simp_rw [monge_point_eq_smul_vsub_vadd_circumcenter, centroid_eq_of_range_eq h,
     circumcenter_eq_of_range_eq h]
 #align affine.simplex.monge_point_eq_of_range_eq Affine.Simplex.mongePoint_eq_of_range_eq
+-/
 
+#print Affine.Simplex.mongePointWeightsWithCircumcenter /-
 /-- The weights for the Monge point of an (n+2)-simplex, in terms of
 `points_with_circumcenter`. -/
 def mongePointWeightsWithCircumcenter (n : ℕ) : PointsWithCircumcenterIndex (n + 2) → ℝ
   | point_index i => ((n + 1 : ℕ) : ℝ)⁻¹
   | circumcenter_index => -2 / ((n + 1 : ℕ) : ℝ)
 #align affine.simplex.monge_point_weights_with_circumcenter Affine.Simplex.mongePointWeightsWithCircumcenter
+-/
 
+#print Affine.Simplex.sum_mongePointWeightsWithCircumcenter /-
 /-- `monge_point_weights_with_circumcenter` sums to 1. -/
 @[simp]
 theorem sum_mongePointWeightsWithCircumcenter (n : ℕ) :
@@ -129,7 +140,9 @@ theorem sum_mongePointWeightsWithCircumcenter (n : ℕ) :
   field_simp [hn1]
   ring
 #align affine.simplex.sum_monge_point_weights_with_circumcenter Affine.Simplex.sum_mongePointWeightsWithCircumcenter
+-/
 
+#print Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter /-
 /-- The Monge point of an (n+2)-simplex, in terms of
 `points_with_circumcenter`. -/
 theorem mongePoint_eq_affineCombination_of_pointsWithCircumcenter {n : ℕ}
@@ -155,22 +168,26 @@ theorem mongePoint_eq_affineCombination_of_pointsWithCircumcenter {n : ℕ}
   · field_simp [hn1]
     ring
 #align affine.simplex.monge_point_eq_affine_combination_of_points_with_circumcenter Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter
+-/
 
+#print Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter /-
 /-- The weights for the Monge point of an (n+2)-simplex, minus the
 centroid of an n-dimensional face, in terms of
 `points_with_circumcenter`.  This definition is only valid when `i₁ ≠ i₂`. -/
-def mongePointVsubFaceCentroidWeightsWithCircumcenter {n : ℕ} (i₁ i₂ : Fin (n + 3)) :
+def mongePointVSubFaceCentroidWeightsWithCircumcenter {n : ℕ} (i₁ i₂ : Fin (n + 3)) :
     PointsWithCircumcenterIndex (n + 2) → ℝ
   | point_index i => if i = i₁ ∨ i = i₂ then ((n + 1 : ℕ) : ℝ)⁻¹ else 0
   | circumcenter_index => -2 / ((n + 1 : ℕ) : ℝ)
-#align affine.simplex.monge_point_vsub_face_centroid_weights_with_circumcenter Affine.Simplex.mongePointVsubFaceCentroidWeightsWithCircumcenter
+#align affine.simplex.monge_point_vsub_face_centroid_weights_with_circumcenter Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter
+-/
 
+#print Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub /-
 /-- `monge_point_vsub_face_centroid_weights_with_circumcenter` is the
 result of subtracting `centroid_weights_with_circumcenter` from
 `monge_point_weights_with_circumcenter`. -/
-theorem mongePointVsubFaceCentroidWeightsWithCircumcenter_eq_sub {n : ℕ} {i₁ i₂ : Fin (n + 3)}
+theorem mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub {n : ℕ} {i₁ i₂ : Fin (n + 3)}
     (h : i₁ ≠ i₂) :
-    mongePointVsubFaceCentroidWeightsWithCircumcenter i₁ i₂ =
+    mongePointVSubFaceCentroidWeightsWithCircumcenter i₁ i₂ =
       mongePointWeightsWithCircumcenter n - centroidWeightsWithCircumcenter ({i₁, i₂}ᶜ) :=
   by
   ext i
@@ -184,32 +201,38 @@ theorem mongePointVsubFaceCentroidWeightsWithCircumcenter_eq_sub {n : ℕ} {i₁
   ·
     simp [monge_point_weights_with_circumcenter, centroid_weights_with_circumcenter,
       monge_point_vsub_face_centroid_weights_with_circumcenter]
-#align affine.simplex.monge_point_vsub_face_centroid_weights_with_circumcenter_eq_sub Affine.Simplex.mongePointVsubFaceCentroidWeightsWithCircumcenter_eq_sub
+#align affine.simplex.monge_point_vsub_face_centroid_weights_with_circumcenter_eq_sub Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub
+-/
 
+#print Affine.Simplex.sum_mongePointVSubFaceCentroidWeightsWithCircumcenter /-
 /-- `monge_point_vsub_face_centroid_weights_with_circumcenter` sums to 0. -/
 @[simp]
-theorem sum_mongePointVsubFaceCentroidWeightsWithCircumcenter {n : ℕ} {i₁ i₂ : Fin (n + 3)}
-    (h : i₁ ≠ i₂) : ∑ i, mongePointVsubFaceCentroidWeightsWithCircumcenter i₁ i₂ i = 0 :=
+theorem sum_mongePointVSubFaceCentroidWeightsWithCircumcenter {n : ℕ} {i₁ i₂ : Fin (n + 3)}
+    (h : i₁ ≠ i₂) : ∑ i, mongePointVSubFaceCentroidWeightsWithCircumcenter i₁ i₂ i = 0 :=
   by
   rw [monge_point_vsub_face_centroid_weights_with_circumcenter_eq_sub h]
   simp_rw [Pi.sub_apply, sum_sub_distrib, sum_monge_point_weights_with_circumcenter]
   rw [sum_centroid_weights_with_circumcenter, sub_self]
   simp [← card_pos, card_compl, h]
-#align affine.simplex.sum_monge_point_vsub_face_centroid_weights_with_circumcenter Affine.Simplex.sum_mongePointVsubFaceCentroidWeightsWithCircumcenter
+#align affine.simplex.sum_monge_point_vsub_face_centroid_weights_with_circumcenter Affine.Simplex.sum_mongePointVSubFaceCentroidWeightsWithCircumcenter
+-/
 
+#print Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter /-
 /-- The Monge point of an (n+2)-simplex, minus the centroid of an
 n-dimensional face, in terms of `points_with_circumcenter`. -/
 theorem mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter {n : ℕ}
     (s : Simplex ℝ P (n + 2)) {i₁ i₂ : Fin (n + 3)} (h : i₁ ≠ i₂) :
     s.mongePoint -ᵥ ({i₁, i₂}ᶜ : Finset (Fin (n + 3))).centroid ℝ s.points =
       (univ : Finset (PointsWithCircumcenterIndex (n + 2))).weightedVSub s.pointsWithCircumcenter
-        (mongePointVsubFaceCentroidWeightsWithCircumcenter i₁ i₂) :=
+        (mongePointVSubFaceCentroidWeightsWithCircumcenter i₁ i₂) :=
   by
   simp_rw [monge_point_eq_affine_combination_of_points_with_circumcenter,
     centroid_eq_affine_combination_of_points_with_circumcenter, affine_combination_vsub,
     monge_point_vsub_face_centroid_weights_with_circumcenter_eq_sub h]
 #align affine.simplex.monge_point_vsub_face_centroid_eq_weighted_vsub_of_points_with_circumcenter Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter
+-/
 
+#print Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub /-
 /-- The Monge point of an (n+2)-simplex, minus the centroid of an
 n-dimensional face, is orthogonal to the difference of the two
 vertices not in that face. -/
@@ -248,7 +271,9 @@ theorem inner_mongePoint_vsub_face_centroid_vsub {n : ℕ} (s : Simplex ℝ P (n
   · intro i hu hi
     simp [hfs i hi]
 #align affine.simplex.inner_monge_point_vsub_face_centroid_vsub Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub
+-/
 
+#print Affine.Simplex.mongePlane /-
 /-- A Monge plane of an (n+2)-simplex is the (n+1)-dimensional affine
 subspace of the subspace spanned by the simplex that passes through
 the centroid of an n-dimensional face and is orthogonal to the
@@ -258,7 +283,9 @@ def mongePlane {n : ℕ} (s : Simplex ℝ P (n + 2)) (i₁ i₂ : Fin (n + 3)) :
   mk' (({i₁, i₂}ᶜ : Finset (Fin (n + 3))).centroid ℝ s.points) (ℝ ∙ s.points i₁ -ᵥ s.points i₂)ᗮ ⊓
     affineSpan ℝ (Set.range s.points)
 #align affine.simplex.monge_plane Affine.Simplex.mongePlane
+-/
 
+#print Affine.Simplex.mongePlane_def /-
 /-- The definition of a Monge plane. -/
 theorem mongePlane_def {n : ℕ} (s : Simplex ℝ P (n + 2)) (i₁ i₂ : Fin (n + 3)) :
     s.mongePlane i₁ i₂ =
@@ -267,7 +294,9 @@ theorem mongePlane_def {n : ℕ} (s : Simplex ℝ P (n + 2)) (i₁ i₂ : Fin (n
         affineSpan ℝ (Set.range s.points) :=
   rfl
 #align affine.simplex.monge_plane_def Affine.Simplex.mongePlane_def
+-/
 
+#print Affine.Simplex.mongePlane_comm /-
 /-- The Monge plane associated with vertices `i₁` and `i₂` equals that
 associated with `i₂` and `i₁`. -/
 theorem mongePlane_comm {n : ℕ} (s : Simplex ℝ P (n + 2)) (i₁ i₂ : Fin (n + 3)) :
@@ -282,7 +311,9 @@ theorem mongePlane_comm {n : ℕ} (s : Simplex ℝ P (n + 2)) (i₁ i₂ : Fin (
     constructor
     all_goals rintro ⟨r, rfl⟩; use -r; rw [neg_smul, ← smul_neg, neg_vsub_eq_vsub_rev]
 #align affine.simplex.monge_plane_comm Affine.Simplex.mongePlane_comm
+-/
 
+#print Affine.Simplex.mongePoint_mem_mongePlane /-
 /-- The Monge point lies in the Monge planes. -/
 theorem mongePoint_mem_mongePlane {n : ℕ} (s : Simplex ℝ P (n + 2)) {i₁ i₂ : Fin (n + 3)} :
     s.mongePoint ∈ s.mongePlane i₁ i₂ :=
@@ -294,7 +325,9 @@ theorem mongePoint_mem_mongePlane {n : ℕ} (s : Simplex ℝ P (n + 2)) {i₁ i
   rcases submodule.mem_span_singleton.mp hv with ⟨r, rfl⟩
   rw [inner_smul_right, s.inner_monge_point_vsub_face_centroid_vsub, MulZeroClass.mul_zero]
 #align affine.simplex.monge_point_mem_monge_plane Affine.Simplex.mongePoint_mem_mongePlane
+-/
 
+#print Affine.Simplex.direction_mongePlane /-
 /-- The direction of a Monge plane. -/
 theorem direction_mongePlane {n : ℕ} (s : Simplex ℝ P (n + 2)) {i₁ i₂ : Fin (n + 3)} :
     (s.mongePlane i₁ i₂).direction =
@@ -303,7 +336,9 @@ theorem direction_mongePlane {n : ℕ} (s : Simplex ℝ P (n + 2)) {i₁ i₂ :
   rw [monge_plane_def, direction_inf_of_mem_inf s.monge_point_mem_monge_plane, direction_mk',
     direction_affineSpan]
 #align affine.simplex.direction_monge_plane Affine.Simplex.direction_mongePlane
+-/
 
+#print Affine.Simplex.eq_mongePoint_of_forall_mem_mongePlane /-
 /-- The Monge point is the only point in all the Monge planes from any
 one vertex. -/
 theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n + 2)} {i₁ : Fin (n + 3)}
@@ -345,14 +380,18 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
     exact (Submodule.mem_inf.1 (h' i₂ h₁₂)).2
   exact Submodule.disjoint_def.1 (vectorSpan ℝ (Set.range s.points)).orthogonal_disjoint _ hv hi
 #align affine.simplex.eq_monge_point_of_forall_mem_monge_plane Affine.Simplex.eq_mongePoint_of_forall_mem_mongePlane
+-/
 
+#print Affine.Simplex.altitude /-
 /-- An altitude of a simplex is the line that passes through a vertex
 and is orthogonal to the opposite face. -/
 def altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) : AffineSubspace ℝ P :=
   mk' (s.points i) (affineSpan ℝ (s.points '' ↑(univ.eraseₓ i))).directionᗮ ⊓
     affineSpan ℝ (Set.range s.points)
 #align affine.simplex.altitude Affine.Simplex.altitude
+-/
 
+#print Affine.Simplex.altitude_def /-
 /-- The definition of an altitude. -/
 theorem altitude_def {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
     s.altitude i =
@@ -360,13 +399,17 @@ theorem altitude_def {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
         affineSpan ℝ (Set.range s.points) :=
   rfl
 #align affine.simplex.altitude_def Affine.Simplex.altitude_def
+-/
 
+#print Affine.Simplex.mem_altitude /-
 /-- A vertex lies in the corresponding altitude. -/
 theorem mem_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
     s.points i ∈ s.altitude i :=
   (mem_inf_iff _ _ _).2 ⟨self_mem_mk' _ _, mem_affineSpan ℝ (Set.mem_range_self _)⟩
 #align affine.simplex.mem_altitude Affine.Simplex.mem_altitude
+-/
 
+#print Affine.Simplex.direction_altitude /-
 /-- The direction of an altitude. -/
 theorem direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
     (s.altitude i).direction =
@@ -376,7 +419,9 @@ theorem direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2
     direction_inf_of_mem (self_mem_mk' (s.points i) _) (mem_affineSpan ℝ (Set.mem_range_self _)),
     direction_mk', direction_affineSpan, direction_affineSpan]
 #align affine.simplex.direction_altitude Affine.Simplex.direction_altitude
+-/
 
+#print Affine.Simplex.vectorSpan_isOrtho_altitude_direction /-
 /-- The vector span of the opposite face lies in the direction
 orthogonal to an altitude. -/
 theorem vectorSpan_isOrtho_altitude_direction {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
@@ -385,9 +430,11 @@ theorem vectorSpan_isOrtho_altitude_direction {n : ℕ} (s : Simplex ℝ P (n +
   rw [direction_altitude]
   exact (Submodule.isOrtho_orthogonal_right _).mono_right inf_le_left
 #align affine.simplex.vector_span_is_ortho_altitude_direction Affine.Simplex.vectorSpan_isOrtho_altitude_direction
+-/
 
 open FiniteDimensional
 
+#print Affine.Simplex.finiteDimensional_direction_altitude /-
 /-- An altitude is finite-dimensional. -/
 instance finiteDimensional_direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
     FiniteDimensional ℝ (s.altitude i).direction :=
@@ -395,7 +442,9 @@ instance finiteDimensional_direction_altitude {n : ℕ} (s : Simplex ℝ P (n +
   rw [direction_altitude]
   infer_instance
 #align affine.simplex.finite_dimensional_direction_altitude Affine.Simplex.finiteDimensional_direction_altitude
+-/
 
+#print Affine.Simplex.finrank_direction_altitude /-
 /-- An altitude is one-dimensional (i.e., a line). -/
 @[simp]
 theorem finrank_direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
@@ -410,7 +459,9 @@ theorem finrank_direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fi
   rw [s.independent.finrank_vector_span (Fintype.card_fin _), ← Finset.coe_image,
     s.independent.finrank_vector_span_image_finset hc]
 #align affine.simplex.finrank_direction_altitude Affine.Simplex.finrank_direction_altitude
+-/
 
+#print Affine.Simplex.affineSpan_pair_eq_altitude_iff /-
 /-- A line through a vertex is the altitude through that vertex if and
 only if it is orthogonal to the opposite face. -/
 theorem affineSpan_pair_eq_altitude_iff {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2))
@@ -447,6 +498,7 @@ theorem affineSpan_pair_eq_altitude_iff {n : ℕ} (s : Simplex ℝ P (n + 1)) (i
       · refine' linearIndependent_singleton _
         simpa using hne
 #align affine.simplex.affine_span_pair_eq_altitude_iff Affine.Simplex.affineSpan_pair_eq_altitude_iff
+-/
 
 end Simplex
 
@@ -457,18 +509,23 @@ open EuclideanGeometry Finset Simplex AffineSubspace FiniteDimensional
 variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
+#print Affine.Triangle.orthocenter /-
 /-- The orthocenter of a triangle is the intersection of its
 altitudes.  It is defined here as the 2-dimensional case of the
 Monge point. -/
 def orthocenter (t : Triangle ℝ P) : P :=
   t.mongePoint
 #align affine.triangle.orthocenter Affine.Triangle.orthocenter
+-/
 
+#print Affine.Triangle.orthocenter_eq_mongePoint /-
 /-- The orthocenter equals the Monge point. -/
 theorem orthocenter_eq_mongePoint (t : Triangle ℝ P) : t.orthocenter = t.mongePoint :=
   rfl
 #align affine.triangle.orthocenter_eq_monge_point Affine.Triangle.orthocenter_eq_mongePoint
+-/
 
+#print Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter /-
 /-- The position of the orthocenter in relation to the circumcenter
 and centroid. -/
 theorem orthocenter_eq_smul_vsub_vadd_circumcenter (t : Triangle ℝ P) :
@@ -479,19 +536,25 @@ theorem orthocenter_eq_smul_vsub_vadd_circumcenter (t : Triangle ℝ P) :
   rw [orthocenter_eq_monge_point, monge_point_eq_smul_vsub_vadd_circumcenter]
   norm_num
 #align affine.triangle.orthocenter_eq_smul_vsub_vadd_circumcenter Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter
+-/
 
+#print Affine.Triangle.orthocenter_mem_affineSpan /-
 /-- The orthocenter lies in the affine span. -/
 theorem orthocenter_mem_affineSpan (t : Triangle ℝ P) :
     t.orthocenter ∈ affineSpan ℝ (Set.range t.points) :=
   t.mongePoint_mem_affineSpan
 #align affine.triangle.orthocenter_mem_affine_span Affine.Triangle.orthocenter_mem_affineSpan
+-/
 
+#print Affine.Triangle.orthocenter_eq_of_range_eq /-
 /-- Two triangles with the same points have the same orthocenter. -/
 theorem orthocenter_eq_of_range_eq {t₁ t₂ : Triangle ℝ P}
     (h : Set.range t₁.points = Set.range t₂.points) : t₁.orthocenter = t₂.orthocenter :=
   mongePoint_eq_of_range_eq h
 #align affine.triangle.orthocenter_eq_of_range_eq Affine.Triangle.orthocenter_eq_of_range_eq
+-/
 
+#print Affine.Triangle.altitude_eq_mongePlane /-
 /-- In the case of a triangle, altitudes are the same thing as Monge
 planes. -/
 theorem altitude_eq_mongePlane (t : Triangle ℝ P) {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃)
@@ -503,7 +566,9 @@ theorem altitude_eq_mongePlane (t : Triangle ℝ P) {i₁ i₂ i₃ : Fin 3} (h
     coe_singleton, vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_insert i₂ _)]
   simp [h₂₃, Submodule.span_insert_eq_span]
 #align affine.triangle.altitude_eq_monge_plane Affine.Triangle.altitude_eq_mongePlane
+-/
 
+#print Affine.Triangle.orthocenter_mem_altitude /-
 /-- The orthocenter lies in the altitudes. -/
 theorem orthocenter_mem_altitude (t : Triangle ℝ P) {i₁ : Fin 3} : t.orthocenter ∈ t.altitude i₁ :=
   by
@@ -511,7 +576,9 @@ theorem orthocenter_mem_altitude (t : Triangle ℝ P) {i₁ : Fin 3} : t.orthoce
   rw [orthocenter_eq_monge_point, t.altitude_eq_monge_plane h₁₂ h₁₃ h₂₃]
   exact t.monge_point_mem_monge_plane
 #align affine.triangle.orthocenter_mem_altitude Affine.Triangle.orthocenter_mem_altitude
+-/
 
+#print Affine.Triangle.eq_orthocenter_of_forall_mem_altitude /-
 /-- The orthocenter is the only point lying in any two of the
 altitudes. -/
 theorem eq_orthocenter_of_forall_mem_altitude {t : Triangle ℝ P} {i₁ i₂ : Fin 3} {p : P}
@@ -530,7 +597,9 @@ theorem eq_orthocenter_of_forall_mem_altitude {t : Triangle ℝ P} {i₁ i₂ :
     · exact hi₁₂ ▸ h₁
   exact eq_monge_point_of_forall_mem_monge_plane ha
 #align affine.triangle.eq_orthocenter_of_forall_mem_altitude Affine.Triangle.eq_orthocenter_of_forall_mem_altitude
+-/
 
+#print Affine.Triangle.dist_orthocenter_reflection_circumcenter /-
 /-- The distance from the orthocenter to the reflection of the
 circumcenter in a side equals the circumradius. -/
 theorem dist_orthocenter_reflection_circumcenter (t : Triangle ℝ P) {i₁ i₂ : Fin 3} (h : i₁ ≠ i₂) :
@@ -551,7 +620,9 @@ theorem dist_orthocenter_reflection_circumcenter (t : Triangle ℝ P) {i₁ i₂
   simp [hi₃₁, hi₃₂]
   norm_num
 #align affine.triangle.dist_orthocenter_reflection_circumcenter Affine.Triangle.dist_orthocenter_reflection_circumcenter
+-/
 
+#print Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset /-
 /-- The distance from the orthocenter to the reflection of the
 circumcenter in a side equals the circumradius, variant using a
 `finset`. -/
@@ -562,7 +633,9 @@ theorem dist_orthocenter_reflection_circumcenter_finset (t : Triangle ℝ P) {i
       t.circumradius :=
   by convert dist_orthocenter_reflection_circumcenter _ h; simp
 #align affine.triangle.dist_orthocenter_reflection_circumcenter_finset Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset
+-/
 
+#print Affine.Triangle.affineSpan_orthocenter_point_le_altitude /-
 /-- The affine span of the orthocenter and a vertex is contained in
 the altitude. -/
 theorem affineSpan_orthocenter_point_le_altitude (t : Triangle ℝ P) (i : Fin 3) :
@@ -572,7 +645,9 @@ theorem affineSpan_orthocenter_point_le_altitude (t : Triangle ℝ P) (i : Fin 3
   rw [Set.insert_subset_iff, Set.singleton_subset_iff]
   exact ⟨t.orthocenter_mem_altitude, t.mem_altitude i⟩
 #align affine.triangle.affine_span_orthocenter_point_le_altitude Affine.Triangle.affineSpan_orthocenter_point_le_altitude
+-/
 
+#print Affine.Triangle.altitude_replace_orthocenter_eq_affineSpan /-
 /-- Suppose we are given a triangle `t₁`, and replace one of its
 vertices by its orthocenter, yielding triangle `t₂` (with vertices not
 necessarily listed in the same order).  Then an altitude of `t₂` from
@@ -615,7 +690,9 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
   rw [hui, Finset.coe_insert, Finset.coe_singleton, Set.image_insert_eq, Set.image_singleton]
   refine' vsub_mem_vectorSpan ℝ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
 #align affine.triangle.altitude_replace_orthocenter_eq_affine_span Affine.Triangle.altitude_replace_orthocenter_eq_affineSpan
+-/
 
+#print Affine.Triangle.orthocenter_replace_orthocenter_eq_point /-
 /-- Suppose we are given a triangle `t₁`, and replace one of its
 vertices by its orthocenter, yielding triangle `t₂` (with vertices not
 necessarily listed in the same order).  Then the orthocenter of `t₂`
@@ -632,6 +709,7 @@ theorem orthocenter_replace_orthocenter_eq_point {t₁ t₂ : Triangle ℝ P} {i
         h₂]
     exact mem_affineSpan ℝ (Set.mem_insert _ _)
 #align affine.triangle.orthocenter_replace_orthocenter_eq_point Affine.Triangle.orthocenter_replace_orthocenter_eq_point
+-/
 
 end Triangle
 
@@ -644,13 +722,16 @@ open Affine AffineSubspace FiniteDimensional
 variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
+#print EuclideanGeometry.OrthocentricSystem /-
 /-- Four points form an orthocentric system if they consist of the
 vertices of a triangle and its orthocenter. -/
 def OrthocentricSystem (s : Set P) : Prop :=
   ∃ t : Triangle ℝ P,
     t.orthocenter ∉ Set.range t.points ∧ s = insert t.orthocenter (Set.range t.points)
 #align euclidean_geometry.orthocentric_system EuclideanGeometry.OrthocentricSystem
+-/
 
+#print EuclideanGeometry.exists_of_range_subset_orthocentricSystem /-
 /-- This is an auxiliary lemma giving information about the relation
 of two triangles in an orthocentric system; it abstracts some
 reasoning, with no geometric content, that is common to some other
@@ -659,7 +740,7 @@ and we are given three points `p` in the orthocentric system.  Then
 either we can find indices `i₁`, `i₂` and `i₃` for `p` such that `p
 i₁` is the orthocenter of `t` and `p i₂` and `p i₃` are points `j₂`
 and `j₃` of `t`, or `p` has the same points as `t`. -/
-theorem exists_of_range_subset_orthocentric_system {t : Triangle ℝ P}
+theorem exists_of_range_subset_orthocentricSystem {t : Triangle ℝ P}
     (ho : t.orthocenter ∉ Set.range t.points) {p : Fin 3 → P}
     (hps : Set.range p ⊆ insert t.orthocenter (Set.range t.points)) (hpi : Function.Injective p) :
     (∃ i₁ i₂ i₃ j₂ j₃ : Fin 3,
@@ -695,8 +776,10 @@ theorem exists_of_range_subset_orthocentric_system {t : Triangle ℝ P}
     rw [Set.insert_diff_self_of_not_mem ho] at hs 
     refine' Set.eq_of_subset_of_card_le hs _
     rw [Set.card_range_of_injective hpi, Set.card_range_of_injective t.independent.injective]
-#align euclidean_geometry.exists_of_range_subset_orthocentric_system EuclideanGeometry.exists_of_range_subset_orthocentric_system
+#align euclidean_geometry.exists_of_range_subset_orthocentric_system EuclideanGeometry.exists_of_range_subset_orthocentricSystem
+-/
 
+#print EuclideanGeometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter /-
 /-- For any three points in an orthocentric system generated by
 triangle `t`, there is a point in the subspace spanned by the triangle
 from which the distance of all those three points equals the circumradius. -/
@@ -731,7 +814,9 @@ theorem exists_dist_eq_circumradius_of_subset_insert_orthocenter {t : Triangle 
     rcases hp₁ with ⟨i, rfl⟩
     exact t.dist_circumcenter_eq_circumradius _
 #align euclidean_geometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter EuclideanGeometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter
+-/
 
+#print EuclideanGeometry.OrthocentricSystem.affineIndependent /-
 /-- Any three points in an orthocentric system are affinely independent. -/
 theorem OrthocentricSystem.affineIndependent {s : Set P} (ho : OrthocentricSystem s) {p : Fin 3 → P}
     (hps : Set.range p ⊆ s) (hpi : Function.Injective p) : AffineIndependent ℝ p :=
@@ -741,7 +826,9 @@ theorem OrthocentricSystem.affineIndependent {s : Set P} (ho : OrthocentricSyste
   rcases exists_dist_eq_circumradius_of_subset_insert_orthocenter hto hps hpi with ⟨c, hcs, hc⟩
   exact cospherical.affine_independent ⟨c, t.circumradius, hc⟩ Set.Subset.rfl hpi
 #align euclidean_geometry.orthocentric_system.affine_independent EuclideanGeometry.OrthocentricSystem.affineIndependent
+-/
 
+#print EuclideanGeometry.affineSpan_of_orthocentricSystem /-
 /-- Any three points in an orthocentric system span the same subspace
 as the whole orthocentric system. -/
 theorem affineSpan_of_orthocentricSystem {s : Set P} (ho : OrthocentricSystem s) {p : Fin 3 → P}
@@ -761,7 +848,9 @@ theorem affineSpan_of_orthocentricSystem {s : Set P} (ho : OrthocentricSystem s)
   rw [hs, direction_affineSpan, direction_affineSpan, ha.finrank_vector_span (Fintype.card_fin _),
     t.independent.finrank_vector_span (Fintype.card_fin _)]
 #align euclidean_geometry.affine_span_of_orthocentric_system EuclideanGeometry.affineSpan_of_orthocentricSystem
+-/
 
+#print EuclideanGeometry.OrthocentricSystem.exists_circumradius_eq /-
 /-- All triangles in an orthocentric system have the same circumradius. -/
 theorem OrthocentricSystem.exists_circumradius_eq {s : Set P} (ho : OrthocentricSystem s) :
     ∃ r : ℝ, ∀ t : Triangle ℝ P, Set.range t.points ⊆ s → t.circumradius = r :=
@@ -782,7 +871,9 @@ theorem OrthocentricSystem.exists_circumradius_eq {s : Set P} (ho : Orthocentric
     affine_span_of_orthocentric_system ⟨t, hto, hts⟩ ht₂s t₂.independent.injective] at hc 
   exact (t₂.eq_circumradius_of_dist_eq hc h).symm
 #align euclidean_geometry.orthocentric_system.exists_circumradius_eq EuclideanGeometry.OrthocentricSystem.exists_circumradius_eq
+-/
 
+#print EuclideanGeometry.OrthocentricSystem.eq_insert_orthocenter /-
 /-- Given any triangle in an orthocentric system, the fourth point is
 its orthocenter. -/
 theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricSystem s)
@@ -809,6 +900,7 @@ theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricS
     convert ht₀s using 2
     exact triangle.orthocenter_eq_of_range_eq hs
 #align euclidean_geometry.orthocentric_system.eq_insert_orthocenter EuclideanGeometry.OrthocentricSystem.eq_insert_orthocenter
+-/
 
 end EuclideanGeometry
 

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

@@ -569,7 +569,7 @@ theorem affineSpan_orthocenter_point_le_altitude (t : Triangle ℝ P) (i : Fin 3
     line[ℝ, t.orthocenter, t.points i] ≤ t.altitude i :=
   by
   refine' span_points_subset_coe_of_subset_coe _
-  rw [Set.insert_subset, Set.singleton_subset_iff]
+  rw [Set.insert_subset_iff, Set.singleton_subset_iff]
   exact ⟨t.orthocenter_mem_altitude, t.mem_altitude i⟩
 #align affine.triangle.affine_span_orthocenter_point_le_altitude Affine.Triangle.affineSpan_orthocenter_point_le_altitude
 
@@ -596,7 +596,7 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
     · have hu : (Finset.univ : Finset (Fin 3)) = {j₁, j₂, j₃} := by clear h₁ h₂ h₃; decide!
       rw [← Set.image_univ, ← Finset.coe_univ, hu, Finset.coe_insert, Finset.coe_insert,
         Finset.coe_singleton, Set.image_insert_eq, Set.image_insert_eq, Set.image_singleton, h₁, h₂,
-        h₃, Set.insert_subset, Set.insert_subset, Set.singleton_subset_iff]
+        h₃, Set.insert_subset_iff, Set.insert_subset_iff, Set.singleton_subset_iff]
       exact
         ⟨t₁.orthocenter_mem_affine_span, mem_affineSpan ℝ (Set.mem_range_self _),
           mem_affineSpan ℝ (Set.mem_range_self _)⟩

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

@@ -69,8 +69,6 @@ open Finset AffineSubspace EuclideanGeometry PointsWithCircumcenterIndex
 variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
-include V
-
 /-- The Monge point of a simplex (in 2 or more dimensions) is a
 generalization of the orthocenter of a triangle.  It is defined to be
 the intersection of the Monge planes, where a Monge plane is the
@@ -113,8 +111,6 @@ theorem mongePoint_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex ℝ P n}
     circumcenter_eq_of_range_eq h]
 #align affine.simplex.monge_point_eq_of_range_eq Affine.Simplex.mongePoint_eq_of_range_eq
 
-omit V
-
 /-- The weights for the Monge point of an (n+2)-simplex, in terms of
 `points_with_circumcenter`. -/
 def mongePointWeightsWithCircumcenter (n : ℕ) : PointsWithCircumcenterIndex (n + 2) → ℝ
@@ -134,8 +130,6 @@ theorem sum_mongePointWeightsWithCircumcenter (n : ℕ) :
   ring
 #align affine.simplex.sum_monge_point_weights_with_circumcenter Affine.Simplex.sum_mongePointWeightsWithCircumcenter
 
-include V
-
 /-- The Monge point of an (n+2)-simplex, in terms of
 `points_with_circumcenter`. -/
 theorem mongePoint_eq_affineCombination_of_pointsWithCircumcenter {n : ℕ}
@@ -162,8 +156,6 @@ theorem mongePoint_eq_affineCombination_of_pointsWithCircumcenter {n : ℕ}
     ring
 #align affine.simplex.monge_point_eq_affine_combination_of_points_with_circumcenter Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter
 
-omit V
-
 /-- The weights for the Monge point of an (n+2)-simplex, minus the
 centroid of an n-dimensional face, in terms of
 `points_with_circumcenter`.  This definition is only valid when `i₁ ≠ i₂`. -/
@@ -205,8 +197,6 @@ theorem sum_mongePointVsubFaceCentroidWeightsWithCircumcenter {n : ℕ} {i₁ i
   simp [← card_pos, card_compl, h]
 #align affine.simplex.sum_monge_point_vsub_face_centroid_weights_with_circumcenter Affine.Simplex.sum_mongePointVsubFaceCentroidWeightsWithCircumcenter
 
-include V
-
 /-- The Monge point of an (n+2)-simplex, minus the centroid of an
 n-dimensional face, in terms of `points_with_circumcenter`. -/
 theorem mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter {n : ℕ}
@@ -467,8 +457,6 @@ open EuclideanGeometry Finset Simplex AffineSubspace FiniteDimensional
 variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
-include V
-
 /-- The orthocenter of a triangle is the intersection of its
 altitudes.  It is defined here as the 2-dimensional case of the
 Monge point. -/
@@ -656,8 +644,6 @@ open Affine AffineSubspace FiniteDimensional
 variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
-include V
-
 /-- Four points form an orthocentric system if they consist of the
 vertices of a triangle and its orthocenter. -/
 def OrthocentricSystem (s : Set P) : Prop :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -125,7 +125,7 @@ def mongePointWeightsWithCircumcenter (n : ℕ) : PointsWithCircumcenterIndex (n
 /-- `monge_point_weights_with_circumcenter` sums to 1. -/
 @[simp]
 theorem sum_mongePointWeightsWithCircumcenter (n : ℕ) :
-    (∑ i, mongePointWeightsWithCircumcenter n i) = 1 :=
+    ∑ i, mongePointWeightsWithCircumcenter n i = 1 :=
   by
   simp_rw [sum_points_with_circumcenter, monge_point_weights_with_circumcenter, sum_const, card_fin,
     nsmul_eq_mul]
@@ -197,7 +197,7 @@ theorem mongePointVsubFaceCentroidWeightsWithCircumcenter_eq_sub {n : ℕ} {i₁
 /-- `monge_point_vsub_face_centroid_weights_with_circumcenter` sums to 0. -/
 @[simp]
 theorem sum_mongePointVsubFaceCentroidWeightsWithCircumcenter {n : ℕ} {i₁ i₂ : Fin (n + 3)}
-    (h : i₁ ≠ i₂) : (∑ i, mongePointVsubFaceCentroidWeightsWithCircumcenter i₁ i₂ i) = 0 :=
+    (h : i₁ ≠ i₂) : ∑ i, mongePointVsubFaceCentroidWeightsWithCircumcenter i₁ i₂ i = 0 :=
   by
   rw [monge_point_vsub_face_centroid_weights_with_circumcenter_eq_sub h]
   simp_rw [Pi.sub_apply, sum_sub_distrib, sum_monge_point_weights_with_circumcenter]
@@ -233,9 +233,8 @@ theorem inner_mongePoint_vsub_face_centroid_vsub {n : ℕ} (s : Simplex ℝ P (n
   · simp [h]
   simp_rw [monge_point_vsub_face_centroid_eq_weighted_vsub_of_points_with_circumcenter s h,
     point_eq_affine_combination_of_points_with_circumcenter, affine_combination_vsub]
-  have hs :
-    (∑ i, (point_weights_with_circumcenter i₁ - point_weights_with_circumcenter i₂) i) = 0 := by
-    simp
+  have hs : ∑ i, (point_weights_with_circumcenter i₁ - point_weights_with_circumcenter i₂) i = 0 :=
+    by simp
   rw [inner_weighted_vsub _ (sum_monge_point_vsub_face_centroid_weights_with_circumcenter h) _ hs,
     sum_points_with_circumcenter, points_with_circumcenter_eq_circumcenter]
   simp only [monge_point_vsub_face_centroid_weights_with_circumcenter,

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

@@ -334,7 +334,7 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
     by
     rw [Submodule.mem_iInf]
     exact fun i => (Submodule.mem_inf.1 (h' i i.property)).1
-  rw [Submodule.iInf_orthogonal, ← Submodule.span_iUnion] at hi
+  rw [Submodule.iInf_orthogonal, ← Submodule.span_iUnion] at hi 
   have hu :
     (⋃ i : { i // i₁ ≠ i }, ({s.points i₁ -ᵥ s.points i} : Set V)) =
       (· -ᵥ ·) (s.points i₁) '' (s.points '' (Set.univ \ {i₁})) :=
@@ -347,7 +347,7 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
       use i, ⟨Set.mem_univ _, i.property.symm⟩
     · rintro ⟨i, ⟨hiu, hi⟩, rfl⟩
       use ⟨i, hi.symm⟩, rfl
-  rw [hu, ← vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_univ _), Set.image_univ] at hi
+  rw [hu, ← vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_univ _), Set.image_univ] at hi 
   have hv : p -ᵥ s.monge_point ∈ vectorSpan ℝ (Set.range s.points) :=
     by
     let s₁ : Finset (Fin (n + 3)) := univ.erase i₁
@@ -439,14 +439,14 @@ theorem affineSpan_pair_eq_altitude_iff {n : ℕ} (s : Simplex ℝ P (n + 1)) (i
   · intro h
     constructor
     · intro heq
-      rw [HEq, Set.pair_eq_singleton, vectorSpan_singleton] at h
+      rw [HEq, Set.pair_eq_singleton, vectorSpan_singleton] at h 
       have hd : finrank ℝ (s.altitude i).direction = 0 := by rw [← h, finrank_bot]
       simpa using hd
     · rw [← Submodule.mem_inf, _root_.inf_comm, ← direction_altitude, ← h]
       exact
         vsub_mem_vectorSpan ℝ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
   · rintro ⟨hne, h⟩
-    rw [← Submodule.mem_inf, _root_.inf_comm, ← direction_altitude] at h
+    rw [← Submodule.mem_inf, _root_.inf_comm, ← direction_altitude] at h 
     rw [vectorSpan_eq_span_vsub_set_left_ne ℝ (Set.mem_insert _ _),
       Set.insert_diff_of_mem _ (Set.mem_singleton _),
       Set.diff_singleton_eq_self fun h => hne (Set.mem_singleton_iff.1 h), Set.image_singleton]
@@ -531,8 +531,8 @@ theorem eq_orthocenter_of_forall_mem_altitude {t : Triangle ℝ P} {i₁ i₂ :
     (h₁₂ : i₁ ≠ i₂) (h₁ : p ∈ t.altitude i₁) (h₂ : p ∈ t.altitude i₂) : p = t.orthocenter :=
   by
   obtain ⟨i₃, h₂₃, h₁₃⟩ : ∃ i₃, i₂ ≠ i₃ ∧ i₁ ≠ i₃ := by clear h₁ h₂; decide!
-  rw [t.altitude_eq_monge_plane h₁₃ h₁₂ h₂₃.symm] at h₁
-  rw [t.altitude_eq_monge_plane h₂₃ h₁₂.symm h₁₃.symm] at h₂
+  rw [t.altitude_eq_monge_plane h₁₃ h₁₂ h₂₃.symm] at h₁ 
+  rw [t.altitude_eq_monge_plane h₂₃ h₁₂.symm h₁₃.symm] at h₂ 
   rw [orthocenter_eq_monge_point]
   have ha : ∀ i, i₃ ≠ i → p ∈ t.monge_plane i₃ i :=
     by
@@ -702,12 +702,12 @@ theorem exists_of_range_subset_orthocentric_system {t : Triangle ℝ P}
     rcases h i₃ h₁₃ with ⟨j₃, h₃⟩
     have hj₂₃ : j₂ ≠ j₃ := by
       intro he
-      rw [he, h₃] at h₂
+      rw [he, h₃] at h₂ 
       exact h₂₃.symm (hpi h₂)
     exact ⟨i₁, i₂, i₃, j₂, j₃, h₁₂, h₁₃, h₂₃, h₁₂₃, h₁, hj₂₃, h₂, h₃⟩
   · right
     have hs := Set.subset_diff_singleton hps h
-    rw [Set.insert_diff_self_of_not_mem ho] at hs
+    rw [Set.insert_diff_self_of_not_mem ho] at hs 
     refine' Set.eq_of_subset_of_card_le hs _
     rw [Set.card_range_of_injective hpi, Set.card_range_of_injective t.independent.injective]
 #align euclidean_geometry.exists_of_range_subset_orthocentric_system EuclideanGeometry.exists_of_range_subset_orthocentric_system
@@ -742,7 +742,7 @@ theorem exists_dist_eq_circumradius_of_subset_insert_orthocenter {t : Triangle 
       exact t.dist_circumcenter_eq_circumradius _
   · use t.circumcenter, t.circumcenter_mem_affine_span
     intro p₁ hp₁
-    rw [hs] at hp₁
+    rw [hs] at hp₁ 
     rcases hp₁ with ⟨i, rfl⟩
     exact t.dist_circumcenter_eq_circumradius _
 #align euclidean_geometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter EuclideanGeometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter
@@ -752,7 +752,7 @@ theorem OrthocentricSystem.affineIndependent {s : Set P} (ho : OrthocentricSyste
     (hps : Set.range p ⊆ s) (hpi : Function.Injective p) : AffineIndependent ℝ p :=
   by
   rcases ho with ⟨t, hto, hst⟩
-  rw [hst] at hps
+  rw [hst] at hps 
   rcases exists_dist_eq_circumradius_of_subset_insert_orthocenter hto hps hpi with ⟨c, hcs, hc⟩
   exact cospherical.affine_independent ⟨c, t.circumradius, hc⟩ Set.Subset.rfl hpi
 #align euclidean_geometry.orthocentric_system.affine_independent EuclideanGeometry.OrthocentricSystem.affineIndependent
@@ -785,16 +785,16 @@ theorem OrthocentricSystem.exists_circumradius_eq {s : Set P} (ho : Orthocentric
   use t.circumradius
   intro t₂ ht₂
   have ht₂s := ht₂
-  rw [hts] at ht₂
+  rw [hts] at ht₂ 
   rcases exists_dist_eq_circumradius_of_subset_insert_orthocenter hto ht₂
       t₂.independent.injective with
     ⟨c, hc, h⟩
-  rw [Set.forall_range_iff] at h
+  rw [Set.forall_range_iff] at h 
   have hs : Set.range t.points ⊆ s := by
     rw [hts]
     exact Set.subset_insert _ _
   rw [affine_span_of_orthocentric_system ⟨t, hto, hts⟩ hs t.independent.injective, ←
-    affine_span_of_orthocentric_system ⟨t, hto, hts⟩ ht₂s t₂.independent.injective] at hc
+    affine_span_of_orthocentric_system ⟨t, hto, hts⟩ ht₂s t₂.independent.injective] at hc 
   exact (t₂.eq_circumradius_of_dist_eq hc h).symm
 #align euclidean_geometry.orthocentric_system.exists_circumradius_eq EuclideanGeometry.OrthocentricSystem.exists_circumradius_eq
 
@@ -805,7 +805,7 @@ theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricS
     s = insert t.orthocenter (Set.range t.points) :=
   by
   rcases ho with ⟨t₀, ht₀o, ht₀s⟩
-  rw [ht₀s] at ht
+  rw [ht₀s] at ht 
   rcases exists_of_range_subset_orthocentric_system ht₀o ht t.independent.injective with
     (⟨i₁, i₂, i₃, j₂, j₃, h₁₂, h₁₃, h₂₃, h₁₂₃, h₁, hj₂₃, h₂, h₃⟩ | hs)
   · obtain ⟨j₁, hj₁₂, hj₁₃, hj₁₂₃⟩ :

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

@@ -54,11 +54,11 @@ generalization, the Monge point of a simplex.
 
 noncomputable section
 
-open BigOperators
+open scoped BigOperators
 
-open Classical
+open scoped Classical
 
-open RealInnerProductSpace
+open scoped RealInnerProductSpace
 
 namespace Affine
 

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

@@ -244,9 +244,7 @@ theorem inner_mongePoint_vsub_face_centroid_vsub {n : ℕ} (s : Simplex ℝ P (n
   have hfs : ∀ i : Fin (n + 3), i ∉ fs → i ≠ i₁ ∧ i ≠ i₂ :=
     by
     intro i hi
-    constructor <;>
-      · intro hj
-        simpa [← hj] using hi
+    constructor <;> · intro hj; simpa [← hj] using hi
   rw [← sum_subset fs.subset_univ _]
   · simp_rw [sum_points_with_circumcenter, points_with_circumcenter_eq_circumcenter,
       points_with_circumcenter_point, Pi.sub_apply, point_weights_with_circumcenter]
@@ -418,10 +416,7 @@ theorem finrank_direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fi
   have h :=
     Submodule.finrank_add_inf_finrank_orthogonal
       (vectorSpan_mono ℝ (Set.image_subset_range s.points ↑(univ.erase i)))
-  have hc : card (univ.erase i) = n + 1 :=
-    by
-    rw [card_erase_of_mem (mem_univ _)]
-    simp
+  have hc : card (univ.erase i) = n + 1 := by rw [card_erase_of_mem (mem_univ _)]; simp
   refine' add_left_cancel (trans h _)
   rw [s.independent.finrank_vector_span (Fintype.card_fin _), ← Finset.coe_image,
     s.independent.finrank_vector_span_image_finset hc]
@@ -535,19 +530,14 @@ altitudes. -/
 theorem eq_orthocenter_of_forall_mem_altitude {t : Triangle ℝ P} {i₁ i₂ : Fin 3} {p : P}
     (h₁₂ : i₁ ≠ i₂) (h₁ : p ∈ t.altitude i₁) (h₂ : p ∈ t.altitude i₂) : p = t.orthocenter :=
   by
-  obtain ⟨i₃, h₂₃, h₁₃⟩ : ∃ i₃, i₂ ≠ i₃ ∧ i₁ ≠ i₃ :=
-    by
-    clear h₁ h₂
-    decide!
+  obtain ⟨i₃, h₂₃, h₁₃⟩ : ∃ i₃, i₂ ≠ i₃ ∧ i₁ ≠ i₃ := by clear h₁ h₂; decide!
   rw [t.altitude_eq_monge_plane h₁₃ h₁₂ h₂₃.symm] at h₁
   rw [t.altitude_eq_monge_plane h₂₃ h₁₂.symm h₁₃.symm] at h₂
   rw [orthocenter_eq_monge_point]
   have ha : ∀ i, i₃ ≠ i → p ∈ t.monge_plane i₃ i :=
     by
     intro i hi
-    have hi₁₂ : i₁ = i ∨ i₂ = i := by
-      clear h₁ h₂
-      decide!
+    have hi₁₂ : i₁ = i ∨ i₂ = i := by clear h₁ h₂; decide!
     cases hi₁₂
     · exact hi₁₂ ▸ h₂
     · exact hi₁₂ ▸ h₁
@@ -583,9 +573,7 @@ theorem dist_orthocenter_reflection_circumcenter_finset (t : Triangle ℝ P) {i
     dist t.orthocenter
         (reflection (affineSpan ℝ (t.points '' ↑({i₁, i₂} : Finset (Fin 3)))) t.circumcenter) =
       t.circumradius :=
-  by
-  convert dist_orthocenter_reflection_circumcenter _ h
-  simp
+  by convert dist_orthocenter_reflection_circumcenter _ h; simp
 #align affine.triangle.dist_orthocenter_reflection_circumcenter_finset Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset
 
 /-- The affine span of the orthocenter and a vertex is contained in
@@ -618,10 +606,7 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
       ext_of_direction_eq _
         ⟨t₁.points i₃, mem_affineSpan ℝ ⟨j₃, h₃⟩, mem_affineSpan ℝ (Set.mem_range_self _)⟩
     refine' eq_of_le_of_finrank_eq (direction_le (span_points_subset_coe_of_subset_coe _)) _
-    · have hu : (Finset.univ : Finset (Fin 3)) = {j₁, j₂, j₃} :=
-        by
-        clear h₁ h₂ h₃
-        decide!
+    · have hu : (Finset.univ : Finset (Fin 3)) = {j₁, j₂, j₃} := by clear h₁ h₂ h₃; decide!
       rw [← Set.image_univ, ← Finset.coe_univ, hu, Finset.coe_insert, Finset.coe_insert,
         Finset.coe_singleton, Set.image_insert_eq, Set.image_insert_eq, Set.image_singleton, h₁, h₂,
         h₃, Set.insert_subset, Set.insert_subset, Set.singleton_subset_iff]
@@ -634,18 +619,12 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
         t₂.independent.finrank_vector_span (Fintype.card_fin _)]
   rw [he]
   use mem_affineSpan ℝ (Set.mem_range_self _)
-  have hu : finset.univ.erase j₂ = {j₁, j₃} :=
-    by
-    clear h₁ h₂ h₃
-    decide!
+  have hu : finset.univ.erase j₂ = {j₁, j₃} := by clear h₁ h₂ h₃; decide!
   rw [hu, Finset.coe_insert, Finset.coe_singleton, Set.image_insert_eq, Set.image_singleton, h₁, h₃]
   have hle : (t₁.altitude i₃).directionᗮ ≤ line[ℝ, t₁.orthocenter, t₁.points i₃].directionᗮ :=
     Submodule.orthogonal_le (direction_le (affine_span_orthocenter_point_le_altitude _ _))
   refine' hle ((t₁.vector_span_is_ortho_altitude_direction i₃) _)
-  have hui : finset.univ.erase i₃ = {i₁, i₂} :=
-    by
-    clear hle h₂ h₃
-    decide!
+  have hui : finset.univ.erase i₃ = {i₁, i₂} := by clear hle h₂ h₃; decide!
   rw [hui, Finset.coe_insert, Finset.coe_singleton, Set.image_insert_eq, Set.image_singleton]
   refine' vsub_mem_vectorSpan ℝ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
 #align affine.triangle.altitude_replace_orthocenter_eq_affine_span Affine.Triangle.altitude_replace_orthocenter_eq_affineSpan
@@ -710,10 +689,8 @@ theorem exists_of_range_subset_orthocentric_system {t : Triangle ℝ P}
   · left
     rcases h with ⟨i₁, h₁⟩
     obtain ⟨i₂, i₃, h₁₂, h₁₃, h₂₃, h₁₂₃⟩ :
-      ∃ i₂ i₃ : Fin 3, i₁ ≠ i₂ ∧ i₁ ≠ i₃ ∧ i₂ ≠ i₃ ∧ ∀ i : Fin 3, i = i₁ ∨ i = i₂ ∨ i = i₃ :=
-      by
-      clear h₁
-      decide!
+      ∃ i₂ i₃ : Fin 3, i₁ ≠ i₂ ∧ i₁ ≠ i₃ ∧ i₂ ≠ i₃ ∧ ∀ i : Fin 3, i = i₁ ∨ i = i₂ ∨ i = i₃ := by
+      clear h₁; decide!
     have h : ∀ i, i₁ ≠ i → ∃ j : Fin 3, t.points j = p i :=
       by
       intro i hi
@@ -793,10 +770,7 @@ theorem affineSpan_of_orthocentricSystem {s : Set P} (ho : OrthocentricSystem s)
   refine'
     ext_of_direction_eq _
       ⟨p 0, mem_affineSpan ℝ (Set.mem_range_self _), mem_affineSpan ℝ (hps (Set.mem_range_self _))⟩
-  have hfd : FiniteDimensional ℝ (affineSpan ℝ s).direction :=
-    by
-    rw [hs]
-    infer_instance
+  have hfd : FiniteDimensional ℝ (affineSpan ℝ s).direction := by rw [hs]; infer_instance
   haveI := hfd
   refine' eq_of_le_of_finrank_eq (direction_le (affineSpan_mono ℝ hps)) _
   rw [hs, direction_affineSpan, direction_affineSpan, ha.finrank_vector_span (Fintype.card_fin _),
@@ -835,19 +809,11 @@ theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricS
   rcases exists_of_range_subset_orthocentric_system ht₀o ht t.independent.injective with
     (⟨i₁, i₂, i₃, j₂, j₃, h₁₂, h₁₃, h₂₃, h₁₂₃, h₁, hj₂₃, h₂, h₃⟩ | hs)
   · obtain ⟨j₁, hj₁₂, hj₁₃, hj₁₂₃⟩ :
-      ∃ j₁ : Fin 3, j₁ ≠ j₂ ∧ j₁ ≠ j₃ ∧ ∀ j : Fin 3, j = j₁ ∨ j = j₂ ∨ j = j₃ :=
-      by
-      clear h₂ h₃
+      ∃ j₁ : Fin 3, j₁ ≠ j₂ ∧ j₁ ≠ j₃ ∧ ∀ j : Fin 3, j = j₁ ∨ j = j₂ ∨ j = j₃ := by clear h₂ h₃;
       decide!
     suffices h : t₀.points j₁ = t.orthocenter
-    · have hui : (Set.univ : Set (Fin 3)) = {i₁, i₂, i₃} :=
-        by
-        ext x
-        simpa using h₁₂₃ x
-      have huj : (Set.univ : Set (Fin 3)) = {j₁, j₂, j₃} :=
-        by
-        ext x
-        simpa using hj₁₂₃ x
+    · have hui : (Set.univ : Set (Fin 3)) = {i₁, i₂, i₃} := by ext x; simpa using h₁₂₃ x
+      have huj : (Set.univ : Set (Fin 3)) = {j₁, j₂, j₃} := by ext x; simpa using hj₁₂₃ x
       rw [← h, ht₀s, ← Set.image_univ, huj, ← Set.image_univ, hui]
       simp_rw [Set.image_insert_eq, Set.image_singleton, h₁, ← h₂, ← h₃]
       rw [Set.insert_comm]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -392,12 +392,12 @@ theorem direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2
 
 /-- The vector span of the opposite face lies in the direction
 orthogonal to an altitude. -/
-theorem vectorSpanIsOrthoAltitudeDirection {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
+theorem vectorSpan_isOrtho_altitude_direction {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
     vectorSpan ℝ (s.points '' ↑(Finset.univ.eraseₓ i)) ⟂ (s.altitude i).direction :=
   by
   rw [direction_altitude]
-  exact (Submodule.isOrthoOrthogonalRight _).mono_right inf_le_left
-#align affine.simplex.vector_span_is_ortho_altitude_direction Affine.Simplex.vectorSpanIsOrthoAltitudeDirection
+  exact (Submodule.isOrtho_orthogonal_right _).mono_right inf_le_left
+#align affine.simplex.vector_span_is_ortho_altitude_direction Affine.Simplex.vectorSpan_isOrtho_altitude_direction
 
 open FiniteDimensional
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -334,16 +334,16 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
     exact h i₂ hne
   have hi : p -ᵥ s.monge_point ∈ ⨅ i₂ : { i // i₁ ≠ i }, (ℝ ∙ s.points i₁ -ᵥ s.points i₂)ᗮ :=
     by
-    rw [Submodule.mem_infᵢ]
+    rw [Submodule.mem_iInf]
     exact fun i => (Submodule.mem_inf.1 (h' i i.property)).1
-  rw [Submodule.infᵢ_orthogonal, ← Submodule.span_unionᵢ] at hi
+  rw [Submodule.iInf_orthogonal, ← Submodule.span_iUnion] at hi
   have hu :
     (⋃ i : { i // i₁ ≠ i }, ({s.points i₁ -ᵥ s.points i} : Set V)) =
       (· -ᵥ ·) (s.points i₁) '' (s.points '' (Set.univ \ {i₁})) :=
     by
     rw [Set.image_image]
     ext x
-    simp_rw [Set.mem_unionᵢ, Set.mem_image, Set.mem_singleton_iff, Set.mem_diff_singleton]
+    simp_rw [Set.mem_iUnion, Set.mem_image, Set.mem_singleton_iff, Set.mem_diff_singleton]
     constructor
     · rintro ⟨i, rfl⟩
       use i, ⟨Set.mem_univ _, i.property.symm⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -392,12 +392,12 @@ theorem direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2
 
 /-- The vector span of the opposite face lies in the direction
 orthogonal to an altitude. -/
-theorem vectorSpan_isOrtho_altitude_direction {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
+theorem vectorSpanIsOrthoAltitudeDirection {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
     vectorSpan ℝ (s.points '' ↑(Finset.univ.eraseₓ i)) ⟂ (s.altitude i).direction :=
   by
   rw [direction_altitude]
-  exact (Submodule.isOrtho_orthogonal_right _).mono_right inf_le_left
-#align affine.simplex.vector_span_is_ortho_altitude_direction Affine.Simplex.vectorSpan_isOrtho_altitude_direction
+  exact (Submodule.isOrthoOrthogonalRight _).mono_right inf_le_left
+#align affine.simplex.vector_span_is_ortho_altitude_direction Affine.Simplex.vectorSpanIsOrthoAltitudeDirection
 
 open FiniteDimensional
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

@@ -209,16 +209,16 @@ include V
 
 /-- The Monge point of an (n+2)-simplex, minus the centroid of an
 n-dimensional face, in terms of `points_with_circumcenter`. -/
-theorem mongePoint_vsub_face_centroid_eq_weightedVsub_of_pointsWithCircumcenter {n : ℕ}
+theorem mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter {n : ℕ}
     (s : Simplex ℝ P (n + 2)) {i₁ i₂ : Fin (n + 3)} (h : i₁ ≠ i₂) :
     s.mongePoint -ᵥ ({i₁, i₂}ᶜ : Finset (Fin (n + 3))).centroid ℝ s.points =
-      (univ : Finset (PointsWithCircumcenterIndex (n + 2))).weightedVsub s.pointsWithCircumcenter
+      (univ : Finset (PointsWithCircumcenterIndex (n + 2))).weightedVSub s.pointsWithCircumcenter
         (mongePointVsubFaceCentroidWeightsWithCircumcenter i₁ i₂) :=
   by
   simp_rw [monge_point_eq_affine_combination_of_points_with_circumcenter,
     centroid_eq_affine_combination_of_points_with_circumcenter, affine_combination_vsub,
     monge_point_vsub_face_centroid_weights_with_circumcenter_eq_sub h]
-#align affine.simplex.monge_point_vsub_face_centroid_eq_weighted_vsub_of_points_with_circumcenter Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVsub_of_pointsWithCircumcenter
+#align affine.simplex.monge_point_vsub_face_centroid_eq_weighted_vsub_of_points_with_circumcenter Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter
 
 /-- The Monge point of an (n+2)-simplex, minus the centroid of an
 n-dimensional face, is orthogonal to the difference of the two

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

@@ -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.monge_point
-! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
+! leanprover-community/mathlib commit 1a4df69ca1a9a0e5e26bfe12e2b92814216016d0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -392,15 +392,12 @@ theorem direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2
 
 /-- The vector span of the opposite face lies in the direction
 orthogonal to an altitude. -/
-theorem vectorSpan_le_altitude_direction_orthogonal {n : ℕ} (s : Simplex ℝ P (n + 1))
-    (i : Fin (n + 2)) :
-    vectorSpan ℝ (s.points '' ↑(Finset.univ.eraseₓ i)) ≤ (s.altitude i).directionᗮ :=
+theorem vectorSpan_isOrtho_altitude_direction {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fin (n + 2)) :
+    vectorSpan ℝ (s.points '' ↑(Finset.univ.eraseₓ i)) ⟂ (s.altitude i).direction :=
   by
   rw [direction_altitude]
-  exact
-    le_trans (vectorSpan ℝ (s.points '' ↑(finset.univ.erase i))).le_orthogonal_orthogonal
-      (Submodule.orthogonal_le inf_le_left)
-#align affine.simplex.vector_span_le_altitude_direction_orthogonal Affine.Simplex.vectorSpan_le_altitude_direction_orthogonal
+  exact (Submodule.isOrtho_orthogonal_right _).mono_right inf_le_left
+#align affine.simplex.vector_span_is_ortho_altitude_direction Affine.Simplex.vectorSpan_isOrtho_altitude_direction
 
 open FiniteDimensional
 
@@ -644,7 +641,7 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
   rw [hu, Finset.coe_insert, Finset.coe_singleton, Set.image_insert_eq, Set.image_singleton, h₁, h₃]
   have hle : (t₁.altitude i₃).directionᗮ ≤ line[ℝ, t₁.orthocenter, t₁.points i₃].directionᗮ :=
     Submodule.orthogonal_le (direction_le (affine_span_orthocenter_point_le_altitude _ _))
-  refine' hle ((t₁.vector_span_le_altitude_direction_orthogonal i₃) _)
+  refine' hle ((t₁.vector_span_is_ortho_altitude_direction i₃) _)
   have hui : finset.univ.erase i₃ = {i₁, i₂} :=
     by
     clear hle h₂ h₃

mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976

@@ -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.monge_point
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 2de9c37fa71dde2f1c6feff19876dd6a7b1519f0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -141,7 +141,7 @@ include V
 theorem mongePoint_eq_affineCombination_of_pointsWithCircumcenter {n : ℕ}
     (s : Simplex ℝ P (n + 2)) :
     s.mongePoint =
-      (univ : Finset (PointsWithCircumcenterIndex (n + 2))).affineCombination
+      (univ : Finset (PointsWithCircumcenterIndex (n + 2))).affineCombination ℝ
         s.pointsWithCircumcenter (mongePointWeightsWithCircumcenter n) :=
   by
   rw [monge_point_eq_smul_vsub_vadd_circumcenter,

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.monge_point
-! leanprover-community/mathlib commit beee53c9d7cee320d01aab6d411a28480af4db1e
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -66,7 +66,8 @@ namespace Simplex
 
 open Finset AffineSubspace EuclideanGeometry PointsWithCircumcenterIndex
 
-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
 
@@ -472,7 +473,8 @@ namespace Triangle
 
 open EuclideanGeometry Finset Simplex AffineSubspace FiniteDimensional
 
-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
 
@@ -676,7 +678,8 @@ namespace EuclideanGeometry
 
 open Affine AffineSubspace FiniteDimensional
 
-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

@@ -304,7 +304,7 @@ theorem mongePoint_mem_mongePlane {n : ℕ} (s : Simplex ℝ P (n + 2)) {i₁ i
   refine' ⟨_, s.monge_point_mem_affine_span⟩
   intro v hv
   rcases submodule.mem_span_singleton.mp hv with ⟨r, rfl⟩
-  rw [inner_smul_right, s.inner_monge_point_vsub_face_centroid_vsub, mul_zero]
+  rw [inner_smul_right, s.inner_monge_point_vsub_face_centroid_vsub, MulZeroClass.mul_zero]
 #align affine.simplex.monge_point_mem_monge_plane Affine.Simplex.mongePoint_mem_mongePlane
 
 /-- The direction of a Monge plane. -/

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

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -763,7 +763,7 @@ theorem OrthocentricSystem.exists_circumradius_eq {s : Set P} (ho : Orthocentric
   rcases exists_dist_eq_circumradius_of_subset_insert_orthocenter hto ht₂
       t₂.independent.injective with
     ⟨c, hc, h⟩
-  rw [Set.forall_range_iff] at h
+  rw [Set.forall_mem_range] at h
   have hs : Set.range t.points ⊆ s := by
     rw [hts]
     exact Set.subset_insert _ _

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

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

@@ -226,7 +226,7 @@ theorem inner_mongePoint_vsub_face_centroid_vsub {n : ℕ} (s : Simplex ℝ P (n
   let fs : Finset (Fin (n + 3)) := {i₁, i₂}
   have hfs : ∀ i : Fin (n + 3), i ∉ fs → i ≠ i₁ ∧ i ≠ i₂ := by
     intro i hi
-    constructor <;> · intro hj; simp [← hj] at hi
+    constructor <;> · intro hj; simp [fs, ← hj] at hi
   rw [← sum_subset fs.subset_univ _]
   · simp_rw [sum_pointsWithCircumcenter, pointsWithCircumcenter_eq_circumcenter,
       pointsWithCircumcenter_point, Pi.sub_apply, pointWeightsWithCircumcenter]
@@ -323,7 +323,7 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
   rw [hu, ← vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_univ _), Set.image_univ] at hi
   have hv : p -ᵥ s.mongePoint ∈ vectorSpan ℝ (Set.range s.points) := by
     let s₁ : Finset (Fin (n + 3)) := univ.erase i₁
-    obtain ⟨i₂, h₂⟩ := card_pos.1 (show 0 < card s₁ by simp [card_erase_of_mem])
+    obtain ⟨i₂, h₂⟩ := card_pos.1 (show 0 < card s₁ by simp [s₁, card_erase_of_mem])
     have h₁₂ : i₁ ≠ i₂ := (ne_of_mem_erase h₂).symm
     exact (Submodule.mem_inf.1 (h' i₂ h₁₂)).2
   exact Submodule.disjoint_def.1 (vectorSpan ℝ (Set.range s.points)).orthogonal_disjoint _ hv hi
@@ -483,9 +483,6 @@ theorem altitude_eq_mongePlane (t : Triangle ℝ P) {i₁ i₂ i₃ : Fin 3} (h
   rw [mongePlane_def, altitude_def, direction_affineSpan, hs, he, centroid_singleton, coe_insert,
     coe_singleton, vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_insert i₂ _)]
   simp [h₂₃, Submodule.span_insert_eq_span]
-  -- Porting note: this didn't need the `congr` and the `fin_cases`
-  congr
-  fin_cases i₂ <;> fin_cases i₃ <;> simp (config := {decide := true}) at h₂₃ ⊢
 #align affine.triangle.altitude_eq_monge_plane Affine.Triangle.altitude_eq_mongePlane
 
 /-- The orthocenter lies in the altitudes. -/

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -483,7 +483,7 @@ theorem altitude_eq_mongePlane (t : Triangle ℝ P) {i₁ i₂ i₃ : Fin 3} (h
   rw [mongePlane_def, altitude_def, direction_affineSpan, hs, he, centroid_singleton, coe_insert,
     coe_singleton, vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_insert i₂ _)]
   simp [h₂₃, Submodule.span_insert_eq_span]
-  -- porting note: this didn't need the `congr` and the `fin_cases`
+  -- Porting note: this didn't need the `congr` and the `fin_cases`
   congr
   fin_cases i₂ <;> fin_cases i₃ <;> simp (config := {decide := true}) at h₂₃ ⊢
 #align affine.triangle.altitude_eq_monge_plane Affine.Triangle.altitude_eq_mongePlane

Classifies by adding issue number #11043 to porting notes claiming:

was decide!

@@ -473,11 +473,11 @@ planes. -/
 theorem altitude_eq_mongePlane (t : Triangle ℝ P) {i₁ i₂ i₃ : Fin 3} (h₁₂ : i₁ ≠ i₂) (h₁₃ : i₁ ≠ i₃)
     (h₂₃ : i₂ ≠ i₃) : t.altitude i₁ = t.mongePlane i₂ i₃ := by
   have hs : ({i₂, i₃}ᶜ : Finset (Fin 3)) = {i₁} := by
-    -- porting note: was `decide!`
+    -- Porting note (#11043): was `decide!`
     fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃
       <;> simp (config := {decide := true}) at h₁₂ h₁₃ h₂₃ ⊢
   have he : univ.erase i₁ = {i₂, i₃} := by
-    -- porting note: was `decide!`
+    -- Porting note (#11043): was `decide!`
     fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃
       <;> simp (config := {decide := true}) at h₁₂ h₁₃ h₂₃ ⊢
   rw [mongePlane_def, altitude_def, direction_affineSpan, hs, he, centroid_singleton, coe_insert,
@@ -492,7 +492,7 @@ theorem altitude_eq_mongePlane (t : Triangle ℝ P) {i₁ i₂ i₃ : Fin 3} (h
 theorem orthocenter_mem_altitude (t : Triangle ℝ P) {i₁ : Fin 3} :
     t.orthocenter ∈ t.altitude i₁ := by
   obtain ⟨i₂, i₃, h₁₂, h₂₃, h₁₃⟩ : ∃ i₂ i₃, i₁ ≠ i₂ ∧ i₂ ≠ i₃ ∧ i₁ ≠ i₃ := by
-    -- porting note: was `decide!`
+    -- Porting note (#11043): was `decide!`
     fin_cases i₁ <;> decide
   rw [orthocenter_eq_mongePoint, t.altitude_eq_mongePlane h₁₂ h₁₃ h₂₃]
   exact t.mongePoint_mem_mongePlane
@@ -504,7 +504,7 @@ theorem eq_orthocenter_of_forall_mem_altitude {t : Triangle ℝ P} {i₁ i₂ :
     (h₁₂ : i₁ ≠ i₂) (h₁ : p ∈ t.altitude i₁) (h₂ : p ∈ t.altitude i₂) : p = t.orthocenter := by
   obtain ⟨i₃, h₂₃, h₁₃⟩ : ∃ i₃, i₂ ≠ i₃ ∧ i₁ ≠ i₃ := by
     clear h₁ h₂
-    -- porting note: was `decide!`
+    -- Porting note (#11043): was `decide!`
     fin_cases i₁ <;> fin_cases i₂ <;> decide
   rw [t.altitude_eq_mongePlane h₁₃ h₁₂ h₂₃.symm] at h₁
   rw [t.altitude_eq_mongePlane h₂₃ h₁₂.symm h₁₃.symm] at h₂
@@ -513,7 +513,7 @@ theorem eq_orthocenter_of_forall_mem_altitude {t : Triangle ℝ P} {i₁ i₂ :
     intro i hi
     have hi₁₂ : i₁ = i ∨ i₂ = i := by
       clear h₁ h₂
-      -- porting note: was `decide!`
+      -- Porting note (#11043): was `decide!`
       fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃ <;> fin_cases i <;> simp at h₁₂ h₁₃ h₂₃ hi ⊢
     cases' hi₁₂ with hi₁₂ hi₁₂
     · exact hi₁₂ ▸ h₂
@@ -536,7 +536,7 @@ theorem dist_orthocenter_reflection_circumcenter (t : Triangle ℝ P) {i₁ i₂
   have hu : ({i₁, i₂} : Finset (Fin 3)) ⊆ univ := subset_univ _
   obtain ⟨i₃, hi₃, hi₃₁, hi₃₂⟩ :
       ∃ i₃, univ \ ({i₁, i₂} : Finset (Fin 3)) = {i₃} ∧ i₃ ≠ i₁ ∧ i₃ ≠ i₂ := by
-    -- porting note: was `decide!`
+    -- Porting note (#11043): was `decide!`
     fin_cases i₁ <;> fin_cases i₂ <;> simp at h <;> decide
   -- Porting note: Original proof was `simp_rw [← sum_sdiff hu, hi₃]; simp [hi₃₁, hi₃₂]; norm_num`
   rw [← sum_sdiff hu, ← sum_sdiff hu, hi₃, sum_singleton, ← sum_sdiff hu, hi₃]
@@ -590,7 +590,7 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
     refine' eq_of_le_of_finrank_eq (direction_le (spanPoints_subset_coe_of_subset_coe _)) _
     · have hu : (Finset.univ : Finset (Fin 3)) = {j₁, j₂, j₃} := by
         clear h₁ h₂ h₃
-        -- porting note: was `decide!`
+        -- Porting note (#11043): was `decide!`
         fin_cases j₁ <;> fin_cases j₂ <;> fin_cases j₃
           <;> simp (config := {decide := true}) at hj₁₂ hj₁₃ hj₂₃ ⊢
       rw [← Set.image_univ, ← Finset.coe_univ, hu, Finset.coe_insert, Finset.coe_insert,
@@ -606,7 +606,7 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
   use mem_affineSpan ℝ (Set.mem_range_self _)
   have hu : Finset.univ.erase j₂ = {j₁, j₃} := by
     clear h₁ h₂ h₃
-    -- porting note: was `decide!`
+    -- Porting note (#11043): was `decide!`
     fin_cases j₁ <;> fin_cases j₂ <;> fin_cases j₃
       <;> simp (config := {decide := true}) at hj₁₂ hj₁₃ hj₂₃ ⊢
   rw [hu, Finset.coe_insert, Finset.coe_singleton, Set.image_insert_eq, Set.image_singleton, h₁, h₃]
@@ -615,7 +615,7 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
   refine' hle ((t₁.vectorSpan_isOrtho_altitude_direction i₃) _)
   have hui : Finset.univ.erase i₃ = {i₁, i₂} := by
     clear hle h₂ h₃
-    -- porting note: was `decide!`
+    -- Porting note (#11043): was `decide!`
     fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃
       <;> simp (config := {decide := true}) at hi₁₂ hi₁₃ hi₂₃ ⊢
   rw [hui, Finset.coe_insert, Finset.coe_singleton, Set.image_insert_eq, Set.image_singleton]
@@ -787,7 +787,7 @@ theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricS
   · obtain ⟨j₁, hj₁₂, hj₁₃, hj₁₂₃⟩ :
         ∃ j₁ : Fin 3, j₁ ≠ j₂ ∧ j₁ ≠ j₃ ∧ ∀ j : Fin 3, j = j₁ ∨ j = j₂ ∨ j = j₃ := by
       clear h₂ h₃
-      -- porting note: was `decide!`
+      -- Porting note (#11043): was `decide!`
       fin_cases j₂ <;> fin_cases j₃ <;> simp (config := {decide := true}) at hj₂₃ ⊢
     suffices h : t₀.points j₁ = t.orthocenter by
       have hui : (Set.univ : Set (Fin 3)) = {i₁, i₂, i₃} := by ext x; simpa using h₁₂₃ x

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

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

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

@@ -619,7 +619,7 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
     fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃
       <;> simp (config := {decide := true}) at hi₁₂ hi₁₃ hi₂₃ ⊢
   rw [hui, Finset.coe_insert, Finset.coe_singleton, Set.image_insert_eq, Set.image_singleton]
-  refine' vsub_mem_vectorSpan ℝ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
+  exact vsub_mem_vectorSpan ℝ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
 #align affine.triangle.altitude_replace_orthocenter_eq_affine_span Affine.Triangle.altitude_replace_orthocenter_eq_affineSpan
 
 /-- Suppose we are given a triangle `t₁`, and replace one of its

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -789,8 +789,8 @@ theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricS
       clear h₂ h₃
       -- porting note: was `decide!`
       fin_cases j₂ <;> fin_cases j₃ <;> simp (config := {decide := true}) at hj₂₃ ⊢
-    suffices h : t₀.points j₁ = t.orthocenter
-    · have hui : (Set.univ : Set (Fin 3)) = {i₁, i₂, i₃} := by ext x; simpa using h₁₂₃ x
+    suffices h : t₀.points j₁ = t.orthocenter by
+      have hui : (Set.univ : Set (Fin 3)) = {i₁, i₂, i₃} := by ext x; simpa using h₁₂₃ x
       have huj : (Set.univ : Set (Fin 3)) = {j₁, j₂, j₃} := by ext x; simpa using hj₁₂₃ x
       rw [← h, ht₀s, ← Set.image_univ, huj, ← Set.image_univ, hui]
       simp_rw [Set.image_insert_eq, Set.image_singleton, h₁, ← h₂, ← h₃]

I used the regex \(\(· (.) ·\) (.)\), replacing with ($2 $1 ·).

@@ -310,7 +310,7 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
   rw [Submodule.iInf_orthogonal, ← Submodule.span_iUnion] at hi
   have hu :
     ⋃ i : { i // i₁ ≠ i }, ({s.points i₁ -ᵥ s.points i} : Set V) =
-      (· -ᵥ ·) (s.points i₁) '' (s.points '' (Set.univ \ {i₁})) := by
+      (s.points i₁ -ᵥ ·) '' (s.points '' (Set.univ \ {i₁})) := by
     rw [Set.image_image]
     ext x
     simp_rw [Set.mem_iUnion, Set.mem_image, Set.mem_singleton_iff, Set.mem_diff_singleton]

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -713,7 +713,7 @@ theorem exists_dist_eq_circumradius_of_subset_insert_orthocenter {t : Triangle 
     have h₁₂₃ := h₁₂₃ i
     repeat' cases' h₁₂₃ with h₁₂₃ h₁₂₃
     · convert Triangle.dist_orthocenter_reflection_circumcenter t hj₂₃
-    · rw [←h₂, dist_reflection_eq_of_mem _
+    · rw [← h₂, dist_reflection_eq_of_mem _
        (mem_affineSpan ℝ (Set.mem_image_of_mem _ (Set.mem_insert _ _)))]
       exact t.dist_circumcenter_eq_circumradius _
     · rw [← h₃,

These inductive types carry data, so these should be functionCase not theorem_case.

It seems that mathport didn't do this.

@@ -111,8 +111,8 @@ theorem mongePoint_eq_of_range_eq {n : ℕ} {s₁ s₂ : Simplex ℝ P n}
 /-- The weights for the Monge point of an (n+2)-simplex, in terms of
 `pointsWithCircumcenter`. -/
 def mongePointWeightsWithCircumcenter (n : ℕ) : PointsWithCircumcenterIndex (n + 2) → ℝ
-  | point_index _ => ((n + 1 : ℕ) : ℝ)⁻¹
-  | circumcenter_index => -2 / ((n + 1 : ℕ) : ℝ)
+  | pointIndex _ => ((n + 1 : ℕ) : ℝ)⁻¹
+  | circumcenterIndex => -2 / ((n + 1 : ℕ) : ℝ)
 #align affine.simplex.monge_point_weights_with_circumcenter Affine.Simplex.mongePointWeightsWithCircumcenter
 
 /-- `mongePointWeightsWithCircumcenter` sums to 1. -/
@@ -161,8 +161,8 @@ centroid of an n-dimensional face, in terms of
 `pointsWithCircumcenter`.  This definition is only valid when `i₁ ≠ i₂`. -/
 def mongePointVSubFaceCentroidWeightsWithCircumcenter {n : ℕ} (i₁ i₂ : Fin (n + 3)) :
     PointsWithCircumcenterIndex (n + 2) → ℝ
-  | point_index i => if i = i₁ ∨ i = i₂ then ((n + 1 : ℕ) : ℝ)⁻¹ else 0
-  | circumcenter_index => -2 / ((n + 1 : ℕ) : ℝ)
+  | pointIndex i => if i = i₁ ∨ i = i₂ then ((n + 1 : ℕ) : ℝ)⁻¹ else 0
+  | circumcenterIndex => -2 / ((n + 1 : ℕ) : ℝ)
 #align affine.simplex.monge_point_vsub_face_centroid_weights_with_circumcenter Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter
 
 /-- `mongePointVSubFaceCentroidWeightsWithCircumcenter` is the

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

@@ -122,7 +122,7 @@ theorem sum_mongePointWeightsWithCircumcenter (n : ℕ) :
   simp_rw [sum_pointsWithCircumcenter, mongePointWeightsWithCircumcenter, sum_const, card_fin,
     nsmul_eq_mul]
   -- Porting note: replaced
-  -- have hn1 : (n + 1 : ℝ) ≠ 0 := by exact_mod_cast Nat.succ_ne_zero _
+  -- have hn1 : (n + 1 : ℝ) ≠ 0 := mod_cast Nat.succ_ne_zero _
   field_simp [n.cast_add_one_ne_zero]
   ring
 #align affine.simplex.sum_monge_point_weights_with_circumcenter Affine.Simplex.sum_mongePointWeightsWithCircumcenter
@@ -141,7 +141,7 @@ theorem mongePoint_eq_affineCombination_of_pointsWithCircumcenter {n : ℕ}
   congr with i
   rw [Pi.add_apply, Pi.smul_apply, smul_eq_mul, Pi.sub_apply]
   -- Porting note: replaced
-  -- have hn1 : (n + 1 : ℝ) ≠ 0 := by exact_mod_cast Nat.succ_ne_zero _
+  -- have hn1 : (n + 1 : ℝ) ≠ 0 := mod_cast Nat.succ_ne_zero _
   have hn1 : (n + 1 : ℝ) ≠ 0 := n.cast_add_one_ne_zero
   cases i <;>
       simp_rw [centroidWeightsWithCircumcenter, circumcenterWeightsWithCircumcenter,
@@ -149,7 +149,7 @@ theorem mongePoint_eq_affineCombination_of_pointsWithCircumcenter {n : ℕ}
     rw [add_tsub_assoc_of_le (by decide : 1 ≤ 2), (by decide : 2 - 1 = 1)]
   · rw [if_pos (mem_univ _), sub_zero, add_zero, card_fin]
     -- Porting note: replaced
-    -- have hn3 : (n + 2 + 1 : ℝ) ≠ 0 := by exact_mod_cast Nat.succ_ne_zero _
+    -- have hn3 : (n + 2 + 1 : ℝ) ≠ 0 := mod_cast Nat.succ_ne_zero _
     have hn3 : (n + 2 + 1 : ℝ) ≠ 0 := by exact_mod_cast (n + 2).cast_add_one_ne_zero
     field_simp [hn1, hn3, mul_comm]
   · field_simp [hn1]

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

@@ -385,8 +385,8 @@ theorem finrank_direction_altitude {n : ℕ} (s : Simplex ℝ P (n + 1)) (i : Fi
     (vectorSpan_mono ℝ (Set.image_subset_range s.points ↑(univ.erase i)))
   have hc : card (univ.erase i) = n + 1 := by rw [card_erase_of_mem (mem_univ _)]; simp
   refine' add_left_cancel (_root_.trans h _)
-  rw [s.Independent.finrank_vectorSpan (Fintype.card_fin _), ← Finset.coe_image,
-    s.Independent.finrank_vectorSpan_image_finset hc]
+  rw [s.independent.finrank_vectorSpan (Fintype.card_fin _), ← Finset.coe_image,
+    s.independent.finrank_vectorSpan_image_finset hc]
 #align affine.simplex.finrank_direction_altitude Affine.Simplex.finrank_direction_altitude
 
 /-- A line through a vertex is the altitude through that vertex if and
@@ -583,7 +583,7 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
   symm
   rw [← h₂, t₂.affineSpan_pair_eq_altitude_iff]
   rw [h₂]
-  use t₁.Independent.injective.ne hi₁₂
+  use t₁.independent.injective.ne hi₁₂
   have he : affineSpan ℝ (Set.range t₂.points) = affineSpan ℝ (Set.range t₁.points) := by
     refine' ext_of_direction_eq _
       ⟨t₁.points i₃, mem_affineSpan ℝ ⟨j₃, h₃⟩, mem_affineSpan ℝ (Set.mem_range_self _)⟩
@@ -600,8 +600,8 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
         ⟨t₁.orthocenter_mem_affineSpan, mem_affineSpan ℝ (Set.mem_range_self _),
           mem_affineSpan ℝ (Set.mem_range_self _)⟩
     · rw [direction_affineSpan, direction_affineSpan,
-        t₁.Independent.finrank_vectorSpan (Fintype.card_fin _),
-        t₂.Independent.finrank_vectorSpan (Fintype.card_fin _)]
+        t₁.independent.finrank_vectorSpan (Fintype.card_fin _),
+        t₂.independent.finrank_vectorSpan (Fintype.card_fin _)]
   rw [he]
   use mem_affineSpan ℝ (Set.mem_range_self _)
   have hu : Finset.univ.erase j₂ = {j₁, j₃} := by
@@ -693,7 +693,7 @@ theorem exists_of_range_subset_orthocentricSystem {t : Triangle ℝ P}
     have hs := Set.subset_diff_singleton hps h
     rw [Set.insert_diff_self_of_not_mem ho] at hs
     refine' Set.eq_of_subset_of_card_le hs _
-    rw [Set.card_range_of_injective hpi, Set.card_range_of_injective t.Independent.injective]
+    rw [Set.card_range_of_injective hpi, Set.card_range_of_injective t.independent.injective]
 #align euclidean_geometry.exists_of_range_subset_orthocentric_system EuclideanGeometry.exists_of_range_subset_orthocentricSystem
 
 /-- For any three points in an orthocentric system generated by
@@ -752,7 +752,7 @@ theorem affineSpan_of_orthocentricSystem {s : Set P} (ho : OrthocentricSystem s)
   haveI := hfd
   refine' eq_of_le_of_finrank_eq (direction_le (affineSpan_mono ℝ hps)) _
   rw [hs, direction_affineSpan, direction_affineSpan, ha.finrank_vectorSpan (Fintype.card_fin _),
-    t.Independent.finrank_vectorSpan (Fintype.card_fin _)]
+    t.independent.finrank_vectorSpan (Fintype.card_fin _)]
 #align euclidean_geometry.affine_span_of_orthocentric_system EuclideanGeometry.affineSpan_of_orthocentricSystem
 
 /-- All triangles in an orthocentric system have the same circumradius. -/
@@ -764,14 +764,14 @@ theorem OrthocentricSystem.exists_circumradius_eq {s : Set P} (ho : Orthocentric
   have ht₂s := ht₂
   rw [hts] at ht₂
   rcases exists_dist_eq_circumradius_of_subset_insert_orthocenter hto ht₂
-      t₂.Independent.injective with
+      t₂.independent.injective with
     ⟨c, hc, h⟩
   rw [Set.forall_range_iff] at h
   have hs : Set.range t.points ⊆ s := by
     rw [hts]
     exact Set.subset_insert _ _
-  rw [affineSpan_of_orthocentricSystem ⟨t, hto, hts⟩ hs t.Independent.injective,
-    ← affineSpan_of_orthocentricSystem ⟨t, hto, hts⟩ ht₂s t₂.Independent.injective] at hc
+  rw [affineSpan_of_orthocentricSystem ⟨t, hto, hts⟩ hs t.independent.injective,
+    ← affineSpan_of_orthocentricSystem ⟨t, hto, hts⟩ ht₂s t₂.independent.injective] at hc
   exact (t₂.eq_circumradius_of_dist_eq hc h).symm
 #align euclidean_geometry.orthocentric_system.exists_circumradius_eq EuclideanGeometry.OrthocentricSystem.exists_circumradius_eq
 
@@ -782,7 +782,7 @@ theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricS
     s = insert t.orthocenter (Set.range t.points) := by
   rcases ho with ⟨t₀, ht₀o, ht₀s⟩
   rw [ht₀s] at ht
-  rcases exists_of_range_subset_orthocentricSystem ht₀o ht t.Independent.injective with
+  rcases exists_of_range_subset_orthocentricSystem ht₀o ht t.independent.injective with
     (⟨i₁, i₂, i₃, j₂, j₃, h₁₂, h₁₃, h₂₃, h₁₂₃, h₁, hj₂₃, h₂, h₃⟩ | hs)
   · obtain ⟨j₁, hj₁₂, hj₁₃, hj₁₂₃⟩ :
         ∃ j₁ : Fin 3, j₁ ≠ j₂ ∧ j₁ ≠ j₃ ∧ ∀ j : Fin 3, j = j₁ ∨ j = j₂ ∨ j = j₃ := by

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>

@@ -474,16 +474,18 @@ theorem altitude_eq_mongePlane (t : Triangle ℝ P) {i₁ i₂ i₃ : Fin 3} (h
     (h₂₃ : i₂ ≠ i₃) : t.altitude i₁ = t.mongePlane i₂ i₃ := by
   have hs : ({i₂, i₃}ᶜ : Finset (Fin 3)) = {i₁} := by
     -- porting note: was `decide!`
-    fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃ <;> simp at h₁₂ h₁₃ h₂₃ ⊢
+    fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃
+      <;> simp (config := {decide := true}) at h₁₂ h₁₃ h₂₃ ⊢
   have he : univ.erase i₁ = {i₂, i₃} := by
     -- porting note: was `decide!`
-    fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃ <;> simp at h₁₂ h₁₃ h₂₃ ⊢
+    fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃
+      <;> simp (config := {decide := true}) at h₁₂ h₁₃ h₂₃ ⊢
   rw [mongePlane_def, altitude_def, direction_affineSpan, hs, he, centroid_singleton, coe_insert,
     coe_singleton, vectorSpan_image_eq_span_vsub_set_left_ne ℝ _ (Set.mem_insert i₂ _)]
   simp [h₂₃, Submodule.span_insert_eq_span]
   -- porting note: this didn't need the `congr` and the `fin_cases`
   congr
-  fin_cases i₂ <;> fin_cases i₃ <;> simp at h₂₃ ⊢
+  fin_cases i₂ <;> fin_cases i₃ <;> simp (config := {decide := true}) at h₂₃ ⊢
 #align affine.triangle.altitude_eq_monge_plane Affine.Triangle.altitude_eq_mongePlane
 
 /-- The orthocenter lies in the altitudes. -/
@@ -589,7 +591,8 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
     · have hu : (Finset.univ : Finset (Fin 3)) = {j₁, j₂, j₃} := by
         clear h₁ h₂ h₃
         -- porting note: was `decide!`
-        fin_cases j₁ <;> fin_cases j₂ <;> fin_cases j₃ <;> simp at hj₁₂ hj₁₃ hj₂₃ ⊢
+        fin_cases j₁ <;> fin_cases j₂ <;> fin_cases j₃
+          <;> simp (config := {decide := true}) at hj₁₂ hj₁₃ hj₂₃ ⊢
       rw [← Set.image_univ, ← Finset.coe_univ, hu, Finset.coe_insert, Finset.coe_insert,
         Finset.coe_singleton, Set.image_insert_eq, Set.image_insert_eq, Set.image_singleton, h₁, h₂,
         h₃, Set.insert_subset_iff, Set.insert_subset_iff, Set.singleton_subset_iff]
@@ -604,7 +607,8 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
   have hu : Finset.univ.erase j₂ = {j₁, j₃} := by
     clear h₁ h₂ h₃
     -- porting note: was `decide!`
-    fin_cases j₁ <;> fin_cases j₂ <;> fin_cases j₃ <;> simp at hj₁₂ hj₁₃ hj₂₃ ⊢
+    fin_cases j₁ <;> fin_cases j₂ <;> fin_cases j₃
+      <;> simp (config := {decide := true}) at hj₁₂ hj₁₃ hj₂₃ ⊢
   rw [hu, Finset.coe_insert, Finset.coe_singleton, Set.image_insert_eq, Set.image_singleton, h₁, h₃]
   have hle : (t₁.altitude i₃).directionᗮ ≤ line[ℝ, t₁.orthocenter, t₁.points i₃].directionᗮ :=
     Submodule.orthogonal_le (direction_le (affineSpan_orthocenter_point_le_altitude _ _))
@@ -612,7 +616,8 @@ theorem altitude_replace_orthocenter_eq_affineSpan {t₁ t₂ : Triangle ℝ P}
   have hui : Finset.univ.erase i₃ = {i₁, i₂} := by
     clear hle h₂ h₃
     -- porting note: was `decide!`
-    fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃ <;> simp at hi₁₂ hi₁₃ hi₂₃ ⊢
+    fin_cases i₁ <;> fin_cases i₂ <;> fin_cases i₃
+      <;> simp (config := {decide := true}) at hi₁₂ hi₁₃ hi₂₃ ⊢
   rw [hui, Finset.coe_insert, Finset.coe_singleton, Set.image_insert_eq, Set.image_singleton]
   refine' vsub_mem_vectorSpan ℝ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
 #align affine.triangle.altitude_replace_orthocenter_eq_affine_span Affine.Triangle.altitude_replace_orthocenter_eq_affineSpan
@@ -783,7 +788,7 @@ theorem OrthocentricSystem.eq_insert_orthocenter {s : Set P} (ho : OrthocentricS
         ∃ j₁ : Fin 3, j₁ ≠ j₂ ∧ j₁ ≠ j₃ ∧ ∀ j : Fin 3, j = j₁ ∨ j = j₂ ∨ j = j₃ := by
       clear h₂ h₃
       -- porting note: was `decide!`
-      fin_cases j₂ <;> fin_cases j₃ <;> simp at hj₂₃ ⊢
+      fin_cases j₂ <;> fin_cases j₃ <;> simp (config := {decide := true}) at hj₂₃ ⊢
     suffices h : t₀.points j₁ = t.orthocenter
     · have hui : (Set.univ : Set (Fin 3)) = {i₁, i₂, i₃} := by ext x; simpa using h₁₂₃ x
       have huj : (Set.univ : Set (Fin 3)) = {j₁, j₂, j₃} := by ext x; simpa using hj₁₂₃ x

Removes nonterminal simps on lines looking like simp [...]

@@ -540,7 +540,11 @@ theorem dist_orthocenter_reflection_circumcenter (t : Triangle ℝ P) {i₁ i₂
   rw [← sum_sdiff hu, ← sum_sdiff hu, hi₃, sum_singleton, ← sum_sdiff hu, hi₃]
   split_ifs with h
   · exact (h.elim hi₃₁ hi₃₂).elim
-  simp [h]
+  simp only [zero_add, Nat.cast_one, inv_one, sub_zero, one_mul, pointsWithCircumcenter_point,
+    sum_singleton, h, ite_false, dist_self, mul_zero, mem_singleton, true_or, ite_true, sub_self,
+    zero_mul, implies_true, sum_insert_of_eq_zero_if_not_mem, or_true, add_zero, div_one,
+    sub_neg_eq_add, pointsWithCircumcenter_eq_circumcenter, dist_circumcenter_eq_circumradius,
+    sum_const_zero, dist_circumcenter_eq_circumradius', mul_one, neg_add_rev, half_add_self]
   norm_num
 #align affine.triangle.dist_orthocenter_reflection_circumcenter Affine.Triangle.dist_orthocenter_reflection_circumcenter
 

A linter that throws on seeing a colon at the start of a line, according to the style guideline that says these operators should go before linebreaks.

@@ -73,8 +73,8 @@ the intersection of the Monge planes, where a Monge plane is the
 simplex that passes through the centroid of an (n-2)-dimensional face
 and is orthogonal to the opposite edge (in 2 dimensions, this is the
 same as an altitude).  The circumcenter O, centroid G and Monge point
-M are collinear in that order on the Euler line, with OG : GM = (n-1)
-: 2.  Here, we use that ratio to define the Monge point (so resulting
+M are collinear in that order on the Euler line, with OG : GM = (n-1): 2.
+Here, we use that ratio to define the Monge point (so resulting
 in a point that equals the centroid in 0 or 1 dimensions), and then
 show in subsequent lemmas that the point so defined lies in the Monge
 planes and is their unique point of intersection. -/

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).

@@ -283,7 +283,7 @@ theorem mongePoint_mem_mongePlane {n : ℕ} (s : Simplex ℝ P (n + 2)) {i₁ i
   refine' ⟨_, s.mongePoint_mem_affineSpan⟩
   intro v hv
   rcases Submodule.mem_span_singleton.mp hv with ⟨r, rfl⟩
-  rw [inner_smul_right, s.inner_mongePoint_vsub_face_centroid_vsub, MulZeroClass.mul_zero]
+  rw [inner_smul_right, s.inner_mongePoint_vsub_face_centroid_vsub, mul_zero]
 #align affine.simplex.monge_point_mem_monge_plane Affine.Simplex.mongePoint_mem_mongePlane
 
 /-- The direction of a Monge plane. -/

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

This has nice performance benefits.

@@ -63,7 +63,7 @@ namespace Simplex
 
 open Finset AffineSubspace EuclideanGeometry PointsWithCircumcenterIndex
 
-variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
+variable {V : Type*} {P : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
 /-- The Monge point of a simplex (in 2 or more dimensions) is a
@@ -431,7 +431,7 @@ namespace Triangle
 
 open EuclideanGeometry Finset Simplex AffineSubspace FiniteDimensional
 
-variable {V : Type _} {P : Type _} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
+variable {V : Type*} {P : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P]
   [NormedAddTorsor V P]
 
 /-- The orthocenter of a triangle is the intersection of its
@@ -636,7 +636,7 @@ namespace EuclideanGeometry
 
 open Affine AffineSubspace FiniteDimensional
 
-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]
 
 /-- Four points form an orthocentric system if they consist of the

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 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.monge_point
-! leanprover-community/mathlib commit 1a4df69ca1a9a0e5e26bfe12e2b92814216016d0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Geometry.Euclidean.Circumcenter
 
+#align_import geometry.euclidean.monge_point from "leanprover-community/mathlib"@"1a4df69ca1a9a0e5e26bfe12e2b92814216016d0"
+
 /-!
 # Monge point and orthocenter
 

@@ -312,7 +312,7 @@ theorem eq_mongePoint_of_forall_mem_mongePlane {n : ℕ} {s : Simplex ℝ P (n +
     exact fun i => (Submodule.mem_inf.1 (h' i i.property)).1
   rw [Submodule.iInf_orthogonal, ← Submodule.span_iUnion] at hi
   have hu :
-    (⋃ i : { i // i₁ ≠ i }, ({s.points i₁ -ᵥ s.points i} : Set V)) =
+    ⋃ i : { i // i₁ ≠ i }, ({s.points i₁ -ᵥ s.points i} : Set V) =
       (· -ᵥ ·) (s.points i₁) '' (s.points '' (Set.univ \ {i₁})) := by
     rw [Set.image_image]
     ext x

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

@@ -174,7 +174,7 @@ result of subtracting `centroidWeightsWithCircumcenter` from
 theorem mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub {n : ℕ} {i₁ i₂ : Fin (n + 3)}
     (h : i₁ ≠ i₂) :
     mongePointVSubFaceCentroidWeightsWithCircumcenter i₁ i₂ =
-      mongePointWeightsWithCircumcenter n - centroidWeightsWithCircumcenter ({i₁, i₂}ᶜ) := by
+      mongePointWeightsWithCircumcenter n - centroidWeightsWithCircumcenter {i₁, i₂}ᶜ := by
   ext i
   cases' i with i
   · rw [Pi.sub_apply, mongePointWeightsWithCircumcenter, centroidWeightsWithCircumcenter,

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>