analysis.convex.extreme ⟷ Mathlib.Analysis.Convex.Extreme

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

@@ -158,7 +158,7 @@ theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F,
 #align is_extreme_sInter isExtreme_sInter
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 #print mem_extremePoints /-
 theorem mem_extremePoints :
     x ∈ A.extremePoints 𝕜 ↔
@@ -300,7 +300,7 @@ variable {𝕜} [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 #print mem_extremePoints_iff_forall_segment /-
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
 that contain it are those with `x` as one of their endpoints. -/

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

@@ -326,7 +326,7 @@ theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
   use fun hx => ⟨hx.1, (isExtreme_singleton.1 hx).convex_diff hA⟩
   rintro ⟨hxA, hAx⟩
   refine' mem_extremePoints_iff_forall_segment.2 ⟨hxA, fun x₁ hx₁ x₂ hx₂ hx => _⟩
-  rw [convex_iff_segment_subset] at hAx 
+  rw [convex_iff_segment_subset] at hAx
   by_contra! h
   exact
     (hAx ⟨hx₁, fun hx₁ => h.1 (mem_singleton_iff.2 hx₁)⟩
@@ -347,7 +347,7 @@ theorem Convex.mem_extremePoints_iff_mem_diff_convexHull_diff (hA : Convex 𝕜
 theorem extremePoints_convexHull_subset : (convexHull 𝕜 A).extremePoints 𝕜 ⊆ A :=
   by
   rintro x hx
-  rw [(convex_convexHull 𝕜 _).mem_extremePoints_iff_convex_diff] at hx 
+  rw [(convex_convexHull 𝕜 _).mem_extremePoints_iff_convex_diff] at hx
   by_contra
   exact
     (convexHull_min (subset_diff.2 ⟨subset_convexHull 𝕜 _, disjoint_singleton_right.2 h⟩) hx.2

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

@@ -327,7 +327,7 @@ theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
   rintro ⟨hxA, hAx⟩
   refine' mem_extremePoints_iff_forall_segment.2 ⟨hxA, fun x₁ hx₁ x₂ hx₂ hx => _⟩
   rw [convex_iff_segment_subset] at hAx 
-  by_contra' h
+  by_contra! h
   exact
     (hAx ⟨hx₁, fun hx₁ => h.1 (mem_singleton_iff.2 hx₁)⟩
           ⟨hx₂, fun hx₂ => h.2 (mem_singleton_iff.2 hx₂)⟩ hx).2

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

@@ -167,16 +167,16 @@ theorem mem_extremePoints :
 #align mem_extreme_points mem_extremePoints
 -/
 
-#print mem_extremePoints_iff_extreme_singleton /-
+#print isExtreme_singleton /-
 /-- x is an extreme point to A iff {x} is an extreme set of A. -/
-theorem mem_extremePoints_iff_extreme_singleton : x ∈ A.extremePoints 𝕜 ↔ IsExtreme 𝕜 A {x} :=
+theorem isExtreme_singleton : x ∈ A.extremePoints 𝕜 ↔ IsExtreme 𝕜 A {x} :=
   by
   refine' ⟨_, fun hx => ⟨singleton_subset_iff.1 hx.1, fun x₁ hx₁ x₂ hx₂ => hx.2 hx₁ hx₂ rfl⟩⟩
   rintro ⟨hxA, hAx⟩
   use singleton_subset_iff.2 hxA
   rintro x₁ hx₁A x₂ hx₂A y (rfl : y = x)
   exact hAx hx₁A hx₂A
-#align mem_extreme_points_iff_extreme_singleton mem_extremePoints_iff_extreme_singleton
+#align mem_extreme_points_iff_extreme_singleton isExtreme_singleton
 -/
 
 #print extremePoints_subset /-
@@ -209,8 +209,7 @@ theorem inter_extremePoints_subset_extremePoints_of_subset (hBA : B ⊆ A) :
 #print IsExtreme.extremePoints_subset_extremePoints /-
 theorem IsExtreme.extremePoints_subset_extremePoints (hAB : IsExtreme 𝕜 A B) :
     B.extremePoints 𝕜 ⊆ A.extremePoints 𝕜 := fun x hx =>
-  mem_extremePoints_iff_extreme_singleton.2
-    (hAB.trans (mem_extremePoints_iff_extreme_singleton.1 hx))
+  isExtreme_singleton.2 (hAB.trans (isExtreme_singleton.1 hx))
 #align is_extreme.extreme_points_subset_extreme_points IsExtreme.extremePoints_subset_extremePoints
 -/
 
@@ -324,7 +323,7 @@ theorem mem_extremePoints_iff_forall_segment :
 theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A ∧ Convex 𝕜 (A \ {x}) :=
   by
-  use fun hx => ⟨hx.1, (mem_extremePoints_iff_extreme_singleton.1 hx).convex_diff hA⟩
+  use fun hx => ⟨hx.1, (isExtreme_singleton.1 hx).convex_diff hA⟩
   rintro ⟨hxA, hAx⟩
   refine' mem_extremePoints_iff_forall_segment.2 ⟨hxA, fun x₁ hx₁ x₂ hx₂ hx => _⟩
   rw [convex_iff_segment_subset] at hAx 

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 -/
-import Mathbin.Analysis.Convex.Hull
+import Analysis.Convex.Hull
 
 #align_import analysis.convex.extreme from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 
@@ -158,7 +158,7 @@ theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F,
 #align is_extreme_sInter isExtreme_sInter
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 #print mem_extremePoints /-
 theorem mem_extremePoints :
     x ∈ A.extremePoints 𝕜 ↔
@@ -301,7 +301,7 @@ variable {𝕜} [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 #print mem_extremePoints_iff_forall_segment /-
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
 that contain it are those with `x` as one of their endpoints. -/

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
-
-! This file was ported from Lean 3 source module analysis.convex.extreme
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Hull
 
+#align_import analysis.convex.extreme from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Extreme sets
 
@@ -161,7 +158,7 @@ theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F,
 #align is_extreme_sInter isExtreme_sInter
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 #print mem_extremePoints /-
 theorem mem_extremePoints :
     x ∈ A.extremePoints 𝕜 ↔
@@ -304,7 +301,7 @@ variable {𝕜} [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 #print mem_extremePoints_iff_forall_segment /-
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
 that contain it are those with `x` as one of their endpoints. -/

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

@@ -84,10 +84,13 @@ protected theorem IsExtreme.refl (A : Set E) : IsExtreme 𝕜 A A :=
 
 variable {𝕜} {A B C : Set E} {x : E}
 
+#print IsExtreme.rfl /-
 protected theorem IsExtreme.rfl : IsExtreme 𝕜 A A :=
   IsExtreme.refl 𝕜 A
 #align is_extreme.rfl IsExtreme.rfl
+-/
 
+#print IsExtreme.trans /-
 @[trans]
 protected theorem IsExtreme.trans (hAB : IsExtreme 𝕜 A B) (hBC : IsExtreme 𝕜 B C) :
     IsExtreme 𝕜 A C :=
@@ -96,6 +99,7 @@ protected theorem IsExtreme.trans (hAB : IsExtreme 𝕜 A B) (hBC : IsExtreme 
   obtain ⟨hx₁B, hx₂B⟩ := hAB.2 hx₁A hx₂A (hBC.1 hxC) hx
   exact hBC.2 hx₁B hx₂B hxC hx
 #align is_extreme.trans IsExtreme.trans
+-/
 
 #print IsExtreme.antisymm /-
 protected theorem IsExtreme.antisymm : AntiSymmetric (IsExtreme 𝕜 : Set E → Set E → Prop) :=
@@ -109,6 +113,7 @@ instance : IsPartialOrder (Set E) (IsExtreme 𝕜)
   trans A B C := IsExtreme.trans
   antisymm := IsExtreme.antisymm
 
+#print IsExtreme.inter /-
 theorem IsExtreme.inter (hAB : IsExtreme 𝕜 A B) (hAC : IsExtreme 𝕜 A C) : IsExtreme 𝕜 A (B ∩ C) :=
   by
   use subset.trans (inter_subset_left _ _) hAB.1
@@ -117,11 +122,14 @@ theorem IsExtreme.inter (hAB : IsExtreme 𝕜 A B) (hAC : IsExtreme 𝕜 A C) :
   obtain ⟨hx₁C, hx₂C⟩ := hAC.2 hx₁A hx₂A hxC hx
   exact ⟨⟨hx₁B, hx₁C⟩, hx₂B, hx₂C⟩
 #align is_extreme.inter IsExtreme.inter
+-/
 
+#print IsExtreme.mono /-
 protected theorem IsExtreme.mono (hAC : IsExtreme 𝕜 A C) (hBA : B ⊆ A) (hCB : C ⊆ B) :
     IsExtreme 𝕜 B C :=
   ⟨hCB, fun x₁ hx₁B x₂ hx₂B x hxC hx => hAC.2 (hBA hx₁B) (hBA hx₂B) hxC hx⟩
 #align is_extreme.mono IsExtreme.mono
+-/
 
 #print isExtreme_iInter /-
 theorem isExtreme_iInter {ι : Sort _} [Nonempty ι] {F : ι → Set E}
@@ -194,22 +202,28 @@ theorem extremePoints_singleton : ({x} : Set E).extremePoints 𝕜 = {x} :=
 #align extreme_points_singleton extremePoints_singleton
 -/
 
+#print inter_extremePoints_subset_extremePoints_of_subset /-
 theorem inter_extremePoints_subset_extremePoints_of_subset (hBA : B ⊆ A) :
     B ∩ A.extremePoints 𝕜 ⊆ B.extremePoints 𝕜 := fun x ⟨hxB, hxA⟩ =>
   ⟨hxB, fun x₁ hx₁ x₂ hx₂ hx => hxA.2 (hBA hx₁) (hBA hx₂) hx⟩
 #align inter_extreme_points_subset_extreme_points_of_subset inter_extremePoints_subset_extremePoints_of_subset
+-/
 
+#print IsExtreme.extremePoints_subset_extremePoints /-
 theorem IsExtreme.extremePoints_subset_extremePoints (hAB : IsExtreme 𝕜 A B) :
     B.extremePoints 𝕜 ⊆ A.extremePoints 𝕜 := fun x hx =>
   mem_extremePoints_iff_extreme_singleton.2
     (hAB.trans (mem_extremePoints_iff_extreme_singleton.1 hx))
 #align is_extreme.extreme_points_subset_extreme_points IsExtreme.extremePoints_subset_extremePoints
+-/
 
+#print IsExtreme.extremePoints_eq /-
 theorem IsExtreme.extremePoints_eq (hAB : IsExtreme 𝕜 A B) :
     B.extremePoints 𝕜 = B ∩ A.extremePoints 𝕜 :=
   Subset.antisymm (fun x hx => ⟨hx.1, hAB.extremePoints_subset_extremePoints hx⟩)
     (inter_extremePoints_subset_extremePoints_of_subset hAB.1)
 #align is_extreme.extreme_points_eq IsExtreme.extremePoints_eq
+-/
 
 end SMul
 
@@ -218,13 +232,16 @@ section OrderedSemiring
 variable [OrderedSemiring 𝕜] [AddCommGroup E] [AddCommGroup F] [∀ i, AddCommGroup (π i)]
   [Module 𝕜 E] [Module 𝕜 F] [∀ i, Module 𝕜 (π i)] {A B : Set E} {x : E}
 
+#print IsExtreme.convex_diff /-
 theorem IsExtreme.convex_diff (hA : Convex 𝕜 A) (hAB : IsExtreme 𝕜 A B) : Convex 𝕜 (A \ B) :=
   convex_iff_openSegment_subset.2 fun x₁ ⟨hx₁A, hx₁B⟩ x₂ ⟨hx₂A, hx₂B⟩ x hx =>
     ⟨hA.openSegment_subset hx₁A hx₂A hx, fun hxB => hx₁B (hAB.2 hx₁A hx₂A hxB hx).1⟩
 #align is_extreme.convex_diff IsExtreme.convex_diff
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print extremePoints_prod /-
 @[simp]
 theorem extremePoints_prod (s : Set E) (t : Set F) :
     (s ×ˢ t).extremePoints 𝕜 = s.extremePoints 𝕜 ×ˢ t.extremePoints 𝕜 :=
@@ -251,6 +268,7 @@ theorem extremePoints_prod (s : Set E) (t : Set F) :
         ⟨h.1 hx₁.1 hx₂.1 ⟨a, b, ha, hb, hab, congr_arg Prod.fst hx'⟩,
           h.2 hx₁.2 hx₂.2 ⟨a, b, ha, hb, hab, congr_arg Prod.snd hx'⟩⟩
 #align extreme_points_prod extremePoints_prod
+-/
 
 #print extremePoints_pi /-
 @[simp]
@@ -287,6 +305,7 @@ variable {𝕜} [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+#print mem_extremePoints_iff_forall_segment /-
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
 that contain it are those with `x` as one of their endpoints. -/
 theorem mem_extremePoints_iff_forall_segment :
@@ -302,7 +321,9 @@ theorem mem_extremePoints_iff_forall_segment :
     rcases H (openSegment_subset_segment _ _ _ hx) with (rfl | rfl)
     exacts [⟨rfl, (left_mem_openSegment_iff.1 hx).symm⟩, ⟨right_mem_openSegment_iff.1 hx, rfl⟩]
 #align mem_extreme_points_iff_forall_segment mem_extremePoints_iff_forall_segment
+-/
 
+#print Convex.mem_extremePoints_iff_convex_diff /-
 theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A ∧ Convex 𝕜 (A \ {x}) :=
   by
@@ -316,13 +337,17 @@ theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
           ⟨hx₂, fun hx₂ => h.2 (mem_singleton_iff.2 hx₂)⟩ hx).2
       rfl
 #align convex.mem_extreme_points_iff_convex_diff Convex.mem_extremePoints_iff_convex_diff
+-/
 
+#print Convex.mem_extremePoints_iff_mem_diff_convexHull_diff /-
 theorem Convex.mem_extremePoints_iff_mem_diff_convexHull_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A \ convexHull 𝕜 (A \ {x}) := by
   rw [hA.mem_extreme_points_iff_convex_diff, hA.convex_remove_iff_not_mem_convex_hull_remove,
     mem_diff]
 #align convex.mem_extreme_points_iff_mem_diff_convex_hull_diff Convex.mem_extremePoints_iff_mem_diff_convexHull_diff
+-/
 
+#print extremePoints_convexHull_subset /-
 theorem extremePoints_convexHull_subset : (convexHull 𝕜 A).extremePoints 𝕜 ⊆ A :=
   by
   rintro x hx
@@ -334,6 +359,7 @@ theorem extremePoints_convexHull_subset : (convexHull 𝕜 A).extremePoints 𝕜
       rfl
   infer_instance
 #align extreme_points_convex_hull_subset extremePoints_convexHull_subset
+-/
 
 end LinearOrderedRing
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -153,7 +153,7 @@ theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F,
 #align is_extreme_sInter isExtreme_sInter
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 #print mem_extremePoints /-
 theorem mem_extremePoints :
     x ∈ A.extremePoints 𝕜 ↔
@@ -286,7 +286,7 @@ variable {𝕜} [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
 that contain it are those with `x` as one of their endpoints. -/
 theorem mem_extremePoints_iff_forall_segment :

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

@@ -71,7 +71,7 @@ def IsExtreme (A B : Set E) : Prop :=
 /-- A point `x` is an extreme point of a set `A` if `x` belongs to no open segment with ends in
 `A`, except for the obvious `open_segment x x`. -/
 def Set.extremePoints (A : Set E) : Set E :=
-  { x ∈ A | ∀ ⦃x₁⦄, x₁ ∈ A → ∀ ⦃x₂⦄, x₂ ∈ A → x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x }
+  {x ∈ A | ∀ ⦃x₁⦄, x₁ ∈ A → ∀ ⦃x₂⦄, x₂ ∈ A → x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x}
 #align set.extreme_points Set.extremePoints
 -/
 

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

@@ -129,7 +129,7 @@ theorem isExtreme_iInter {ι : Sort _} [Nonempty ι] {F : ι → Set E}
   by
   obtain i := Classical.arbitrary ι
   refine' ⟨Inter_subset_of_subset i (hAF i).1, fun x₁ hx₁A x₂ hx₂A x hxF hx => _⟩
-  simp_rw [mem_Inter] at hxF⊢
+  simp_rw [mem_Inter] at hxF ⊢
   have h := fun i => (hAF i).2 hx₁A hx₂A (hxF i) hx
   exact ⟨fun i => (h i).1, fun i => (h i).2⟩
 #align is_extreme_Inter isExtreme_iInter
@@ -147,7 +147,7 @@ theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F,
     IsExtreme 𝕜 A (⋂₀ F) := by
   obtain ⟨B, hB⟩ := hF
   refine' ⟨(sInter_subset_of_mem hB).trans (hAF B hB).1, fun x₁ hx₁A x₂ hx₂A x hxF hx => _⟩
-  simp_rw [mem_sInter] at hxF⊢
+  simp_rw [mem_sInter] at hxF ⊢
   have h := fun B hB => (hAF B hB).2 hx₁A hx₂A (hxF B hB) hx
   exact ⟨fun B hB => (h B hB).1, fun B hB => (h B hB).2⟩
 #align is_extreme_sInter isExtreme_sInter
@@ -297,10 +297,10 @@ theorem mem_extremePoints_iff_forall_segment :
   constructor
   · rw [← insert_endpoints_openSegment]
     rintro H (rfl | rfl | hx)
-    exacts[Or.inl rfl, Or.inr rfl, Or.inl <| (H hx).1]
+    exacts [Or.inl rfl, Or.inr rfl, Or.inl <| (H hx).1]
   · intro H hx
     rcases H (openSegment_subset_segment _ _ _ hx) with (rfl | rfl)
-    exacts[⟨rfl, (left_mem_openSegment_iff.1 hx).symm⟩, ⟨right_mem_openSegment_iff.1 hx, rfl⟩]
+    exacts [⟨rfl, (left_mem_openSegment_iff.1 hx).symm⟩, ⟨right_mem_openSegment_iff.1 hx, rfl⟩]
 #align mem_extreme_points_iff_forall_segment mem_extremePoints_iff_forall_segment
 
 theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
@@ -309,7 +309,7 @@ theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
   use fun hx => ⟨hx.1, (mem_extremePoints_iff_extreme_singleton.1 hx).convex_diff hA⟩
   rintro ⟨hxA, hAx⟩
   refine' mem_extremePoints_iff_forall_segment.2 ⟨hxA, fun x₁ hx₁ x₂ hx₂ hx => _⟩
-  rw [convex_iff_segment_subset] at hAx
+  rw [convex_iff_segment_subset] at hAx 
   by_contra' h
   exact
     (hAx ⟨hx₁, fun hx₁ => h.1 (mem_singleton_iff.2 hx₁)⟩
@@ -326,7 +326,7 @@ theorem Convex.mem_extremePoints_iff_mem_diff_convexHull_diff (hA : Convex 𝕜
 theorem extremePoints_convexHull_subset : (convexHull 𝕜 A).extremePoints 𝕜 ⊆ A :=
   by
   rintro x hx
-  rw [(convex_convexHull 𝕜 _).mem_extremePoints_iff_convex_diff] at hx
+  rw [(convex_convexHull 𝕜 _).mem_extremePoints_iff_convex_diff] at hx 
   by_contra
   exact
     (convexHull_min (subset_diff.2 ⟨subset_convexHull 𝕜 _, disjoint_singleton_right.2 h⟩) hx.2

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

@@ -51,7 +51,7 @@ More not-yet-PRed stuff is available on the branch `sperner_again`.
 
 open Function Set
 
-open Affine Classical
+open scoped Affine Classical
 
 variable {𝕜 E F ι : Type _} {π : ι → Type _}
 

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

@@ -84,22 +84,10 @@ protected theorem IsExtreme.refl (A : Set E) : IsExtreme 𝕜 A A :=
 
 variable {𝕜} {A B C : Set E} {x : E}
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_extreme.rfl IsExtreme.rflₓ'. -/
 protected theorem IsExtreme.rfl : IsExtreme 𝕜 A A :=
   IsExtreme.refl 𝕜 A
 #align is_extreme.rfl IsExtreme.rfl
 
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-Case conversion may be inaccurate. Consider using '#align is_extreme.trans IsExtreme.transₓ'. -/
 @[trans]
 protected theorem IsExtreme.trans (hAB : IsExtreme 𝕜 A B) (hBC : IsExtreme 𝕜 B C) :
     IsExtreme 𝕜 A C :=
@@ -121,12 +109,6 @@ instance : IsPartialOrder (Set E) (IsExtreme 𝕜)
   trans A B C := IsExtreme.trans
   antisymm := IsExtreme.antisymm
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_extreme.inter IsExtreme.interₓ'. -/
 theorem IsExtreme.inter (hAB : IsExtreme 𝕜 A B) (hAC : IsExtreme 𝕜 A C) : IsExtreme 𝕜 A (B ∩ C) :=
   by
   use subset.trans (inter_subset_left _ _) hAB.1
@@ -136,12 +118,6 @@ theorem IsExtreme.inter (hAB : IsExtreme 𝕜 A B) (hAC : IsExtreme 𝕜 A C) :
   exact ⟨⟨hx₁B, hx₁C⟩, hx₂B, hx₂C⟩
 #align is_extreme.inter IsExtreme.inter
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_extreme.mono IsExtreme.monoₓ'. -/
 protected theorem IsExtreme.mono (hAC : IsExtreme 𝕜 A C) (hBA : B ⊆ A) (hCB : C ⊆ B) :
     IsExtreme 𝕜 B C :=
   ⟨hCB, fun x₁ hx₁B x₂ hx₂B x hxC hx => hAC.2 (hBA hx₁B) (hBA hx₂B) hxC hx⟩
@@ -218,35 +194,17 @@ theorem extremePoints_singleton : ({x} : Set E).extremePoints 𝕜 = {x} :=
 #align extreme_points_singleton extremePoints_singleton
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align inter_extreme_points_subset_extreme_points_of_subset inter_extremePoints_subset_extremePoints_of_subsetₓ'. -/
 theorem inter_extremePoints_subset_extremePoints_of_subset (hBA : B ⊆ A) :
     B ∩ A.extremePoints 𝕜 ⊆ B.extremePoints 𝕜 := fun x ⟨hxB, hxA⟩ =>
   ⟨hxB, fun x₁ hx₁ x₂ hx₂ hx => hxA.2 (hBA hx₁) (hBA hx₂) hx⟩
 #align inter_extreme_points_subset_extreme_points_of_subset inter_extremePoints_subset_extremePoints_of_subset
 
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {A : Set.{u2} E} {B : Set.{u2} E}, (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A B) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 B) (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A))
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-Case conversion may be inaccurate. Consider using '#align is_extreme.extreme_points_subset_extreme_points IsExtreme.extremePoints_subset_extremePointsₓ'. -/
 theorem IsExtreme.extremePoints_subset_extremePoints (hAB : IsExtreme 𝕜 A B) :
     B.extremePoints 𝕜 ⊆ A.extremePoints 𝕜 := fun x hx =>
   mem_extremePoints_iff_extreme_singleton.2
     (hAB.trans (mem_extremePoints_iff_extreme_singleton.1 hx))
 #align is_extreme.extreme_points_subset_extreme_points IsExtreme.extremePoints_subset_extremePoints
 
-/- warning: is_extreme.extreme_points_eq -> IsExtreme.extremePoints_eq is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_extreme.extreme_points_eq IsExtreme.extremePoints_eqₓ'. -/
 theorem IsExtreme.extremePoints_eq (hAB : IsExtreme 𝕜 A B) :
     B.extremePoints 𝕜 = B ∩ A.extremePoints 𝕜 :=
   Subset.antisymm (fun x hx => ⟨hx.1, hAB.extremePoints_subset_extremePoints hx⟩)
@@ -260,20 +218,11 @@ section OrderedSemiring
 variable [OrderedSemiring 𝕜] [AddCommGroup E] [AddCommGroup F] [∀ i, AddCommGroup (π i)]
   [Module 𝕜 E] [Module 𝕜 F] [∀ i, Module 𝕜 (π i)] {A B : Set E} {x : E}
 
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-Case conversion may be inaccurate. Consider using '#align is_extreme.convex_diff IsExtreme.convex_diffₓ'. -/
 theorem IsExtreme.convex_diff (hA : Convex 𝕜 A) (hAB : IsExtreme 𝕜 A B) : Convex 𝕜 (A \ B) :=
   convex_iff_openSegment_subset.2 fun x₁ ⟨hx₁A, hx₁B⟩ x₂ ⟨hx₂A, hx₂B⟩ x hx =>
     ⟨hA.openSegment_subset hx₁A hx₂A hx, fun hxB => hx₁B (hAB.2 hx₁A hx₂A hxB hx).1⟩
 #align is_extreme.convex_diff IsExtreme.convex_diff
 
-/- warning: extreme_points_prod -> extremePoints_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align extreme_points_prod extremePoints_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -337,9 +286,6 @@ variable {𝕜} [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
-/- warning: mem_extreme_points_iff_forall_segment -> mem_extremePoints_iff_forall_segment is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mem_extreme_points_iff_forall_segment mem_extremePoints_iff_forall_segmentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
 that contain it are those with `x` as one of their endpoints. -/
@@ -357,9 +303,6 @@ theorem mem_extremePoints_iff_forall_segment :
     exacts[⟨rfl, (left_mem_openSegment_iff.1 hx).symm⟩, ⟨right_mem_openSegment_iff.1 hx, rfl⟩]
 #align mem_extreme_points_iff_forall_segment mem_extremePoints_iff_forall_segment
 
-/- warning: convex.mem_extreme_points_iff_convex_diff -> Convex.mem_extremePoints_iff_convex_diff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align convex.mem_extreme_points_iff_convex_diff Convex.mem_extremePoints_iff_convex_diffₓ'. -/
 theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A ∧ Convex 𝕜 (A \ {x}) :=
   by
@@ -374,18 +317,12 @@ theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
       rfl
 #align convex.mem_extreme_points_iff_convex_diff Convex.mem_extremePoints_iff_convex_diff
 
-/- warning: convex.mem_extreme_points_iff_mem_diff_convex_hull_diff -> Convex.mem_extremePoints_iff_mem_diff_convexHull_diff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align convex.mem_extreme_points_iff_mem_diff_convex_hull_diff Convex.mem_extremePoints_iff_mem_diff_convexHull_diffₓ'. -/
 theorem Convex.mem_extremePoints_iff_mem_diff_convexHull_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A \ convexHull 𝕜 (A \ {x}) := by
   rw [hA.mem_extreme_points_iff_convex_diff, hA.convex_remove_iff_not_mem_convex_hull_remove,
     mem_diff]
 #align convex.mem_extreme_points_iff_mem_diff_convex_hull_diff Convex.mem_extremePoints_iff_mem_diff_convexHull_diff
 
-/- warning: extreme_points_convex_hull_subset -> extremePoints_convexHull_subset is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align extreme_points_convex_hull_subset extremePoints_convexHull_subsetₓ'. -/
 theorem extremePoints_convexHull_subset : (convexHull 𝕜 A).extremePoints 𝕜 ⊆ A :=
   by
   rintro x hx

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

@@ -161,8 +161,7 @@ theorem isExtreme_iInter {ι : Sort _} [Nonempty ι] {F : ι → Set E}
 
 #print isExtreme_biInter /-
 theorem isExtreme_biInter {F : Set (Set E)} (hF : F.Nonempty) (hA : ∀ B ∈ F, IsExtreme 𝕜 A B) :
-    IsExtreme 𝕜 A (⋂ B ∈ F, B) := by
-  haveI := hF.to_subtype
+    IsExtreme 𝕜 A (⋂ B ∈ F, B) := by haveI := hF.to_subtype;
   simpa only [Inter_subtype] using isExtreme_iInter fun i : F => hA _ i.2
 #align is_extreme_bInter isExtreme_biInter
 -/

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

@@ -273,10 +273,7 @@ theorem IsExtreme.convex_diff (hA : Convex 𝕜 A) (hAB : IsExtreme 𝕜 A B) :
 #align is_extreme.convex_diff IsExtreme.convex_diff
 
 /- warning: extreme_points_prod -> extremePoints_prod is a dubious translation:
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-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : AddCommGroup.{u2} F] [_inst_5 : Module.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_6 : Module.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_3)] (s : Set.{u3} E) (t : Set.{u2} F), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (Prod.{u3, u2} E F)) (Set.extremePoints.{u1, max u3 u2} 𝕜 (Prod.{u3, u2} E F) _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (AddCommGroup.toAddCommMonoid.{u2} F _inst_3)) (Prod.smul.{u1, u3, u2} 𝕜 E F (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_3) _inst_6))))) (Set.prod.{u3, u2} E F s t)) (Set.prod.{u3, u2} E F (Set.extremePoints.{u1, u3} 𝕜 E _inst_1 (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))) s) (Set.extremePoints.{u1, u2} 𝕜 F _inst_1 (AddCommGroup.toAddCommMonoid.{u2} F _inst_3) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_3) _inst_6)))) t))
+<too large>
 Case conversion may be inaccurate. Consider using '#align extreme_points_prod extremePoints_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -342,10 +339,7 @@ variable {𝕜} [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
 /- warning: mem_extreme_points_iff_forall_segment -> mem_extremePoints_iff_forall_segment is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x A) (forall (x₁ : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x₁ A) -> (forall (x₂ : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x₂ A) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x₁ x₂)) -> (Or (Eq.{succ u2} E x₁ x) (Eq.{succ u2} E x₂ x)))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x A) (forall (x₁ : E), (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x₁ A) -> (forall (x₂ : E), (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x₂ A) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x₁ x₂)) -> (Or (Eq.{succ u2} E x₁ x) (Eq.{succ u2} E x₂ x)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mem_extreme_points_iff_forall_segment mem_extremePoints_iff_forall_segmentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
@@ -365,10 +359,7 @@ theorem mem_extremePoints_iff_forall_segment :
 #align mem_extreme_points_iff_forall_segment mem_extremePoints_iff_forall_segment
 
 /- warning: convex.mem_extreme_points_iff_convex_diff -> Convex.mem_extremePoints_iff_convex_diff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x A) (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x)))))
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-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] {A : Set.{u1} E} {x : E}, (Convex.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (Set.extremePoints.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A)) (And (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x A) (Convex.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align convex.mem_extreme_points_iff_convex_diff Convex.mem_extremePoints_iff_convex_diffₓ'. -/
 theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A ∧ Convex 𝕜 (A \ {x}) :=
@@ -385,10 +376,7 @@ theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
 #align convex.mem_extreme_points_iff_convex_diff Convex.mem_extremePoints_iff_convex_diff
 
 /- warning: convex.mem_extreme_points_iff_mem_diff_convex_hull_diff -> Convex.mem_extremePoints_iff_mem_diff_convexHull_diff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x))))))
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-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] {A : Set.{u1} E} {x : E}, (Convex.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (Set.extremePoints.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A)) (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A (OrderHom.toFun.{u1, u1} (Set.{u1} E) (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (ClosureOperator.toOrderHom.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align convex.mem_extreme_points_iff_mem_diff_convex_hull_diff Convex.mem_extremePoints_iff_mem_diff_convexHull_diffₓ'. -/
 theorem Convex.mem_extremePoints_iff_mem_diff_convexHull_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A \ convexHull 𝕜 (A \ {x}) := by
@@ -397,10 +385,7 @@ theorem Convex.mem_extremePoints_iff_mem_diff_convexHull_diff (hA : Convex 𝕜
 #align convex.mem_extreme_points_iff_mem_diff_convex_hull_diff Convex.mem_extremePoints_iff_mem_diff_convexHull_diff
 
 /- warning: extreme_points_convex_hull_subset -> extremePoints_convexHull_subset is a dubious translation:
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E}, HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) A)) A
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E}, HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (OrderHom.toFun.{u2, u2} (Set.{u2} E) (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.instCompleteBooleanAlgebraSet.{u2} E))))))) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.instCompleteBooleanAlgebraSet.{u2} E))))))) (ClosureOperator.toOrderHom.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.instCompleteBooleanAlgebraSet.{u2} E))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) A)) A
+<too large>
 Case conversion may be inaccurate. Consider using '#align extreme_points_convex_hull_subset extremePoints_convexHull_subsetₓ'. -/
 theorem extremePoints_convexHull_subset : (convexHull 𝕜 A).extremePoints 𝕜 ⊆ A :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -343,7 +343,7 @@ variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
 /- warning: mem_extreme_points_iff_forall_segment -> mem_extremePoints_iff_forall_segment is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x A) (forall (x₁ : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x₁ A) -> (forall (x₂ : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x₂ A) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x₁ x₂)) -> (Or (Eq.{succ u2} E x₁ x) (Eq.{succ u2} E x₂ x)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x A) (forall (x₁ : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x₁ A) -> (forall (x₂ : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x₂ A) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x₁ x₂)) -> (Or (Eq.{succ u2} E x₁ x) (Eq.{succ u2} E x₂ x)))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x A) (forall (x₁ : E), (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x₁ A) -> (forall (x₂ : E), (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x₂ A) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x₁ x₂)) -> (Or (Eq.{succ u2} E x₁ x) (Eq.{succ u2} E x₂ x)))))
 Case conversion may be inaccurate. Consider using '#align mem_extreme_points_iff_forall_segment mem_extremePoints_iff_forall_segmentₓ'. -/
@@ -366,7 +366,7 @@ theorem mem_extremePoints_iff_forall_segment :
 
 /- warning: convex.mem_extreme_points_iff_convex_diff -> Convex.mem_extremePoints_iff_convex_diff is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x A) (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x A) (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x)))))
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] {A : Set.{u1} E} {x : E}, (Convex.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (Set.extremePoints.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A)) (And (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x A) (Convex.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x)))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_extreme_points_iff_convex_diff Convex.mem_extremePoints_iff_convex_diffₓ'. -/
@@ -386,7 +386,7 @@ theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
 
 /- warning: convex.mem_extreme_points_iff_mem_diff_convex_hull_diff -> Convex.mem_extremePoints_iff_mem_diff_convexHull_diff is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x))))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x))))))
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] {A : Set.{u1} E} {x : E}, (Convex.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (Set.extremePoints.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A)) (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A (OrderHom.toFun.{u1, u1} (Set.{u1} E) (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (ClosureOperator.toOrderHom.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_extreme_points_iff_mem_diff_convex_hull_diff Convex.mem_extremePoints_iff_mem_diff_convexHull_diffₓ'. -/
@@ -398,7 +398,7 @@ theorem Convex.mem_extremePoints_iff_mem_diff_convexHull_diff (hA : Convex 𝕜
 
 /- warning: extreme_points_convex_hull_subset -> extremePoints_convexHull_subset is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E}, HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) A)) A
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E}, HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) A)) A
 but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E}, HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (OrderHom.toFun.{u2, u2} (Set.{u2} E) (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.instCompleteBooleanAlgebraSet.{u2} E))))))) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.instCompleteBooleanAlgebraSet.{u2} E))))))) (ClosureOperator.toOrderHom.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.instCompleteBooleanAlgebraSet.{u2} E))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) A)) A
 Case conversion may be inaccurate. Consider using '#align extreme_points_convex_hull_subset extremePoints_convexHull_subsetₓ'. -/

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

@@ -147,8 +147,8 @@ protected theorem IsExtreme.mono (hAC : IsExtreme 𝕜 A C) (hBA : B ⊆ A) (hCB
   ⟨hCB, fun x₁ hx₁B x₂ hx₂B x hxC hx => hAC.2 (hBA hx₁B) (hBA hx₂B) hxC hx⟩
 #align is_extreme.mono IsExtreme.mono
 
-#print isExtreme_interᵢ /-
-theorem isExtreme_interᵢ {ι : Sort _} [Nonempty ι] {F : ι → Set E}
+#print isExtreme_iInter /-
+theorem isExtreme_iInter {ι : Sort _} [Nonempty ι] {F : ι → Set E}
     (hAF : ∀ i : ι, IsExtreme 𝕜 A (F i)) : IsExtreme 𝕜 A (⋂ i : ι, F i) :=
   by
   obtain i := Classical.arbitrary ι
@@ -156,26 +156,26 @@ theorem isExtreme_interᵢ {ι : Sort _} [Nonempty ι] {F : ι → Set E}
   simp_rw [mem_Inter] at hxF⊢
   have h := fun i => (hAF i).2 hx₁A hx₂A (hxF i) hx
   exact ⟨fun i => (h i).1, fun i => (h i).2⟩
-#align is_extreme_Inter isExtreme_interᵢ
+#align is_extreme_Inter isExtreme_iInter
 -/
 
-#print isExtreme_binterᵢ /-
-theorem isExtreme_binterᵢ {F : Set (Set E)} (hF : F.Nonempty) (hA : ∀ B ∈ F, IsExtreme 𝕜 A B) :
+#print isExtreme_biInter /-
+theorem isExtreme_biInter {F : Set (Set E)} (hF : F.Nonempty) (hA : ∀ B ∈ F, IsExtreme 𝕜 A B) :
     IsExtreme 𝕜 A (⋂ B ∈ F, B) := by
   haveI := hF.to_subtype
-  simpa only [Inter_subtype] using isExtreme_interᵢ fun i : F => hA _ i.2
-#align is_extreme_bInter isExtreme_binterᵢ
+  simpa only [Inter_subtype] using isExtreme_iInter fun i : F => hA _ i.2
+#align is_extreme_bInter isExtreme_biInter
 -/
 
-#print isExtreme_interₛ /-
-theorem isExtreme_interₛ {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F, IsExtreme 𝕜 A B) :
+#print isExtreme_sInter /-
+theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F, IsExtreme 𝕜 A B) :
     IsExtreme 𝕜 A (⋂₀ F) := by
   obtain ⟨B, hB⟩ := hF
   refine' ⟨(sInter_subset_of_mem hB).trans (hAF B hB).1, fun x₁ hx₁A x₂ hx₂A x hxF hx => _⟩
   simp_rw [mem_sInter] at hxF⊢
   have h := fun B hB => (hAF B hB).2 hx₁A hx₂A (hxF B hB) hx
   exact ⟨fun B hB => (h B hB).1, fun B hB => (h B hB).2⟩
-#align is_extreme_sInter isExtreme_interₛ
+#align is_extreme_sInter isExtreme_sInter
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module analysis.convex.extreme
-! leanprover-community/mathlib commit c5773405394e073885e2a144c9ca14637e8eb963
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.Convex.Hull
 /-!
 # Extreme sets
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines extreme sets and extreme points for sets in a module.
 
 An extreme set of `A` is a subset of `A` that is as far as it can get in any outward direction: If

mathlib commit https://github.com/leanprover-community/mathlib/commit/0148d455199ed64bf8eb2f493a1e7eb9211ce170

@@ -56,29 +56,47 @@ section SMul
 
 variable (𝕜) [OrderedSemiring 𝕜] [AddCommMonoid E] [SMul 𝕜 E]
 
+#print IsExtreme /-
 /-- A set `B` is an extreme subset of `A` if `B ⊆ A` and all points of `B` only belong to open
 segments whose ends are in `B`. -/
 def IsExtreme (A B : Set E) : Prop :=
   B ⊆ A ∧ ∀ ⦃x₁⦄, x₁ ∈ A → ∀ ⦃x₂⦄, x₂ ∈ A → ∀ ⦃x⦄, x ∈ B → x ∈ openSegment 𝕜 x₁ x₂ → x₁ ∈ B ∧ x₂ ∈ B
 #align is_extreme IsExtreme
+-/
 
+#print Set.extremePoints /-
 /-- A point `x` is an extreme point of a set `A` if `x` belongs to no open segment with ends in
 `A`, except for the obvious `open_segment x x`. -/
 def Set.extremePoints (A : Set E) : Set E :=
   { x ∈ A | ∀ ⦃x₁⦄, x₁ ∈ A → ∀ ⦃x₂⦄, x₂ ∈ A → x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x }
 #align set.extreme_points Set.extremePoints
+-/
 
+#print IsExtreme.refl /-
 @[refl]
 protected theorem IsExtreme.refl (A : Set E) : IsExtreme 𝕜 A A :=
   ⟨Subset.rfl, fun x₁ hx₁A x₂ hx₂A x hxA hx => ⟨hx₁A, hx₂A⟩⟩
 #align is_extreme.refl IsExtreme.refl
+-/
 
 variable {𝕜} {A B C : Set E} {x : E}
 
+/- warning: is_extreme.rfl -> IsExtreme.rfl is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {A : Set.{u2} E}, IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A A
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : SMul.{u2, u1} 𝕜 E] {A : Set.{u1} E}, IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A A
+Case conversion may be inaccurate. Consider using '#align is_extreme.rfl IsExtreme.rflₓ'. -/
 protected theorem IsExtreme.rfl : IsExtreme 𝕜 A A :=
   IsExtreme.refl 𝕜 A
 #align is_extreme.rfl IsExtreme.rfl
 
+/- warning: is_extreme.trans -> IsExtreme.trans is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {A : Set.{u2} E} {B : Set.{u2} E} {C : Set.{u2} E}, (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A B) -> (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 B C) -> (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A C)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : SMul.{u2, u1} 𝕜 E] {A : Set.{u1} E} {B : Set.{u1} E} {C : Set.{u1} E}, (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A B) -> (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 B C) -> (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A C)
+Case conversion may be inaccurate. Consider using '#align is_extreme.trans IsExtreme.transₓ'. -/
 @[trans]
 protected theorem IsExtreme.trans (hAB : IsExtreme 𝕜 A B) (hBC : IsExtreme 𝕜 B C) :
     IsExtreme 𝕜 A C :=
@@ -88,9 +106,11 @@ protected theorem IsExtreme.trans (hAB : IsExtreme 𝕜 A B) (hBC : IsExtreme 
   exact hBC.2 hx₁B hx₂B hxC hx
 #align is_extreme.trans IsExtreme.trans
 
+#print IsExtreme.antisymm /-
 protected theorem IsExtreme.antisymm : AntiSymmetric (IsExtreme 𝕜 : Set E → Set E → Prop) :=
   fun A B hAB hBA => Subset.antisymm hBA.1 hAB.1
 #align is_extreme.antisymm IsExtreme.antisymm
+-/
 
 instance : IsPartialOrder (Set E) (IsExtreme 𝕜)
     where
@@ -98,6 +118,12 @@ instance : IsPartialOrder (Set E) (IsExtreme 𝕜)
   trans A B C := IsExtreme.trans
   antisymm := IsExtreme.antisymm
 
+/- warning: is_extreme.inter -> IsExtreme.inter is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {A : Set.{u2} E} {B : Set.{u2} E} {C : Set.{u2} E}, (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A B) -> (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A C) -> (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) B C))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : SMul.{u2, u1} 𝕜 E] {A : Set.{u1} E} {B : Set.{u1} E} {C : Set.{u1} E}, (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A B) -> (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A C) -> (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) B C))
+Case conversion may be inaccurate. Consider using '#align is_extreme.inter IsExtreme.interₓ'. -/
 theorem IsExtreme.inter (hAB : IsExtreme 𝕜 A B) (hAC : IsExtreme 𝕜 A C) : IsExtreme 𝕜 A (B ∩ C) :=
   by
   use subset.trans (inter_subset_left _ _) hAB.1
@@ -107,11 +133,18 @@ theorem IsExtreme.inter (hAB : IsExtreme 𝕜 A B) (hAC : IsExtreme 𝕜 A C) :
   exact ⟨⟨hx₁B, hx₁C⟩, hx₂B, hx₂C⟩
 #align is_extreme.inter IsExtreme.inter
 
+/- warning: is_extreme.mono -> IsExtreme.mono is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {A : Set.{u2} E} {B : Set.{u2} E} {C : Set.{u2} E}, (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A C) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) B A) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) C B) -> (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 B C)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : SMul.{u2, u1} 𝕜 E] {A : Set.{u1} E} {B : Set.{u1} E} {C : Set.{u1} E}, (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A C) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) B A) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) C B) -> (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 B C)
+Case conversion may be inaccurate. Consider using '#align is_extreme.mono IsExtreme.monoₓ'. -/
 protected theorem IsExtreme.mono (hAC : IsExtreme 𝕜 A C) (hBA : B ⊆ A) (hCB : C ⊆ B) :
     IsExtreme 𝕜 B C :=
   ⟨hCB, fun x₁ hx₁B x₂ hx₂B x hxC hx => hAC.2 (hBA hx₁B) (hBA hx₂B) hxC hx⟩
 #align is_extreme.mono IsExtreme.mono
 
+#print isExtreme_interᵢ /-
 theorem isExtreme_interᵢ {ι : Sort _} [Nonempty ι] {F : ι → Set E}
     (hAF : ∀ i : ι, IsExtreme 𝕜 A (F i)) : IsExtreme 𝕜 A (⋂ i : ι, F i) :=
   by
@@ -121,13 +154,17 @@ theorem isExtreme_interᵢ {ι : Sort _} [Nonempty ι] {F : ι → Set E}
   have h := fun i => (hAF i).2 hx₁A hx₂A (hxF i) hx
   exact ⟨fun i => (h i).1, fun i => (h i).2⟩
 #align is_extreme_Inter isExtreme_interᵢ
+-/
 
-theorem isExtreme_bInter {F : Set (Set E)} (hF : F.Nonempty) (hA : ∀ B ∈ F, IsExtreme 𝕜 A B) :
+#print isExtreme_binterᵢ /-
+theorem isExtreme_binterᵢ {F : Set (Set E)} (hF : F.Nonempty) (hA : ∀ B ∈ F, IsExtreme 𝕜 A B) :
     IsExtreme 𝕜 A (⋂ B ∈ F, B) := by
   haveI := hF.to_subtype
   simpa only [Inter_subtype] using isExtreme_interᵢ fun i : F => hA _ i.2
-#align is_extreme_bInter isExtreme_bInter
+#align is_extreme_bInter isExtreme_binterᵢ
+-/
 
+#print isExtreme_interₛ /-
 theorem isExtreme_interₛ {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F, IsExtreme 𝕜 A B) :
     IsExtreme 𝕜 A (⋂₀ F) := by
   obtain ⟨B, hB⟩ := hF
@@ -136,14 +173,18 @@ theorem isExtreme_interₛ {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈
   have h := fun B hB => (hAF B hB).2 hx₁A hx₂A (hxF B hB) hx
   exact ⟨fun B hB => (h B hB).1, fun B hB => (h B hB).2⟩
 #align is_extreme_sInter isExtreme_interₛ
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+#print mem_extremePoints /-
 theorem mem_extremePoints :
     x ∈ A.extremePoints 𝕜 ↔
       x ∈ A ∧ ∀ (x₁) (_ : x₁ ∈ A) (x₂) (_ : x₂ ∈ A), x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x :=
   Iff.rfl
 #align mem_extreme_points mem_extremePoints
+-/
 
+#print mem_extremePoints_iff_extreme_singleton /-
 /-- x is an extreme point to A iff {x} is an extreme set of A. -/
 theorem mem_extremePoints_iff_extreme_singleton : x ∈ A.extremePoints 𝕜 ↔ IsExtreme 𝕜 A {x} :=
   by
@@ -153,32 +194,57 @@ theorem mem_extremePoints_iff_extreme_singleton : x ∈ A.extremePoints 𝕜 ↔
   rintro x₁ hx₁A x₂ hx₂A y (rfl : y = x)
   exact hAx hx₁A hx₂A
 #align mem_extreme_points_iff_extreme_singleton mem_extremePoints_iff_extreme_singleton
+-/
 
+#print extremePoints_subset /-
 theorem extremePoints_subset : A.extremePoints 𝕜 ⊆ A := fun x hx => hx.1
 #align extreme_points_subset extremePoints_subset
+-/
 
+#print extremePoints_empty /-
 @[simp]
 theorem extremePoints_empty : (∅ : Set E).extremePoints 𝕜 = ∅ :=
   subset_empty_iff.1 extremePoints_subset
 #align extreme_points_empty extremePoints_empty
+-/
 
+#print extremePoints_singleton /-
 @[simp]
 theorem extremePoints_singleton : ({x} : Set E).extremePoints 𝕜 = {x} :=
   extremePoints_subset.antisymm <|
     singleton_subset_iff.2 ⟨mem_singleton x, fun x₁ hx₁ x₂ hx₂ _ => ⟨hx₁, hx₂⟩⟩
 #align extreme_points_singleton extremePoints_singleton
+-/
 
+/- warning: inter_extreme_points_subset_extreme_points_of_subset -> inter_extremePoints_subset_extremePoints_of_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {A : Set.{u2} E} {B : Set.{u2} E}, (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) B A) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) B (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A)) (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 B))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {A : Set.{u2} E} {B : Set.{u2} E}, (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) B A) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Inter.inter.{u2} (Set.{u2} E) (Set.instInterSet.{u2} E) B (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A)) (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 B))
+Case conversion may be inaccurate. Consider using '#align inter_extreme_points_subset_extreme_points_of_subset inter_extremePoints_subset_extremePoints_of_subsetₓ'. -/
 theorem inter_extremePoints_subset_extremePoints_of_subset (hBA : B ⊆ A) :
     B ∩ A.extremePoints 𝕜 ⊆ B.extremePoints 𝕜 := fun x ⟨hxB, hxA⟩ =>
   ⟨hxB, fun x₁ hx₁ x₂ hx₂ hx => hxA.2 (hBA hx₁) (hBA hx₂) hx⟩
 #align inter_extreme_points_subset_extreme_points_of_subset inter_extremePoints_subset_extremePoints_of_subset
 
+/- warning: is_extreme.extreme_points_subset_extreme_points -> IsExtreme.extremePoints_subset_extremePoints is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {A : Set.{u2} E} {B : Set.{u2} E}, (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A B) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 B) (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : SMul.{u2, u1} 𝕜 E] {A : Set.{u1} E} {B : Set.{u1} E}, (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A B) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) (Set.extremePoints.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 B) (Set.extremePoints.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A))
+Case conversion may be inaccurate. Consider using '#align is_extreme.extreme_points_subset_extreme_points IsExtreme.extremePoints_subset_extremePointsₓ'. -/
 theorem IsExtreme.extremePoints_subset_extremePoints (hAB : IsExtreme 𝕜 A B) :
     B.extremePoints 𝕜 ⊆ A.extremePoints 𝕜 := fun x hx =>
   mem_extremePoints_iff_extreme_singleton.2
     (hAB.trans (mem_extremePoints_iff_extreme_singleton.1 hx))
 #align is_extreme.extreme_points_subset_extreme_points IsExtreme.extremePoints_subset_extremePoints
 
+/- warning: is_extreme.extreme_points_eq -> IsExtreme.extremePoints_eq is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {A : Set.{u2} E} {B : Set.{u2} E}, (IsExtreme.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A B) -> (Eq.{succ u2} (Set.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 B) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) B (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 A)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : SMul.{u2, u1} 𝕜 E] {A : Set.{u1} E} {B : Set.{u1} E}, (IsExtreme.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A B) -> (Eq.{succ u1} (Set.{u1} E) (Set.extremePoints.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 B) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) B (Set.extremePoints.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 A)))
+Case conversion may be inaccurate. Consider using '#align is_extreme.extreme_points_eq IsExtreme.extremePoints_eqₓ'. -/
 theorem IsExtreme.extremePoints_eq (hAB : IsExtreme 𝕜 A B) :
     B.extremePoints 𝕜 = B ∩ A.extremePoints 𝕜 :=
   Subset.antisymm (fun x hx => ⟨hx.1, hAB.extremePoints_subset_extremePoints hx⟩)
@@ -192,11 +258,23 @@ section OrderedSemiring
 variable [OrderedSemiring 𝕜] [AddCommGroup E] [AddCommGroup F] [∀ i, AddCommGroup (π i)]
   [Module 𝕜 E] [Module 𝕜 F] [∀ i, Module 𝕜 (π i)] {A B : Set E} {x : E}
 
+/- warning: is_extreme.convex_diff -> IsExtreme.convex_diff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {A : Set.{u2} E} {B : Set.{u2} E}, (Convex.{u1, u2} 𝕜 E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) A) -> (IsExtreme.{u1, u2} 𝕜 E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) A B) -> (Convex.{u1, u2} 𝕜 E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A B))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {A : Set.{u1} E} {B : Set.{u1} E}, (Convex.{u2, u1} 𝕜 E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_5)))) A) -> (IsExtreme.{u2, u1} 𝕜 E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_5)))) A B) -> (Convex.{u2, u1} 𝕜 E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_5)))) (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A B))
+Case conversion may be inaccurate. Consider using '#align is_extreme.convex_diff IsExtreme.convex_diffₓ'. -/
 theorem IsExtreme.convex_diff (hA : Convex 𝕜 A) (hAB : IsExtreme 𝕜 A B) : Convex 𝕜 (A \ B) :=
   convex_iff_openSegment_subset.2 fun x₁ ⟨hx₁A, hx₁B⟩ x₂ ⟨hx₂A, hx₂B⟩ x hx =>
     ⟨hA.openSegment_subset hx₁A hx₂A hx, fun hxB => hx₁B (hAB.2 hx₁A hx₂A hxB hx).1⟩
 #align is_extreme.convex_diff IsExtreme.convex_diff
 
+/- warning: extreme_points_prod -> extremePoints_prod is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_6 : Module.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)] (s : Set.{u2} E) (t : Set.{u3} F), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.extremePoints.{u1, max u2 u3} 𝕜 (Prod.{u2, u3} E F) _inst_1 (Prod.addCommMonoid.{u2, u3} E F (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)) (Prod.smul.{u1, u2, u3} 𝕜 E F (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_6))))) (Set.prod.{u2, u3} E F s t)) (Set.prod.{u2, u3} E F (Set.extremePoints.{u1, u2} 𝕜 E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) s) (Set.extremePoints.{u1, u3} 𝕜 F _inst_1 (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) _inst_6)))) t))
+but is expected to have type
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(SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_3) _inst_6))))) (Set.prod.{u3, u2} E F s t)) (Set.prod.{u3, u2} E F (Set.extremePoints.{u1, u3} 𝕜 E _inst_1 (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_5)))) s) (Set.extremePoints.{u1, u2} 𝕜 F _inst_1 (AddCommGroup.toAddCommMonoid.{u2} F _inst_3) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F _inst_3))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} F _inst_3) _inst_6)))) t))
+Case conversion may be inaccurate. Consider using '#align extreme_points_prod extremePoints_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -226,6 +304,7 @@ theorem extremePoints_prod (s : Set E) (t : Set F) :
           h.2 hx₁.2 hx₂.2 ⟨a, b, ha, hb, hab, congr_arg Prod.snd hx'⟩⟩
 #align extreme_points_prod extremePoints_prod
 
+#print extremePoints_pi /-
 @[simp]
 theorem extremePoints_pi (s : ∀ i, Set (π i)) :
     (univ.pi s).extremePoints 𝕜 = univ.pi fun i => (s i).extremePoints 𝕜 :=
@@ -249,6 +328,7 @@ theorem extremePoints_pi (s : ∀ i, Set (π i)) :
     simp_rw [funext_iff, ← forall_and]
     exact fun i => h _ _ (hx₁ _) _ (hx₂ _) ⟨a, b, ha, hb, hab, congr_fun hx' _⟩
 #align extreme_points_pi extremePoints_pi
+-/
 
 end OrderedSemiring
 
@@ -258,6 +338,12 @@ variable {𝕜} [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
+/- warning: mem_extreme_points_iff_forall_segment -> mem_extremePoints_iff_forall_segment is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x A) (forall (x₁ : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x₁ A) -> (forall (x₂ : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x₂ A) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x₁ x₂)) -> (Or (Eq.{succ u2} E x₁ x) (Eq.{succ u2} E x₂ x)))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x A) (forall (x₁ : E), (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x₁ A) -> (forall (x₂ : E), (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x₂ A) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x₁ x₂)) -> (Or (Eq.{succ u2} E x₁ x) (Eq.{succ u2} E x₂ x)))))
+Case conversion may be inaccurate. Consider using '#align mem_extreme_points_iff_forall_segment mem_extremePoints_iff_forall_segmentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
 that contain it are those with `x` as one of their endpoints. -/
@@ -275,6 +361,12 @@ theorem mem_extremePoints_iff_forall_segment :
     exacts[⟨rfl, (left_mem_openSegment_iff.1 hx).symm⟩, ⟨right_mem_openSegment_iff.1 hx, rfl⟩]
 #align mem_extreme_points_iff_forall_segment mem_extremePoints_iff_forall_segment
 
+/- warning: convex.mem_extreme_points_iff_convex_diff -> Convex.mem_extremePoints_iff_convex_diff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (And (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x A) (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x)))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] {A : Set.{u1} E} {x : E}, (Convex.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (Set.extremePoints.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A)) (And (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x A) (Convex.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x)))))
+Case conversion may be inaccurate. Consider using '#align convex.mem_extreme_points_iff_convex_diff Convex.mem_extremePoints_iff_convex_diffₓ'. -/
 theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A ∧ Convex 𝕜 (A \ {x}) :=
   by
@@ -289,12 +381,24 @@ theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
       rfl
 #align convex.mem_extreme_points_iff_convex_diff Convex.mem_extremePoints_iff_convex_diff
 
+/- warning: convex.mem_extreme_points_iff_mem_diff_convex_hull_diff -> Convex.mem_extremePoints_iff_mem_diff_convexHull_diff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E} {x : E}, (Convex.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) A)) (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) (SDiff.sdiff.{u2} (Set.{u2} E) (BooleanAlgebra.toHasSdiff.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E)) A (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x))))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] {A : Set.{u1} E} {x : E}, (Convex.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (Set.extremePoints.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) A)) (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A (OrderHom.toFun.{u1, u1} (Set.{u1} E) (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (ClosureOperator.toOrderHom.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)) (SDiff.sdiff.{u1} (Set.{u1} E) (Set.instSDiffSet.{u1} E) A (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x))))))
+Case conversion may be inaccurate. Consider using '#align convex.mem_extreme_points_iff_mem_diff_convex_hull_diff Convex.mem_extremePoints_iff_mem_diff_convexHull_diffₓ'. -/
 theorem Convex.mem_extremePoints_iff_mem_diff_convexHull_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A \ convexHull 𝕜 (A \ {x}) := by
   rw [hA.mem_extreme_points_iff_convex_diff, hA.convex_remove_iff_not_mem_convex_hull_remove,
     mem_diff]
 #align convex.mem_extreme_points_iff_mem_diff_convex_hull_diff Convex.mem_extremePoints_iff_mem_diff_convexHull_diff
 
+/- warning: extreme_points_convex_hull_subset -> extremePoints_convexHull_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E}, HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3) A)) A
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] {A : Set.{u2} E}, HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.extremePoints.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (OrderHom.toFun.{u2, u2} (Set.{u2} E) (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.instCompleteBooleanAlgebraSet.{u2} E))))))) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.instCompleteBooleanAlgebraSet.{u2} E))))))) (ClosureOperator.toOrderHom.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.instCompleteBooleanAlgebraSet.{u2} E))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) A)) A
+Case conversion may be inaccurate. Consider using '#align extreme_points_convex_hull_subset extremePoints_convexHull_subsetₓ'. -/
 theorem extremePoints_convexHull_subset : (convexHull 𝕜 A).extremePoints 𝕜 ⊆ A :=
   by
   rintro x hx

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module analysis.convex.extreme
-! leanprover-community/mathlib commit 0da544672fd2b9b9d17c733798caef598c533f65
+! leanprover-community/mathlib commit c5773405394e073885e2a144c9ca14637e8eb963
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -40,21 +40,21 @@ See chapter 8 of [Barry Simon, *Convexity*][simon2011]
 
 ## TODO
 
-Define intrinsic frontier and prove lemmas related to extreme sets and points.
+Prove lemmas relating extreme sets and points to the intrinsic frontier.
 
 More not-yet-PRed stuff is available on the branch `sperner_again`.
 -/
 
 
-open Classical Affine
+open Function Set
 
-open Set
+open Affine Classical
 
-variable (𝕜 : Type _) {E : Type _}
+variable {𝕜 E F ι : Type _} {π : ι → Type _}
 
 section SMul
 
-variable [OrderedSemiring 𝕜] [AddCommMonoid E] [SMul 𝕜 E]
+variable (𝕜) [OrderedSemiring 𝕜] [AddCommMonoid E] [SMul 𝕜 E]
 
 /-- A set `B` is an extreme subset of `A` if `B ⊆ A` and all points of `B` only belong to open
 segments whose ends are in `B`. -/
@@ -112,7 +112,7 @@ protected theorem IsExtreme.mono (hAC : IsExtreme 𝕜 A C) (hBA : B ⊆ A) (hCB
   ⟨hCB, fun x₁ hx₁B x₂ hx₂B x hxC hx => hAC.2 (hBA hx₁B) (hBA hx₂B) hxC hx⟩
 #align is_extreme.mono IsExtreme.mono
 
-theorem isExtreme_interᵢ {ι : Type _} [Nonempty ι] {F : ι → Set E}
+theorem isExtreme_interᵢ {ι : Sort _} [Nonempty ι] {F : ι → Set E}
     (hAF : ∀ i : ι, IsExtreme 𝕜 A (F i)) : IsExtreme 𝕜 A (⋂ i : ι, F i) :=
   by
   obtain i := Classical.arbitrary ι
@@ -122,13 +122,10 @@ theorem isExtreme_interᵢ {ι : Type _} [Nonempty ι] {F : ι → Set E}
   exact ⟨fun i => (h i).1, fun i => (h i).2⟩
 #align is_extreme_Inter isExtreme_interᵢ
 
-theorem isExtreme_bInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F, IsExtreme 𝕜 A B) :
+theorem isExtreme_bInter {F : Set (Set E)} (hF : F.Nonempty) (hA : ∀ B ∈ F, IsExtreme 𝕜 A B) :
     IsExtreme 𝕜 A (⋂ B ∈ F, B) := by
-  obtain ⟨B, hB⟩ := hF
-  refine' ⟨(bInter_subset_of_mem hB).trans (hAF B hB).1, fun x₁ hx₁A x₂ hx₂A x hxF hx => _⟩
-  simp_rw [mem_Inter₂] at hxF⊢
-  have h := fun B hB => (hAF B hB).2 hx₁A hx₂A (hxF B hB) hx
-  exact ⟨fun B hB => (h B hB).1, fun B hB => (h B hB).2⟩
+  haveI := hF.to_subtype
+  simpa only [Inter_subtype] using isExtreme_interᵢ fun i : F => hA _ i.2
 #align is_extreme_bInter isExtreme_bInter
 
 theorem isExtreme_interₛ {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F, IsExtreme 𝕜 A B) :
@@ -141,11 +138,11 @@ theorem isExtreme_interₛ {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈
 #align is_extreme_sInter isExtreme_interₛ
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
-theorem extremePoints_def :
+theorem mem_extremePoints :
     x ∈ A.extremePoints 𝕜 ↔
       x ∈ A ∧ ∀ (x₁) (_ : x₁ ∈ A) (x₂) (_ : x₂ ∈ A), x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x :=
   Iff.rfl
-#align extreme_points_def extremePoints_def
+#align mem_extreme_points mem_extremePoints
 
 /-- x is an extreme point to A iff {x} is an extreme set of A. -/
 theorem mem_extremePoints_iff_extreme_singleton : x ∈ A.extremePoints 𝕜 ↔ IsExtreme 𝕜 A {x} :=
@@ -192,13 +189,67 @@ end SMul
 
 section OrderedSemiring
 
-variable {𝕜} [OrderedSemiring 𝕜] [AddCommGroup E] [Module 𝕜 E] {A B : Set E} {x : E}
+variable [OrderedSemiring 𝕜] [AddCommGroup E] [AddCommGroup F] [∀ i, AddCommGroup (π i)]
+  [Module 𝕜 E] [Module 𝕜 F] [∀ i, Module 𝕜 (π i)] {A B : Set E} {x : E}
 
 theorem IsExtreme.convex_diff (hA : Convex 𝕜 A) (hAB : IsExtreme 𝕜 A B) : Convex 𝕜 (A \ B) :=
   convex_iff_openSegment_subset.2 fun x₁ ⟨hx₁A, hx₁B⟩ x₂ ⟨hx₂A, hx₂B⟩ x hx =>
     ⟨hA.openSegment_subset hx₁A hx₂A hx, fun hxB => hx₁B (hAB.2 hx₁A hx₂A hxB hx).1⟩
 #align is_extreme.convex_diff IsExtreme.convex_diff
 
+/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+@[simp]
+theorem extremePoints_prod (s : Set E) (t : Set F) :
+    (s ×ˢ t).extremePoints 𝕜 = s.extremePoints 𝕜 ×ˢ t.extremePoints 𝕜 :=
+  by
+  ext
+  refine' (and_congr_right fun hx => ⟨fun h => _, fun h => _⟩).trans (and_and_and_comm _ _ _ _)
+  constructor
+  · rintro x₁ hx₁ x₂ hx₂ hx_fst
+    refine'
+      (h (mk_mem_prod hx₁ hx.2) (mk_mem_prod hx₂ hx.2) _).imp (congr_arg Prod.fst)
+        (congr_arg Prod.fst)
+    rw [← Prod.image_mk_openSegment_left]
+    exact ⟨_, hx_fst, Prod.mk.eta⟩
+  · rintro x₁ hx₁ x₂ hx₂ hx_snd
+    refine'
+      (h (mk_mem_prod hx.1 hx₁) (mk_mem_prod hx.1 hx₂) _).imp (congr_arg Prod.snd)
+        (congr_arg Prod.snd)
+    rw [← Prod.image_mk_openSegment_right]
+    exact ⟨_, hx_snd, Prod.mk.eta⟩
+  · rintro x₁ hx₁ x₂ hx₂ ⟨a, b, ha, hb, hab, hx'⟩
+    simp_rw [Prod.ext_iff]
+    exact
+      (and_and_and_comm _ _ _ _).1
+        ⟨h.1 hx₁.1 hx₂.1 ⟨a, b, ha, hb, hab, congr_arg Prod.fst hx'⟩,
+          h.2 hx₁.2 hx₂.2 ⟨a, b, ha, hb, hab, congr_arg Prod.snd hx'⟩⟩
+#align extreme_points_prod extremePoints_prod
+
+@[simp]
+theorem extremePoints_pi (s : ∀ i, Set (π i)) :
+    (univ.pi s).extremePoints 𝕜 = univ.pi fun i => (s i).extremePoints 𝕜 :=
+  by
+  ext
+  simp only [mem_extremePoints, mem_pi, mem_univ, true_imp_iff, @forall_and ι]
+  refine' and_congr_right fun hx => ⟨fun h i => _, fun h => _⟩
+  · rintro x₁ hx₁ x₂ hx₂ hi
+    refine'
+      (h (update x i x₁) _ (update x i x₂) _ _).imp (fun h₁ => by rw [← h₁, update_same]) fun h₂ =>
+        by rw [← h₂, update_same]
+    iterate 2 
+      rintro j
+      obtain rfl | hji := eq_or_ne j i
+      · rwa [update_same]
+      · rw [update_noteq hji]
+        exact hx _
+    rw [← Pi.image_update_openSegment]
+    exact ⟨_, hi, update_eq_self _ _⟩
+  · rintro x₁ hx₁ x₂ hx₂ ⟨a, b, ha, hb, hab, hx'⟩
+    simp_rw [funext_iff, ← forall_and]
+    exact fun i => h _ _ (hx₁ _) _ (hx₂ _) ⟨a, b, ha, hb, hab, congr_fun hx' _⟩
+#align extreme_points_pi extremePoints_pi
+
 end OrderedSemiring
 
 section LinearOrderedRing

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

@@ -140,7 +140,7 @@ theorem isExtreme_interₛ {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈
   exact ⟨fun B hB => (h B hB).1, fun B hB => (h B hB).2⟩
 #align is_extreme_sInter isExtreme_interₛ
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 theorem extremePoints_def :
     x ∈ A.extremePoints 𝕜 ↔
       x ∈ A ∧ ∀ (x₁) (_ : x₁ ∈ A) (x₂) (_ : x₂ ∈ A), x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x :=
@@ -207,7 +207,7 @@ variable {𝕜} [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x₁ x₂ «expr ∈ » A) -/
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
 that contain it are those with `x` as one of their endpoints. -/
 theorem mem_extremePoints_iff_forall_segment :

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -251,7 +251,6 @@ end OrderedRing
 section LinearOrderedRing
 
 variable [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
-
 variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -45,7 +45,8 @@ More not-yet-PRed stuff is available on the mathlib3 branch `sperner_again`.
 
 open Function Set
 
-open Affine Classical
+open scoped Classical
+open Affine
 
 variable {𝕜 E F ι : Type*} {π : ι → Type*}
 

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -234,7 +234,7 @@ end OrderedSemiring
 
 section OrderedRing
 variable {L : Type*} [OrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E] [AddCommGroup F] [Module 𝕜 F]
-  [LinearEquivClass L 𝕜 E F]
+  [EquivLike L E F] [LinearEquivClass L 𝕜 E F]
 
 lemma image_extremePoints (f : L) (s : Set E) :
     f '' extremePoints 𝕜 s = extremePoints 𝕜 (f '' s) := by

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -127,7 +127,7 @@ theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F,
 #align is_extreme_sInter isExtreme_sInter
 
 theorem mem_extremePoints : x ∈ A.extremePoints 𝕜 ↔
-    x ∈ A ∧ ∀ (x₁) (_ : x₁ ∈ A) (x₂) (_ : x₂ ∈ A), x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x :=
+    x ∈ A ∧ ∀ᵉ (x₁ ∈ A) (x₂ ∈ A), x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x :=
   Iff.rfl
 #align mem_extreme_points mem_extremePoints
 
@@ -256,7 +256,7 @@ variable [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] {A B : Set E} {x : E}
 /-- A useful restatement using `segment`: `x` is an extreme point iff the only (closed) segments
 that contain it are those with `x` as one of their endpoints. -/
 theorem mem_extremePoints_iff_forall_segment : x ∈ A.extremePoints 𝕜 ↔
-    x ∈ A ∧ ∀ (x₁) (_ : x₁ ∈ A) (x₂) (_ : x₂ ∈ A), x ∈ segment 𝕜 x₁ x₂ → x₁ = x ∨ x₂ = x := by
+    x ∈ A ∧ ∀ᵉ (x₁ ∈ A) (x₂ ∈ A), x ∈ segment 𝕜 x₁ x₂ → x₁ = x ∨ x₂ = x := by
   refine' and_congr_right fun hxA ↦ forall₄_congr fun x₁ h₁ x₂ h₂ ↦ _
   constructor
   · rw [← insert_endpoints_openSegment]

To fit with the "please try harder" convention of ! tactics.

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

@@ -273,7 +273,7 @@ theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
   rintro ⟨hxA, hAx⟩
   refine' mem_extremePoints_iff_forall_segment.2 ⟨hxA, fun x₁ hx₁ x₂ hx₂ hx ↦ _⟩
   rw [convex_iff_segment_subset] at hAx
-  by_contra' h
+  by_contra! h
   exact (hAx ⟨hx₁, fun hx₁ ↦ h.1 (mem_singleton_iff.2 hx₁)⟩
       ⟨hx₂, fun hx₂ ↦ h.2 (mem_singleton_iff.2 hx₂)⟩ hx).2 rfl
 #align convex.mem_extreme_points_iff_convex_diff Convex.mem_extremePoints_iff_convex_diff

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

@@ -164,7 +164,7 @@ theorem inter_extremePoints_subset_extremePoints_of_subset (hBA : B ⊆ A) :
 
 theorem IsExtreme.extremePoints_subset_extremePoints (hAB : IsExtreme 𝕜 A B) :
     B.extremePoints 𝕜 ⊆ A.extremePoints 𝕜 :=
-  fun _ ↦ by simpa only [←isExtreme_singleton] using hAB.trans
+  fun _ ↦ by simpa only [← isExtreme_singleton] using hAB.trans
 #align is_extreme.extreme_points_subset_extreme_points IsExtreme.extremePoints_subset_extremePoints
 
 theorem IsExtreme.extremePoints_eq (hAB : IsExtreme 𝕜 A B) :

Prove that extreme points are preserved under affine equivalences, and the less trivial statement that a continuous affine map sends extreme points of a compact set to a superset of the extreme points of the image of that set.

Also fix a few name and tweak the API a bit.

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

@@ -123,12 +123,7 @@ theorem isExtreme_biInter {F : Set (Set E)} (hF : F.Nonempty) (hA : ∀ B ∈ F,
 #align is_extreme_bInter isExtreme_biInter
 
 theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F, IsExtreme 𝕜 A B) :
-    IsExtreme 𝕜 A (⋂₀ F) := by
-  obtain ⟨B, hB⟩ := hF
-  refine' ⟨(sInter_subset_of_mem hB).trans (hAF B hB).1, fun x₁ hx₁A x₂ hx₂A x hxF hx ↦ _⟩
-  simp_rw [mem_sInter] at hxF ⊢
-  have h := fun B hB ↦ (hAF B hB).2 hx₁A hx₂A (hxF B hB) hx
-  exact ⟨fun B hB ↦ (h B hB).1, fun B hB ↦ (h B hB).2⟩
+    IsExtreme 𝕜 A (⋂₀ F) := by simpa [sInter_eq_biInter] using isExtreme_biInter hF hAF
 #align is_extreme_sInter isExtreme_sInter
 
 theorem mem_extremePoints : x ∈ A.extremePoints 𝕜 ↔
@@ -137,13 +132,15 @@ theorem mem_extremePoints : x ∈ A.extremePoints 𝕜 ↔
 #align mem_extreme_points mem_extremePoints
 
 /-- x is an extreme point to A iff {x} is an extreme set of A. -/
-theorem mem_extremePoints_iff_extreme_singleton : x ∈ A.extremePoints 𝕜 ↔ IsExtreme 𝕜 A {x} := by
-  refine' ⟨_, fun hx ↦ ⟨singleton_subset_iff.1 hx.1, fun x₁ hx₁ x₂ hx₂ ↦ hx.2 hx₁ hx₂ rfl⟩⟩
+@[simp] lemma isExtreme_singleton : IsExtreme 𝕜 A {x} ↔ x ∈ A.extremePoints 𝕜 := by
+  refine ⟨fun hx ↦ ⟨singleton_subset_iff.1 hx.1, fun x₁ hx₁ x₂ hx₂ ↦ hx.2 hx₁ hx₂ rfl⟩, ?_⟩
   rintro ⟨hxA, hAx⟩
   use singleton_subset_iff.2 hxA
   rintro x₁ hx₁A x₂ hx₂A y (rfl : y = x)
   exact hAx hx₁A hx₂A
-#align mem_extreme_points_iff_extreme_singleton mem_extremePoints_iff_extreme_singleton
+#align mem_extreme_points_iff_extreme_singleton isExtreme_singleton
+
+alias ⟨IsExtreme.mem_extremePoints, _⟩ := isExtreme_singleton
 
 theorem extremePoints_subset : A.extremePoints 𝕜 ⊆ A :=
   fun _ hx ↦ hx.1
@@ -167,8 +164,7 @@ theorem inter_extremePoints_subset_extremePoints_of_subset (hBA : B ⊆ A) :
 
 theorem IsExtreme.extremePoints_subset_extremePoints (hAB : IsExtreme 𝕜 A B) :
     B.extremePoints 𝕜 ⊆ A.extremePoints 𝕜 :=
-  fun _ hx ↦ mem_extremePoints_iff_extreme_singleton.2
-    (hAB.trans (mem_extremePoints_iff_extreme_singleton.1 hx))
+  fun _ ↦ by simpa only [←isExtreme_singleton] using hAB.trans
 #align is_extreme.extreme_points_subset_extreme_points IsExtreme.extremePoints_subset_extremePoints
 
 theorem IsExtreme.extremePoints_eq (hAB : IsExtreme 𝕜 A B) :
@@ -236,6 +232,21 @@ theorem extremePoints_pi (s : ∀ i, Set (π i)) :
 
 end OrderedSemiring
 
+section OrderedRing
+variable {L : Type*} [OrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E] [AddCommGroup F] [Module 𝕜 F]
+  [LinearEquivClass L 𝕜 E F]
+
+lemma image_extremePoints (f : L) (s : Set E) :
+    f '' extremePoints 𝕜 s = extremePoints 𝕜 (f '' s) := by
+  ext b
+  obtain ⟨a, rfl⟩ := EquivLike.surjective f b
+  have : ∀ x y, f '' openSegment 𝕜 x y = openSegment 𝕜 (f x) (f y) :=
+    image_openSegment _ (LinearMapClass.linearMap f).toAffineMap
+  simp only [mem_extremePoints, (EquivLike.surjective f).forall,
+    (EquivLike.injective f).mem_set_image, (EquivLike.injective f).eq_iff, ← this]
+
+end OrderedRing
+
 section LinearOrderedRing
 
 variable [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
@@ -258,7 +269,7 @@ theorem mem_extremePoints_iff_forall_segment : x ∈ A.extremePoints 𝕜 ↔
 
 theorem Convex.mem_extremePoints_iff_convex_diff (hA : Convex 𝕜 A) :
     x ∈ A.extremePoints 𝕜 ↔ x ∈ A ∧ Convex 𝕜 (A \ {x}) := by
-  use fun hx ↦ ⟨hx.1, (mem_extremePoints_iff_extreme_singleton.1 hx).convex_diff hA⟩
+  use fun hx ↦ ⟨hx.1, (isExtreme_singleton.2 hx).convex_diff hA⟩
   rintro ⟨hxA, hAx⟩
   refine' mem_extremePoints_iff_forall_segment.2 ⟨hxA, fun x₁ hx₁ x₂ hx₂ hx ↦ _⟩
   rw [convex_iff_segment_subset] at hAx

Removing from Mathlib.Init.Data.Prod from the early parts of the import hierarchy.

While at it, remove unnecessary uses of Prod.mk.eta across the library.

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

@@ -199,12 +199,12 @@ theorem extremePoints_prod (s : Set E) (t : Set F) :
     refine' (h (mk_mem_prod hx₁ hx.2) (mk_mem_prod hx₂ hx.2) _).imp (congr_arg Prod.fst)
         (congr_arg Prod.fst)
     rw [← Prod.image_mk_openSegment_left]
-    exact ⟨_, hx_fst, Prod.mk.eta⟩
+    exact ⟨_, hx_fst, rfl⟩
   · rintro x₁ hx₁ x₂ hx₂ hx_snd
     refine' (h (mk_mem_prod hx.1 hx₁) (mk_mem_prod hx.1 hx₂) _).imp (congr_arg Prod.snd)
         (congr_arg Prod.snd)
     rw [← Prod.image_mk_openSegment_right]
-    exact ⟨_, hx_snd, Prod.mk.eta⟩
+    exact ⟨_, hx_snd, rfl⟩
   · rintro x₁ hx₁ x₂ hx₂ ⟨a, b, ha, hb, hab, hx'⟩
     simp_rw [Prod.ext_iff]
     exact and_and_and_comm.1

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

This has nice performance benefits.

@@ -47,7 +47,7 @@ open Function Set
 
 open Affine Classical
 
-variable {𝕜 E F ι : Type _} {π : ι → Type _}
+variable {𝕜 E F ι : Type*} {π : ι → Type*}
 
 section SMul
 
@@ -107,7 +107,7 @@ protected theorem IsExtreme.mono (hAC : IsExtreme 𝕜 A C) (hBA : B ⊆ A) (hCB
   ⟨hCB, fun _ hx₁B _ hx₂B _ hxC hx ↦ hAC.2 (hBA hx₁B) (hBA hx₂B) hxC hx⟩
 #align is_extreme.mono IsExtreme.mono
 
-theorem isExtreme_iInter {ι : Sort _} [Nonempty ι] {F : ι → Set E}
+theorem isExtreme_iInter {ι : Sort*} [Nonempty ι] {F : ι → Set E}
     (hAF : ∀ i : ι, IsExtreme 𝕜 A (F i)) : IsExtreme 𝕜 A (⋂ i : ι, F i) := by
   obtain i := Classical.arbitrary ι
   refine' ⟨iInter_subset_of_subset i (hAF i).1, fun x₁ hx₁A x₂ hx₂A x hxF hx ↦ _⟩

• 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) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Bhavik Mehta
-
-! This file was ported from Lean 3 source module analysis.convex.extreme
-! leanprover-community/mathlib commit c5773405394e073885e2a144c9ca14637e8eb963
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Convex.Hull
 
+#align_import analysis.convex.extreme from "leanprover-community/mathlib"@"c5773405394e073885e2a144c9ca14637e8eb963"
+
 /-!
 # Extreme sets
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -114,7 +114,7 @@ theorem isExtreme_iInter {ι : Sort _} [Nonempty ι] {F : ι → Set E}
     (hAF : ∀ i : ι, IsExtreme 𝕜 A (F i)) : IsExtreme 𝕜 A (⋂ i : ι, F i) := by
   obtain i := Classical.arbitrary ι
   refine' ⟨iInter_subset_of_subset i (hAF i).1, fun x₁ hx₁A x₂ hx₂A x hxF hx ↦ _⟩
-  simp_rw [mem_iInter] at hxF⊢
+  simp_rw [mem_iInter] at hxF ⊢
   have h := fun i ↦ (hAF i).2 hx₁A hx₂A (hxF i) hx
   exact ⟨fun i ↦ (h i).1, fun i ↦ (h i).2⟩
 #align is_extreme_Inter isExtreme_iInter
@@ -129,7 +129,7 @@ theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F,
     IsExtreme 𝕜 A (⋂₀ F) := by
   obtain ⟨B, hB⟩ := hF
   refine' ⟨(sInter_subset_of_mem hB).trans (hAF B hB).1, fun x₁ hx₁A x₂ hx₂A x hxF hx ↦ _⟩
-  simp_rw [mem_sInter] at hxF⊢
+  simp_rw [mem_sInter] at hxF ⊢
   have h := fun B hB ↦ (hAF B hB).2 hx₁A hx₂A (hxF B hB) hx
   exact ⟨fun B hB ↦ (h B hB).1, fun B hB ↦ (h B hB).2⟩
 #align is_extreme_sInter isExtreme_sInter

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -110,29 +110,29 @@ protected theorem IsExtreme.mono (hAC : IsExtreme 𝕜 A C) (hBA : B ⊆ A) (hCB
   ⟨hCB, fun _ hx₁B _ hx₂B _ hxC hx ↦ hAC.2 (hBA hx₁B) (hBA hx₂B) hxC hx⟩
 #align is_extreme.mono IsExtreme.mono
 
-theorem isExtreme_interᵢ {ι : Sort _} [Nonempty ι] {F : ι → Set E}
+theorem isExtreme_iInter {ι : Sort _} [Nonempty ι] {F : ι → Set E}
     (hAF : ∀ i : ι, IsExtreme 𝕜 A (F i)) : IsExtreme 𝕜 A (⋂ i : ι, F i) := by
   obtain i := Classical.arbitrary ι
-  refine' ⟨interᵢ_subset_of_subset i (hAF i).1, fun x₁ hx₁A x₂ hx₂A x hxF hx ↦ _⟩
-  simp_rw [mem_interᵢ] at hxF⊢
+  refine' ⟨iInter_subset_of_subset i (hAF i).1, fun x₁ hx₁A x₂ hx₂A x hxF hx ↦ _⟩
+  simp_rw [mem_iInter] at hxF⊢
   have h := fun i ↦ (hAF i).2 hx₁A hx₂A (hxF i) hx
   exact ⟨fun i ↦ (h i).1, fun i ↦ (h i).2⟩
-#align is_extreme_Inter isExtreme_interᵢ
+#align is_extreme_Inter isExtreme_iInter
 
-theorem isExtreme_binterᵢ {F : Set (Set E)} (hF : F.Nonempty) (hA : ∀ B ∈ F, IsExtreme 𝕜 A B) :
+theorem isExtreme_biInter {F : Set (Set E)} (hF : F.Nonempty) (hA : ∀ B ∈ F, IsExtreme 𝕜 A B) :
     IsExtreme 𝕜 A (⋂ B ∈ F, B) := by
   haveI := hF.to_subtype
-  simpa only [interᵢ_subtype] using isExtreme_interᵢ fun i : F ↦ hA _ i.2
-#align is_extreme_bInter isExtreme_binterᵢ
+  simpa only [iInter_subtype] using isExtreme_iInter fun i : F ↦ hA _ i.2
+#align is_extreme_bInter isExtreme_biInter
 
-theorem isExtreme_interₛ {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F, IsExtreme 𝕜 A B) :
+theorem isExtreme_sInter {F : Set (Set E)} (hF : F.Nonempty) (hAF : ∀ B ∈ F, IsExtreme 𝕜 A B) :
     IsExtreme 𝕜 A (⋂₀ F) := by
   obtain ⟨B, hB⟩ := hF
-  refine' ⟨(interₛ_subset_of_mem hB).trans (hAF B hB).1, fun x₁ hx₁A x₂ hx₂A x hxF hx ↦ _⟩
-  simp_rw [mem_interₛ] at hxF⊢
+  refine' ⟨(sInter_subset_of_mem hB).trans (hAF B hB).1, fun x₁ hx₁A x₂ hx₂A x hxF hx ↦ _⟩
+  simp_rw [mem_sInter] at hxF⊢
   have h := fun B hB ↦ (hAF B hB).2 hx₁A hx₂A (hxF B hB) hx
   exact ⟨fun B hB ↦ (h B hB).1, fun B hB ↦ (h B hB).2⟩
-#align is_extreme_sInter isExtreme_interₛ
+#align is_extreme_sInter isExtreme_sInter
 
 theorem mem_extremePoints : x ∈ A.extremePoints 𝕜 ↔
     x ∈ A ∧ ∀ (x₁) (_ : x₁ ∈ A) (x₂) (_ : x₂ ∈ A), x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x :=

@@ -42,7 +42,7 @@ See chapter 8 of [Barry Simon, *Convexity*][simon2011]
 
 Prove lemmas relating extreme sets and points to the intrinsic frontier.
 
-More not-yet-PRed stuff is available on the branch `sperner_again`.
+More not-yet-PRed stuff is available on the mathlib3 branch `sperner_again`.
 -/
 
 
@@ -63,7 +63,7 @@ def IsExtreme (A B : Set E) : Prop :=
 #align is_extreme IsExtreme
 
 /-- A point `x` is an extreme point of a set `A` if `x` belongs to no open segment with ends in
-`A`, except for the obvious `open_segment x x`. -/
+`A`, except for the obvious `openSegment x x`. -/
 def Set.extremePoints (A : Set E) : Set E :=
   { x ∈ A | ∀ ⦃x₁⦄, x₁ ∈ A → ∀ ⦃x₂⦄, x₂ ∈ A → x ∈ openSegment 𝕜 x₁ x₂ → x₁ = x ∧ x₂ = x }
 #align set.extreme_points Set.extremePoints

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>