analysis.convex.caratheodory | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

e6fab1dc

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

9d2f0748

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -70,7 +70,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
     apply s.exists_min_image fun z => f z / g z
     obtain ⟨x, hx, hgx⟩ : ∃ x ∈ t, 0 < g x := gpos
     exact ⟨x, mem_filter.mpr ⟨hx, hgx⟩⟩
-  have hg : 0 < g i₀ := by rw [mem_filter] at mem ; exact mem.2
+  have hg : 0 < g i₀ := by rw [mem_filter] at mem; exact mem.2
   have hi₀ : i₀ ∈ t := filter_subset _ _ mem
   let k : E → 𝕜 := fun z => f z - f i₀ / g i₀ * g z
   have hk : k i₀ = 0 := by field_simp [k, ne_of_gt hg]
@@ -84,7 +84,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
   · simp only [and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]
     intro e hei₀ het
     by_cases hes : e ∈ s
-    · have hge : 0 < g e := by rw [mem_filter] at hes ; exact hes.2
+    · have hge : 0 < g e := by rw [mem_filter] at hes; exact hes.2
       rw [← le_div_iff hge]
       exact w _ hes
     · calc
@@ -161,7 +161,7 @@ theorem affineIndependent_minCardFinsetOfMemConvexHull :
       (Set.Subset.trans (Finset.erase_subset (↑p) (min_card_finset_of_mem_convex_hull hx))
         (min_card_finset_of_mem_convex_hull_subseteq hx))
       hp
-  rw [← not_lt] at contra 
+  rw [← not_lt] at contra
   apply contra
   erw [card_erase_of_mem p.2, hk]
   exact lt_add_one _
@@ -198,10 +198,10 @@ theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜
       ∃ (z : ι → E) (w : ι → 𝕜) (hss : Set.range z ⊆ s) (hai : AffineIndependent 𝕜 z) (hw :
         ∀ i, 0 < w i), ∑ i, w i = 1 ∧ ∑ i, w i • z i = x :=
   by
-  rw [convexHull_eq_union] at hx 
-  simp only [exists_prop, Set.mem_iUnion] at hx 
+  rw [convexHull_eq_union] at hx
+  simp only [exists_prop, Set.mem_iUnion] at hx
   obtain ⟨t, ht₁, ht₂, ht₃⟩ := hx
-  simp only [t.convex_hull_eq, exists_prop, Set.mem_setOf_eq] at ht₃ 
+  simp only [t.convex_hull_eq, exists_prop, Set.mem_setOf_eq] at ht₃
   obtain ⟨w, hw₁, hw₂, hw₃⟩ := ht₃
   let t' := t.filter fun i => w i ≠ 0
   refine' ⟨t', t'.fintype_coe_sort, (coe : t' → E), w ∘ (coe : t' → E), _, _, _, _, _⟩
@@ -213,7 +213,7 @@ theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜
   · erw [Finset.sum_attach, Finset.sum_filter_ne_zero, hw₂]
   · change ∑ i : t' in t'.attach, (fun e => w e • e) ↑i = x
     erw [Finset.sum_attach, Finset.sum_filter_of_ne]
-    · rw [t.center_mass_eq_of_sum_1 id hw₂] at hw₃ ; exact hw₃
+    · rw [t.center_mass_eq_of_sum_1 id hw₂] at hw₃; exact hw₃
     · intro e he hwe contra; apply hwe; rw [contra, zero_smul]
 #align eq_pos_convex_span_of_mem_convex_hull eq_pos_convex_span_of_mem_convexHull
 -/

9d2f0748

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -154,6 +154,17 @@ theorem affineIndependent_minCardFinsetOfMemConvexHull :
     (Nat.succ_pred_eq_of_pos
         (finset.card_pos.mpr (min_card_finset_of_mem_convex_hull_nonempty hx))).symm
   classical
+  by_contra
+  obtain ⟨p, hp⟩ := mem_convex_hull_erase h (mem_min_card_finset_of_mem_convex_hull hx)
+  have contra :=
+    min_card_finset_of_mem_convex_hull_card_le_card hx
+      (Set.Subset.trans (Finset.erase_subset (↑p) (min_card_finset_of_mem_convex_hull hx))
+        (min_card_finset_of_mem_convex_hull_subseteq hx))
+      hp
+  rw [← not_lt] at contra 
+  apply contra
+  erw [card_erase_of_mem p.2, hk]
+  exact lt_add_one _
 #align caratheodory.affine_independent_min_card_finset_of_mem_convex_hull Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull
 -/

9d2f0748

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -154,17 +154,6 @@ theorem affineIndependent_minCardFinsetOfMemConvexHull :
     (Nat.succ_pred_eq_of_pos
         (finset.card_pos.mpr (min_card_finset_of_mem_convex_hull_nonempty hx))).symm
   classical
-  by_contra
-  obtain ⟨p, hp⟩ := mem_convex_hull_erase h (mem_min_card_finset_of_mem_convex_hull hx)
-  have contra :=
-    min_card_finset_of_mem_convex_hull_card_le_card hx
-      (Set.Subset.trans (Finset.erase_subset (↑p) (min_card_finset_of_mem_convex_hull hx))
-        (min_card_finset_of_mem_convex_hull_subseteq hx))
-      hp
-  rw [← not_lt] at contra 
-  apply contra
-  erw [card_erase_of_mem p.2, hk]
-  exact lt_add_one _
 #align caratheodory.affine_independent_min_card_finset_of_mem_convex_hull Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull
 -/

9d2f0748

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison
 -/
-import Mathbin.Analysis.Convex.Combination
-import Mathbin.LinearAlgebra.AffineSpace.Independent
-import Mathbin.Tactic.FieldSimp
+import Analysis.Convex.Combination
+import LinearAlgebra.AffineSpace.Independent
+import Tactic.FieldSimp
 
 #align_import analysis.convex.caratheodory from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"

9d2f0748

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison
-
-! This file was ported from Lean 3 source module analysis.convex.caratheodory
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Combination
 import Mathbin.LinearAlgebra.AffineSpace.Independent
 import Mathbin.Tactic.FieldSimp
 
+#align_import analysis.convex.caratheodory from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 # Carathéodory's convexity theorem

9d2f0748

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -55,6 +55,7 @@ variable {𝕜 : Type _} {E : Type u} [LinearOrderedField 𝕜] [AddCommGroup E]
 
 namespace Caratheodory
 
+#print Caratheodory.mem_convexHull_erase /-
 /-- If `x` is in the convex hull of some finset `t` whose elements are not affine-independent,
 then it is in the convex hull of a strict subset of `t`. -/
 theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndependent 𝕜 (coe : t → E))
@@ -105,11 +106,10 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
     simp only [sub_smul, mul_smul, sum_sub_distrib, ← smul_sum, gcombo, smul_zero, sub_zero,
       center_mass, fsum, inv_one, one_smul, id.def]
 #align caratheodory.mem_convex_hull_erase Caratheodory.mem_convexHull_erase
+-/
 
 variable {s : Set E} {x : E} (hx : x ∈ convexHull 𝕜 s)
 
-include hx
-
 #print Caratheodory.minCardFinsetOfMemConvexHull /-
 /-- Given a point `x` in the convex hull of a set `s`, this is a finite subset of `s` of minimum
 cardinality, whose convex hull contains `x`. -/
@@ -120,26 +120,35 @@ noncomputable def minCardFinsetOfMemConvexHull : Finset E :=
 #align caratheodory.min_card_finset_of_mem_convex_hull Caratheodory.minCardFinsetOfMemConvexHull
 -/
 
+#print Caratheodory.minCardFinsetOfMemConvexHull_subseteq /-
 theorem minCardFinsetOfMemConvexHull_subseteq : ↑(minCardFinsetOfMemConvexHull hx) ⊆ s :=
   (Function.argminOn_mem _ _ {t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E)} _).1
 #align caratheodory.min_card_finset_of_mem_convex_hull_subseteq Caratheodory.minCardFinsetOfMemConvexHull_subseteq
+-/
 
+#print Caratheodory.mem_minCardFinsetOfMemConvexHull /-
 theorem mem_minCardFinsetOfMemConvexHull :
     x ∈ convexHull 𝕜 (minCardFinsetOfMemConvexHull hx : Set E) :=
   (Function.argminOn_mem _ _ {t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E)} _).2
 #align caratheodory.mem_min_card_finset_of_mem_convex_hull Caratheodory.mem_minCardFinsetOfMemConvexHull
+-/
 
+#print Caratheodory.minCardFinsetOfMemConvexHull_nonempty /-
 theorem minCardFinsetOfMemConvexHull_nonempty : (minCardFinsetOfMemConvexHull hx).Nonempty :=
   by
   rw [← Finset.coe_nonempty, ← @convexHull_nonempty_iff 𝕜]
   exact ⟨x, mem_min_card_finset_of_mem_convex_hull hx⟩
 #align caratheodory.min_card_finset_of_mem_convex_hull_nonempty Caratheodory.minCardFinsetOfMemConvexHull_nonempty
+-/
 
+#print Caratheodory.minCardFinsetOfMemConvexHull_card_le_card /-
 theorem minCardFinsetOfMemConvexHull_card_le_card {t : Finset E} (ht₁ : ↑t ⊆ s)
     (ht₂ : x ∈ convexHull 𝕜 (t : Set E)) : (minCardFinsetOfMemConvexHull hx).card ≤ t.card :=
   Function.argminOn_le _ _ _ ⟨ht₁, ht₂⟩
 #align caratheodory.min_card_finset_of_mem_convex_hull_card_le_card Caratheodory.minCardFinsetOfMemConvexHull_card_le_card
+-/
 
+#print Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull /-
 theorem affineIndependent_minCardFinsetOfMemConvexHull :
     AffineIndependent 𝕜 (coe : minCardFinsetOfMemConvexHull hx → E) :=
   by
@@ -160,11 +169,13 @@ theorem affineIndependent_minCardFinsetOfMemConvexHull :
   erw [card_erase_of_mem p.2, hk]
   exact lt_add_one _
 #align caratheodory.affine_independent_min_card_finset_of_mem_convex_hull Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull
+-/
 
 end Caratheodory
 
 variable {s : Set E}
 
+#print convexHull_eq_union /-
 /-- **Carathéodory's convexity theorem** -/
 theorem convexHull_eq_union :
     convexHull 𝕜 s =
@@ -181,7 +192,9 @@ theorem convexHull_eq_union :
   · iterate 3 convert Set.iUnion_subset _; intro
     exact convexHull_mono ‹_›
 #align convex_hull_eq_union convexHull_eq_union
+-/
 
+#print eq_pos_convex_span_of_mem_convexHull /-
 /-- A more explicit version of `convex_hull_eq_union`. -/
 theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜 s) :
     ∃ (ι : Sort (u + 1)) (_ : Fintype ι),
@@ -206,4 +219,5 @@ theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜
     · rw [t.center_mass_eq_of_sum_1 id hw₂] at hw₃ ; exact hw₃
     · intro e he hwe contra; apply hwe; rw [contra, zero_smul]
 #align eq_pos_convex_span_of_mem_convex_hull eq_pos_convex_span_of_mem_convexHull
+-/

9d2f0748

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -76,11 +76,11 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
   have hi₀ : i₀ ∈ t := filter_subset _ _ mem
   let k : E → 𝕜 := fun z => f z - f i₀ / g i₀ * g z
   have hk : k i₀ = 0 := by field_simp [k, ne_of_gt hg]
-  have ksum : (∑ e in t.erase i₀, k e) = 1 := by
+  have ksum : ∑ e in t.erase i₀, k e = 1 := by
     calc
-      (∑ e in t.erase i₀, k e) = ∑ e in t, k e := by
+      ∑ e in t.erase i₀, k e = ∑ e in t, k e := by
         conv_rhs => rw [← insert_erase hi₀, sum_insert (not_mem_erase i₀ t), hk, zero_add]
-      _ = ∑ e in t, f e - f i₀ / g i₀ * g e := rfl
+      _ = ∑ e in t, (f e - f i₀ / g i₀ * g e) := rfl
       _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, MulZeroClass.mul_zero, sub_zero]
   refine' ⟨⟨i₀, hi₀⟩, k, _, by convert ksum, _⟩
   · simp only [and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]
@@ -99,7 +99,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
       · simpa only [mem_filter, het, true_and_iff, not_lt] using hes
   · simp only [Subtype.coe_mk, center_mass_eq_of_sum_1 _ id ksum, id]
     calc
-      (∑ e in t.erase i₀, k e • e) = ∑ e in t, k e • e := sum_erase _ (by rw [hk, zero_smul])
+      ∑ e in t.erase i₀, k e • e = ∑ e in t, k e • e := sum_erase _ (by rw [hk, zero_smul])
       _ = ∑ e in t, (f e - f i₀ / g i₀ * g e) • e := rfl
       _ = t.center_mass f id := _
     simp only [sub_smul, mul_smul, sum_sub_distrib, ← smul_sum, gcombo, smul_zero, sub_zero,
@@ -186,7 +186,7 @@ theorem convexHull_eq_union :
 theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜 s) :
     ∃ (ι : Sort (u + 1)) (_ : Fintype ι),
       ∃ (z : ι → E) (w : ι → 𝕜) (hss : Set.range z ⊆ s) (hai : AffineIndependent 𝕜 z) (hw :
-        ∀ i, 0 < w i), (∑ i, w i) = 1 ∧ (∑ i, w i • z i) = x :=
+        ∀ i, 0 < w i), ∑ i, w i = 1 ∧ ∑ i, w i • z i = x :=
   by
   rw [convexHull_eq_union] at hx 
   simp only [exists_prop, Set.mem_iUnion] at hx 
@@ -201,7 +201,7 @@ theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜
     exact fun i =>
       (hw₁ _ (finset.mem_filter.mp i.2).1).lt_of_ne (finset.mem_filter.mp i.property).2.symm
   · erw [Finset.sum_attach, Finset.sum_filter_ne_zero, hw₂]
-  · change (∑ i : t' in t'.attach, (fun e => w e • e) ↑i) = x
+  · change ∑ i : t' in t'.attach, (fun e => w e • e) ↑i = x
     erw [Finset.sum_attach, Finset.sum_filter_of_ne]
     · rw [t.center_mass_eq_of_sum_1 id hw₂] at hw₃ ; exact hw₃
     · intro e he hwe contra; apply hwe; rw [contra, zero_smul]

9d2f0748

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -82,7 +82,6 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
         conv_rhs => rw [← insert_erase hi₀, sum_insert (not_mem_erase i₀ t), hk, zero_add]
       _ = ∑ e in t, f e - f i₀ / g i₀ * g e := rfl
       _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, MulZeroClass.mul_zero, sub_zero]
-      
   refine' ⟨⟨i₀, hi₀⟩, k, _, by convert ksum, _⟩
   · simp only [and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]
     intro e hei₀ het
@@ -96,7 +95,6 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
             _ ≤
             f e :=
           fpos e het
-        
       · apply div_nonneg (fpos i₀ (mem_of_subset (filter_subset _ t) mem)) (le_of_lt hg)
       · simpa only [mem_filter, het, true_and_iff, not_lt] using hes
   · simp only [Subtype.coe_mk, center_mass_eq_of_sum_1 _ id ksum, id]
@@ -104,7 +102,6 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
       (∑ e in t.erase i₀, k e • e) = ∑ e in t, k e • e := sum_erase _ (by rw [hk, zero_smul])
       _ = ∑ e in t, (f e - f i₀ / g i₀ * g e) • e := rfl
       _ = t.center_mass f id := _
-      
     simp only [sub_smul, mul_smul, sum_sub_distrib, ← smul_sum, gcombo, smul_zero, sub_zero,
       center_mass, fsum, inv_one, one_smul, id.def]
 #align caratheodory.mem_convex_hull_erase Caratheodory.mem_convexHull_erase

9d2f0748

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -117,19 +117,19 @@ include hx
 /-- Given a point `x` in the convex hull of a set `s`, this is a finite subset of `s` of minimum
 cardinality, whose convex hull contains `x`. -/
 noncomputable def minCardFinsetOfMemConvexHull : Finset E :=
-  Function.argminOn Finset.card Nat.lt_wfRel { t | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E) }
+  Function.argminOn Finset.card Nat.lt_wfRel {t | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E)}
     (by
       simpa only [convexHull_eq_union_convexHull_finite_subsets s, exists_prop, mem_Union] using hx)
 #align caratheodory.min_card_finset_of_mem_convex_hull Caratheodory.minCardFinsetOfMemConvexHull
 -/
 
 theorem minCardFinsetOfMemConvexHull_subseteq : ↑(minCardFinsetOfMemConvexHull hx) ⊆ s :=
-  (Function.argminOn_mem _ _ { t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E) } _).1
+  (Function.argminOn_mem _ _ {t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E)} _).1
 #align caratheodory.min_card_finset_of_mem_convex_hull_subseteq Caratheodory.minCardFinsetOfMemConvexHull_subseteq
 
 theorem mem_minCardFinsetOfMemConvexHull :
     x ∈ convexHull 𝕜 (minCardFinsetOfMemConvexHull hx : Set E) :=
-  (Function.argminOn_mem _ _ { t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E) } _).2
+  (Function.argminOn_mem _ _ {t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E)} _).2
 #align caratheodory.mem_min_card_finset_of_mem_convex_hull Caratheodory.mem_minCardFinsetOfMemConvexHull
 
 theorem minCardFinsetOfMemConvexHull_nonempty : (minCardFinsetOfMemConvexHull hx).Nonempty :=
@@ -151,17 +151,17 @@ theorem affineIndependent_minCardFinsetOfMemConvexHull :
     (Nat.succ_pred_eq_of_pos
         (finset.card_pos.mpr (min_card_finset_of_mem_convex_hull_nonempty hx))).symm
   classical
-    by_contra
-    obtain ⟨p, hp⟩ := mem_convex_hull_erase h (mem_min_card_finset_of_mem_convex_hull hx)
-    have contra :=
-      min_card_finset_of_mem_convex_hull_card_le_card hx
-        (Set.Subset.trans (Finset.erase_subset (↑p) (min_card_finset_of_mem_convex_hull hx))
-          (min_card_finset_of_mem_convex_hull_subseteq hx))
-        hp
-    rw [← not_lt] at contra 
-    apply contra
-    erw [card_erase_of_mem p.2, hk]
-    exact lt_add_one _
+  by_contra
+  obtain ⟨p, hp⟩ := mem_convex_hull_erase h (mem_min_card_finset_of_mem_convex_hull hx)
+  have contra :=
+    min_card_finset_of_mem_convex_hull_card_le_card hx
+      (Set.Subset.trans (Finset.erase_subset (↑p) (min_card_finset_of_mem_convex_hull hx))
+        (min_card_finset_of_mem_convex_hull_subseteq hx))
+      hp
+  rw [← not_lt] at contra 
+  apply contra
+  erw [card_erase_of_mem p.2, hk]
+  exact lt_add_one _
 #align caratheodory.affine_independent_min_card_finset_of_mem_convex_hull Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull
 
 end Caratheodory

9d2f0748

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -61,7 +61,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
     {x : E} (m : x ∈ convexHull 𝕜 (↑t : Set E)) :
     ∃ y : (↑t : Set E), x ∈ convexHull 𝕜 (↑(t.eraseₓ y) : Set E) :=
   by
-  simp only [Finset.convexHull_eq, mem_set_of_eq] at m⊢
+  simp only [Finset.convexHull_eq, mem_set_of_eq] at m ⊢
   obtain ⟨f, fpos, fsum, rfl⟩ := m
   obtain ⟨g, gcombo, gsum, gpos⟩ := exists_nontrivial_relation_sum_zero_of_not_affine_ind h
   replace gpos := exists_pos_of_sum_zero_of_exists_nonzero g gsum gpos
@@ -72,7 +72,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
     apply s.exists_min_image fun z => f z / g z
     obtain ⟨x, hx, hgx⟩ : ∃ x ∈ t, 0 < g x := gpos
     exact ⟨x, mem_filter.mpr ⟨hx, hgx⟩⟩
-  have hg : 0 < g i₀ := by rw [mem_filter] at mem; exact mem.2
+  have hg : 0 < g i₀ := by rw [mem_filter] at mem ; exact mem.2
   have hi₀ : i₀ ∈ t := filter_subset _ _ mem
   let k : E → 𝕜 := fun z => f z - f i₀ / g i₀ * g z
   have hk : k i₀ = 0 := by field_simp [k, ne_of_gt hg]
@@ -87,7 +87,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
   · simp only [and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]
     intro e hei₀ het
     by_cases hes : e ∈ s
-    · have hge : 0 < g e := by rw [mem_filter] at hes; exact hes.2
+    · have hge : 0 < g e := by rw [mem_filter] at hes ; exact hes.2
       rw [← le_div_iff hge]
       exact w _ hes
     · calc
@@ -158,7 +158,7 @@ theorem affineIndependent_minCardFinsetOfMemConvexHull :
         (Set.Subset.trans (Finset.erase_subset (↑p) (min_card_finset_of_mem_convex_hull hx))
           (min_card_finset_of_mem_convex_hull_subseteq hx))
         hp
-    rw [← not_lt] at contra
+    rw [← not_lt] at contra 
     apply contra
     erw [card_erase_of_mem p.2, hk]
     exact lt_add_one _
@@ -187,14 +187,14 @@ theorem convexHull_eq_union :
 
 /-- A more explicit version of `convex_hull_eq_union`. -/
 theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜 s) :
-    ∃ (ι : Sort (u + 1))(_ : Fintype ι),
-      ∃ (z : ι → E)(w : ι → 𝕜)(hss : Set.range z ⊆ s)(hai : AffineIndependent 𝕜 z)(hw :
+    ∃ (ι : Sort (u + 1)) (_ : Fintype ι),
+      ∃ (z : ι → E) (w : ι → 𝕜) (hss : Set.range z ⊆ s) (hai : AffineIndependent 𝕜 z) (hw :
         ∀ i, 0 < w i), (∑ i, w i) = 1 ∧ (∑ i, w i • z i) = x :=
   by
-  rw [convexHull_eq_union] at hx
-  simp only [exists_prop, Set.mem_iUnion] at hx
+  rw [convexHull_eq_union] at hx 
+  simp only [exists_prop, Set.mem_iUnion] at hx 
   obtain ⟨t, ht₁, ht₂, ht₃⟩ := hx
-  simp only [t.convex_hull_eq, exists_prop, Set.mem_setOf_eq] at ht₃
+  simp only [t.convex_hull_eq, exists_prop, Set.mem_setOf_eq] at ht₃ 
   obtain ⟨w, hw₁, hw₂, hw₃⟩ := ht₃
   let t' := t.filter fun i => w i ≠ 0
   refine' ⟨t', t'.fintype_coe_sort, (coe : t' → E), w ∘ (coe : t' → E), _, _, _, _, _⟩
@@ -206,7 +206,7 @@ theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜
   · erw [Finset.sum_attach, Finset.sum_filter_ne_zero, hw₂]
   · change (∑ i : t' in t'.attach, (fun e => w e • e) ↑i) = x
     erw [Finset.sum_attach, Finset.sum_filter_of_ne]
-    · rw [t.center_mass_eq_of_sum_1 id hw₂] at hw₃; exact hw₃
+    · rw [t.center_mass_eq_of_sum_1 id hw₂] at hw₃ ; exact hw₃
     · intro e he hwe contra; apply hwe; rw [contra, zero_smul]
 #align eq_pos_convex_span_of_mem_convex_hull eq_pos_convex_span_of_mem_convexHull

9d2f0748

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -47,7 +47,7 @@ convex hull, caratheodory
 
 open Set Finset
 
-open BigOperators
+open scoped BigOperators
 
 universe u

9d2f0748

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -55,9 +55,6 @@ variable {𝕜 : Type _} {E : Type u} [LinearOrderedField 𝕜] [AddCommGroup E]
 
 namespace Caratheodory
 
-/- warning: caratheodory.mem_convex_hull_erase -> Caratheodory.mem_convexHull_erase is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align caratheodory.mem_convex_hull_erase Caratheodory.mem_convexHull_eraseₓ'. -/
 /-- If `x` is in the convex hull of some finset `t` whose elements are not affine-independent,
 then it is in the convex hull of a strict subset of `t`. -/
 theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndependent 𝕜 (coe : t → E))
@@ -126,56 +123,26 @@ noncomputable def minCardFinsetOfMemConvexHull : Finset E :=
 #align caratheodory.min_card_finset_of_mem_convex_hull Caratheodory.minCardFinsetOfMemConvexHull
 -/
 
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 theorem minCardFinsetOfMemConvexHull_subseteq : ↑(minCardFinsetOfMemConvexHull hx) ⊆ s :=
   (Function.argminOn_mem _ _ { t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E) } _).1
 #align caratheodory.min_card_finset_of_mem_convex_hull_subseteq Caratheodory.minCardFinsetOfMemConvexHull_subseteq
 
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-Case conversion may be inaccurate. Consider using '#align caratheodory.mem_min_card_finset_of_mem_convex_hull Caratheodory.mem_minCardFinsetOfMemConvexHullₓ'. -/
 theorem mem_minCardFinsetOfMemConvexHull :
     x ∈ convexHull 𝕜 (minCardFinsetOfMemConvexHull hx : Set E) :=
   (Function.argminOn_mem _ _ { t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E) } _).2
 #align caratheodory.mem_min_card_finset_of_mem_convex_hull Caratheodory.mem_minCardFinsetOfMemConvexHull
 
-/- warning: caratheodory.min_card_finset_of_mem_convex_hull_nonempty -> Caratheodory.minCardFinsetOfMemConvexHull_nonempty is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align caratheodory.min_card_finset_of_mem_convex_hull_nonempty Caratheodory.minCardFinsetOfMemConvexHull_nonemptyₓ'. -/
 theorem minCardFinsetOfMemConvexHull_nonempty : (minCardFinsetOfMemConvexHull hx).Nonempty :=
   by
   rw [← Finset.coe_nonempty, ← @convexHull_nonempty_iff 𝕜]
   exact ⟨x, mem_min_card_finset_of_mem_convex_hull hx⟩
 #align caratheodory.min_card_finset_of_mem_convex_hull_nonempty Caratheodory.minCardFinsetOfMemConvexHull_nonempty
 
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-Case conversion may be inaccurate. Consider using '#align caratheodory.min_card_finset_of_mem_convex_hull_card_le_card Caratheodory.minCardFinsetOfMemConvexHull_card_le_cardₓ'. -/
 theorem minCardFinsetOfMemConvexHull_card_le_card {t : Finset E} (ht₁ : ↑t ⊆ s)
     (ht₂ : x ∈ convexHull 𝕜 (t : Set E)) : (minCardFinsetOfMemConvexHull hx).card ≤ t.card :=
   Function.argminOn_le _ _ _ ⟨ht₁, ht₂⟩
 #align caratheodory.min_card_finset_of_mem_convex_hull_card_le_card Caratheodory.minCardFinsetOfMemConvexHull_card_le_card
 
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 theorem affineIndependent_minCardFinsetOfMemConvexHull :
     AffineIndependent 𝕜 (coe : minCardFinsetOfMemConvexHull hx → E) :=
   by
@@ -201,9 +168,6 @@ end Caratheodory
 
 variable {s : Set E}
 
-/- warning: convex_hull_eq_union -> convexHull_eq_union is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align convex_hull_eq_union convexHull_eq_unionₓ'. -/
 /-- **Carathéodory's convexity theorem** -/
 theorem convexHull_eq_union :
     convexHull 𝕜 s =
@@ -221,9 +185,6 @@ theorem convexHull_eq_union :
     exact convexHull_mono ‹_›
 #align convex_hull_eq_union convexHull_eq_union
 
-/- warning: eq_pos_convex_span_of_mem_convex_hull -> eq_pos_convex_span_of_mem_convexHull is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align eq_pos_convex_span_of_mem_convex_hull eq_pos_convex_span_of_mem_convexHullₓ'. -/
 /-- A more explicit version of `convex_hull_eq_union`. -/
 theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜 s) :
     ∃ (ι : Sort (u + 1))(_ : Fintype ι),

9d2f0748

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -75,9 +75,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
     apply s.exists_min_image fun z => f z / g z
     obtain ⟨x, hx, hgx⟩ : ∃ x ∈ t, 0 < g x := gpos
     exact ⟨x, mem_filter.mpr ⟨hx, hgx⟩⟩
-  have hg : 0 < g i₀ := by
-    rw [mem_filter] at mem
-    exact mem.2
+  have hg : 0 < g i₀ := by rw [mem_filter] at mem; exact mem.2
   have hi₀ : i₀ ∈ t := filter_subset _ _ mem
   let k : E → 𝕜 := fun z => f z - f i₀ / g i₀ * g z
   have hk : k i₀ = 0 := by field_simp [k, ne_of_gt hg]
@@ -92,9 +90,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
   · simp only [and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]
     intro e hei₀ het
     by_cases hes : e ∈ s
-    · have hge : 0 < g e := by
-        rw [mem_filter] at hes
-        exact hes.2
+    · have hge : 0 < g e := by rw [mem_filter] at hes; exact hes.2
       rw [← le_div_iff hge]
       exact w _ hes
     · calc
@@ -241,8 +237,7 @@ theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜
   obtain ⟨w, hw₁, hw₂, hw₃⟩ := ht₃
   let t' := t.filter fun i => w i ≠ 0
   refine' ⟨t', t'.fintype_coe_sort, (coe : t' → E), w ∘ (coe : t' → E), _, _, _, _, _⟩
-  · rw [Subtype.range_coe_subtype]
-    exact subset.trans (Finset.filter_subset _ t) ht₁
+  · rw [Subtype.range_coe_subtype]; exact subset.trans (Finset.filter_subset _ t) ht₁
   · exact ht₂.comp_embedding ⟨_, inclusion_injective (Finset.filter_subset (fun i => w i ≠ 0) t)⟩
   ·
     exact fun i =>
@@ -250,10 +245,7 @@ theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜
   · erw [Finset.sum_attach, Finset.sum_filter_ne_zero, hw₂]
   · change (∑ i : t' in t'.attach, (fun e => w e • e) ↑i) = x
     erw [Finset.sum_attach, Finset.sum_filter_of_ne]
-    · rw [t.center_mass_eq_of_sum_1 id hw₂] at hw₃
-      exact hw₃
-    · intro e he hwe contra
-      apply hwe
-      rw [contra, zero_smul]
+    · rw [t.center_mass_eq_of_sum_1 id hw₂] at hw₃; exact hw₃
+    · intro e he hwe contra; apply hwe; rw [contra, zero_smul]
 #align eq_pos_convex_span_of_mem_convex_hull eq_pos_convex_span_of_mem_convexHull

9d2f0748

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -56,10 +56,7 @@ variable {𝕜 : Type _} {E : Type u} [LinearOrderedField 𝕜] [AddCommGroup E]
 namespace Caratheodory
 
 /- warning: caratheodory.mem_convex_hull_erase -> Caratheodory.mem_convexHull_erase is a dubious translation:
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-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DecidableEq.{succ u2} E] {t : Finset.{u2} E}, (Not (AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)))) -> (forall {x : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (Finset.toSet.{u2} E t))) -> (Exists.{succ u2} (Set.Elem.{u2} E (Finset.toSet.{u2} E t)) (fun (y : Set.Elem.{u2} E (Finset.toSet.{u2} E t)) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (Finset.toSet.{u2} E (Finset.erase.{u2} E (fun (a : E) (b : E) => _inst_4 a b) t (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Finset.toSet.{u2} E t)) y)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align caratheodory.mem_convex_hull_erase Caratheodory.mem_convexHull_eraseₓ'. -/
 /-- If `x` is in the convex hull of some finset `t` whose elements are not affine-independent,
 then it is in the convex hull of a strict subset of `t`. -/
@@ -209,10 +206,7 @@ end Caratheodory
 variable {s : Set E}
 
 /- warning: convex_hull_eq_union -> convexHull_eq_union is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align convex_hull_eq_union convexHull_eq_unionₓ'. -/
 /-- **Carathéodory's convexity theorem** -/
 theorem convexHull_eq_union :
@@ -232,10 +226,7 @@ theorem convexHull_eq_union :
 #align convex_hull_eq_union convexHull_eq_union
 
 /- warning: eq_pos_convex_span_of_mem_convex_hull -> eq_pos_convex_span_of_mem_convexHull is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align eq_pos_convex_span_of_mem_convex_hull eq_pos_convex_span_of_mem_convexHullₓ'. -/
 /-- A more explicit version of `convex_hull_eq_union`. -/
 theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜 s) :

9d2f0748

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -233,7 +233,7 @@ theorem convexHull_eq_union :
 
 /- warning: eq_pos_convex_span_of_mem_convex_hull -> eq_pos_convex_span_of_mem_convexHull is a dubious translation:
 lean 3 declaration is
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(LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) s)) -> (Exists.{succ (succ u1)} Type.{u1} (fun (ι : Type.{u1}) => Exists.{succ u1} (Fintype.{u1} ι) (fun (_x : Fintype.{u1} ι) => Exists.{succ u1} (ι -> E) (fun (z : ι -> E) => Exists.{max (succ u1) (succ u2)} (ι -> 𝕜) (fun (w : ι -> 𝕜) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) (Set.range.{u1, succ u1} E ι z) s) (fun (hss : HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) (Set.range.{u1, succ u1} E ι z) s) => Exists.{0} (AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) ι z) (fun (hai : AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) ι z) => Exists.{0} (forall (i : ι), LT.lt.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u2} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))))) (OfNat.ofNat.{u2} 𝕜 0 (OfNat.mk.{u2} 𝕜 0 (Zero.zero.{u2} 𝕜 (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))))))))) (w i)) (fun (hw : forall (i : ι), LT.lt.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u2} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))))) (OfNat.ofNat.{u2} 𝕜 0 (OfNat.mk.{u2} 𝕜 0 (Zero.zero.{u2} 𝕜 (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))))))))) (w i)) => And (Eq.{succ u2} 𝕜 (Finset.sum.{u2, u1} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u2} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))) (Finset.univ.{u1} ι _x) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} 𝕜 1 (OfNat.mk.{u2} 𝕜 1 (One.one.{u2} 𝕜 (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))))))))) (Eq.{succ u1} E (Finset.sum.{u1, u1} E ι (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Finset.univ.{u1} ι _x) (fun (i : ι) => SMul.smul.{u2, u1} 𝕜 E (SMulZeroClass.toHasSmul.{u2, u1} 𝕜 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u1} 𝕜 E (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (w i) (z i))) x)))))))))
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E} {x : E}, (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) s)) -> (Exists.{succ (succ u1)} Type.{u1} (fun (ι : Type.{u1}) => Exists.{succ u1} (Fintype.{u1} ι) (fun (_x : Fintype.{u1} ι) => Exists.{succ u1} (ι -> E) (fun (z : ι -> E) => Exists.{max (succ u1) (succ u2)} (ι -> 𝕜) (fun (w : ι -> 𝕜) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) (Set.range.{u1, succ u1} E ι z) s) (fun (hss : HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) (Set.range.{u1, succ u1} E ι z) s) => Exists.{0} (AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) ι z) (fun (hai : AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) ι z) => Exists.{0} (forall (i : ι), LT.lt.{u2} 𝕜 (Preorder.toHasLt.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u2} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))))) (OfNat.ofNat.{u2} 𝕜 0 (OfNat.mk.{u2} 𝕜 0 (Zero.zero.{u2} 𝕜 (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))))))))) (w i)) (fun (hw : forall (i : ι), LT.lt.{u2} 𝕜 (Preorder.toHasLt.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u2} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))))) (OfNat.ofNat.{u2} 𝕜 0 (OfNat.mk.{u2} 𝕜 0 (Zero.zero.{u2} 𝕜 (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))))))))) (w i)) => And (Eq.{succ u2} 𝕜 (Finset.sum.{u2, u1} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u2} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))) (Finset.univ.{u1} ι _x) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} 𝕜 1 (OfNat.mk.{u2} 𝕜 1 (One.one.{u2} 𝕜 (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))))))))) (Eq.{succ u1} E (Finset.sum.{u1, u1} E ι (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Finset.univ.{u1} ι _x) (fun (i : ι) => SMul.smul.{u2, u1} 𝕜 E (SMulZeroClass.toHasSmul.{u2, u1} 𝕜 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u1} 𝕜 E (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (w i) (z i))) x)))))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {x : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s)) -> (Exists.{succ (succ u2)} Type.{u2} (fun (ι : Type.{u2}) => Exists.{succ u2} (Fintype.{u2} ι) (fun (_x : Fintype.{u2} ι) => Exists.{succ u2} (ι -> E) (fun (z : ι -> E) => Exists.{max (succ u2) (succ u1)} (ι -> 𝕜) (fun (w : ι -> 𝕜) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.range.{u2, succ u2} E ι z) s) (fun (hss : HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.range.{u2, succ u2} E ι z) s) => Exists.{0} (AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) ι z) (fun (hai : AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) ι z) => Exists.{0} (forall (i : ι), LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (w i)) (fun (hw : forall (i : ι), LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (w i)) => And (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u2} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))) (Finset.univ.{u2} ι _x) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Eq.{succ u2} E (Finset.sum.{u2, u2} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Finset.univ.{u2} ι _x) (fun (i : ι) => HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (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 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{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 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{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 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (w i) (z i))) x)))))))))
 Case conversion may be inaccurate. Consider using '#align eq_pos_convex_span_of_mem_convex_hull eq_pos_convex_span_of_mem_convexHullₓ'. -/

9d2f0748

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -210,9 +210,9 @@ variable {s : Set E}
 
 /- warning: convex_hull_eq_union -> convexHull_eq_union is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E}, Eq.{succ u1} (Set.{u1} E) (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) 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𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) s) (Set.unionᵢ.{u1, succ u1} E (Finset.{u1} E) (fun (t : Finset.{u1} E) => Set.unionᵢ.{u1, 0} E (HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) t) s) (fun (hss : HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) t) s) => Set.unionᵢ.{u1, 0} E (AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 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E) x t))))))) (fun (hai : AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (coeSubtype.{succ u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Finset.{u1} E) (Finset.hasMem.{u1} E) x t))))))) => coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) t)))))
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E}, Eq.{succ u1} (Set.{u1} E) (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) s) (Set.iUnion.{u1, succ u1} E (Finset.{u1} E) (fun (t : Finset.{u1} E) => Set.iUnion.{u1, 0} E (HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) t) s) (fun (hss : HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) t) s) => Set.iUnion.{u1, 0} E (AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (coeSubtype.{succ u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Finset.{u1} E) (Finset.hasMem.{u1} E) x t))))))) (fun (hai : AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) E (coeSubtype.{succ u1} E (fun (x : E) => Membership.Mem.{u1, u1} E (Finset.{u1} E) (Finset.hasMem.{u1} E) x t))))))) => coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) t)))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, Eq.{succ u2} (Set.{u2} E) (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s) (Set.unionᵢ.{u2, succ u2} E (Finset.{u2} E) (fun (t : Finset.{u2} E) => Set.unionᵢ.{u2, 0} E (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Finset.toSet.{u2} E t) s) (fun (hss : HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Finset.toSet.{u2} E t) s) => Set.unionᵢ.{u2, 0} E (AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t))) (fun (hai : AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t))) => 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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (Finset.toSet.{u2} E t)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, Eq.{succ u2} (Set.{u2} E) (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s) (Set.iUnion.{u2, succ u2} E (Finset.{u2} E) (fun (t : Finset.{u2} E) => Set.iUnion.{u2, 0} E (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Finset.toSet.{u2} E t) s) (fun (hss : HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Finset.toSet.{u2} E t) s) => Set.iUnion.{u2, 0} E (AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t))) (fun (hai : AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t))) => 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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (Finset.toSet.{u2} E t)))))
 Case conversion may be inaccurate. Consider using '#align convex_hull_eq_union convexHull_eq_unionₓ'. -/
 /-- **Carathéodory's convexity theorem** -/
 theorem convexHull_eq_union :
@@ -221,13 +221,13 @@ theorem convexHull_eq_union :
   by
   apply Set.Subset.antisymm
   · intro x hx
-    simp only [exists_prop, Set.mem_unionᵢ]
+    simp only [exists_prop, Set.mem_iUnion]
     exact
       ⟨Caratheodory.minCardFinsetOfMemConvexHull hx,
         Caratheodory.minCardFinsetOfMemConvexHull_subseteq hx,
         Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull hx,
         Caratheodory.mem_minCardFinsetOfMemConvexHull hx⟩
-  · iterate 3 convert Set.unionᵢ_subset _; intro
+  · iterate 3 convert Set.iUnion_subset _; intro
     exact convexHull_mono ‹_›
 #align convex_hull_eq_union convexHull_eq_union
 
@@ -244,7 +244,7 @@ theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜
         ∀ i, 0 < w i), (∑ i, w i) = 1 ∧ (∑ i, w i • z i) = x :=
   by
   rw [convexHull_eq_union] at hx
-  simp only [exists_prop, Set.mem_unionᵢ] at hx
+  simp only [exists_prop, Set.mem_iUnion] at hx
   obtain ⟨t, ht₁, ht₂, ht₃⟩ := hx
   simp only [t.convex_hull_eq, exists_prop, Set.mem_setOf_eq] at ht₃
   obtain ⟨w, hw₁, hw₂, hw₃⟩ := ht₃

9d2f0748

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -235,7 +235,7 @@ theorem convexHull_eq_union :
 lean 3 declaration is
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E} {x : E}, (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) s)) -> (Exists.{succ (succ u1)} Type.{u1} (fun (ι : Type.{u1}) => Exists.{succ u1} (Fintype.{u1} ι) (fun (_x : Fintype.{u1} ι) => Exists.{succ u1} (ι -> E) (fun (z : ι -> E) => Exists.{max (succ u1) (succ u2)} (ι -> 𝕜) (fun (w : ι -> 𝕜) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) (Set.range.{u1, succ u1} E ι z) s) (fun (hss : HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) (Set.range.{u1, succ u1} E ι z) s) => Exists.{0} (AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) ι z) (fun (hai : AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) ι z) => Exists.{0} (forall (i : ι), LT.lt.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u2} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))))) (OfNat.ofNat.{u2} 𝕜 0 (OfNat.mk.{u2} 𝕜 0 (Zero.zero.{u2} 𝕜 (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))))))))) (w i)) (fun (hw : forall (i : ι), LT.lt.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u2} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))))) (OfNat.ofNat.{u2} 𝕜 0 (OfNat.mk.{u2} 𝕜 0 (Zero.zero.{u2} 𝕜 (MulZeroClass.toHasZero.{u2} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))))))))) (w i)) => And (Eq.{succ u2} 𝕜 (Finset.sum.{u2, u1} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u2} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))) (Finset.univ.{u1} ι _x) (fun (i : ι) => w i)) (OfNat.ofNat.{u2} 𝕜 1 (OfNat.mk.{u2} 𝕜 1 (One.one.{u2} 𝕜 (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))))))))) (Eq.{succ u1} E (Finset.sum.{u1, u1} E ι (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (Finset.univ.{u1} ι _x) (fun (i : ι) => SMul.smul.{u2, u1} 𝕜 E (SMulZeroClass.toHasSmul.{u2, u1} 𝕜 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u2, u1} 𝕜 E (MulZeroClass.toHasZero.{u2} 𝕜 (MulZeroOneClass.toMulZeroClass.{u2} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (w i) (z i))) x)))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {x : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s)) -> (Exists.{succ (succ u2)} Type.{u2} (fun (ι : Type.{u2}) => Exists.{succ u2} (Fintype.{u2} ι) (fun (_x : Fintype.{u2} ι) => Exists.{succ u2} (ι -> E) (fun (z : ι -> E) => Exists.{max (succ u2) (succ u1)} (ι -> 𝕜) (fun (w : ι -> 𝕜) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.range.{u2, succ u2} E ι z) s) (fun (hss : HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.range.{u2, succ u2} E ι z) s) => Exists.{0} (AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) ι z) (fun (hai : AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) ι z) => Exists.{0} (forall (i : ι), LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (w i)) (fun (hw : forall (i : ι), LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (w i)) => And (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u2} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))) (Finset.univ.{u2} ι _x) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (Eq.{succ u2} E (Finset.sum.{u2, u2} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Finset.univ.{u2} ι _x) (fun (i : ι) => HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (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 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{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 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{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 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (w i) (z i))) x)))))))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {x : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s)) -> (Exists.{succ (succ u2)} Type.{u2} (fun (ι : Type.{u2}) => Exists.{succ u2} (Fintype.{u2} ι) (fun (_x : Fintype.{u2} ι) => Exists.{succ u2} (ι -> E) (fun (z : ι -> E) => Exists.{max (succ u2) (succ u1)} (ι -> 𝕜) (fun (w : ι -> 𝕜) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.range.{u2, succ u2} E ι z) s) (fun (hss : HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.range.{u2, succ u2} E ι z) s) => Exists.{0} (AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) ι z) (fun (hai : AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) ι z) => Exists.{0} (forall (i : ι), LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (w i)) (fun (hw : forall (i : ι), LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (w i)) => And (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u2} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))) (Finset.univ.{u2} ι _x) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Eq.{succ u2} E (Finset.sum.{u2, u2} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Finset.univ.{u2} ι _x) (fun (i : ι) => HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (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 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{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 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{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 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (w i) (z i))) x)))))))))
 Case conversion may be inaccurate. Consider using '#align eq_pos_convex_span_of_mem_convex_hull eq_pos_convex_span_of_mem_convexHullₓ'. -/
 /-- A more explicit version of `convex_hull_eq_union`. -/
 theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜 s) :

9d2f0748

bump to nightly-2023-04-28-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

473bb540

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison
 
 ! This file was ported from Lean 3 source module analysis.convex.caratheodory
-! leanprover-community/mathlib commit e6fab1dc073396d45da082c644642c4f8bff2264
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Tactic.FieldSimp
 /-!
 # Carathéodory's convexity theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Convex hull can be regarded as a refinement of affine span. Both are closure operators but whereas
 convex hull takes values in the lattice of convex subsets, affine span takes values in the much
 coarser sublattice of affine subspaces.

e6fab1dc

bump to nightly-2023-04-25-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

b13fd1ba

Diff

@@ -52,6 +52,12 @@ variable {𝕜 : Type _} {E : Type u} [LinearOrderedField 𝕜] [AddCommGroup E]
 
 namespace Caratheodory
 
+/- warning: caratheodory.mem_convex_hull_erase -> Caratheodory.mem_convexHull_erase is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : DecidableEq.{succ u1} E] {t : Finset.{u1} E}, (Not (AffineIndependent.{u2, u1, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) (coeSort.{succ u1, succ (succ u1)} (Finset.{u1} E) Type.{u1} (Finset.hasCoeToSort.{u1} E) t) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ 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+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : DecidableEq.{succ u2} E] {t : Finset.{u2} E}, (Not (AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)))) -> (forall {x : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (Finset.toSet.{u2} E t))) -> (Exists.{succ u2} (Set.Elem.{u2} E (Finset.toSet.{u2} E t)) (fun (y : Set.Elem.{u2} E (Finset.toSet.{u2} E t)) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (Finset.toSet.{u2} E (Finset.erase.{u2} E (fun (a : E) (b : E) => _inst_4 a b) t (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (Finset.toSet.{u2} E t)) y)))))))
+Case conversion may be inaccurate. Consider using '#align caratheodory.mem_convex_hull_erase Caratheodory.mem_convexHull_eraseₓ'. -/
 /-- If `x` is in the convex hull of some finset `t` whose elements are not affine-independent,
 then it is in the convex hull of a strict subset of `t`. -/
 theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndependent 𝕜 (coe : t → E))
@@ -114,6 +120,7 @@ variable {s : Set E} {x : E} (hx : x ∈ convexHull 𝕜 s)
 
 include hx
 
+#print Caratheodory.minCardFinsetOfMemConvexHull /-
 /-- Given a point `x` in the convex hull of a set `s`, this is a finite subset of `s` of minimum
 cardinality, whose convex hull contains `x`. -/
 noncomputable def minCardFinsetOfMemConvexHull : Finset E :=
@@ -121,27 +128,58 @@ noncomputable def minCardFinsetOfMemConvexHull : Finset E :=
     (by
       simpa only [convexHull_eq_union_convexHull_finite_subsets s, exists_prop, mem_Union] using hx)
 #align caratheodory.min_card_finset_of_mem_convex_hull Caratheodory.minCardFinsetOfMemConvexHull
+-/
 
+/- warning: caratheodory.min_card_finset_of_mem_convex_hull_subseteq -> Caratheodory.minCardFinsetOfMemConvexHull_subseteq is a dubious translation:
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+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E} {x : E} (hx : Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) s)), HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) (Caratheodory.minCardFinsetOfMemConvexHull.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 s x hx)) s
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {x : E} (hx : Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s)), HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Finset.toSet.{u2} E (Caratheodory.minCardFinsetOfMemConvexHull.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 s x hx)) s
+Case conversion may be inaccurate. Consider using '#align caratheodory.min_card_finset_of_mem_convex_hull_subseteq Caratheodory.minCardFinsetOfMemConvexHull_subseteqₓ'. -/
 theorem minCardFinsetOfMemConvexHull_subseteq : ↑(minCardFinsetOfMemConvexHull hx) ⊆ s :=
   (Function.argminOn_mem _ _ { t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E) } _).1
 #align caratheodory.min_card_finset_of_mem_convex_hull_subseteq Caratheodory.minCardFinsetOfMemConvexHull_subseteq
 
+/- warning: caratheodory.mem_min_card_finset_of_mem_convex_hull -> Caratheodory.mem_minCardFinsetOfMemConvexHull is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E} {x : E} (hx : Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) s)), Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) (Caratheodory.minCardFinsetOfMemConvexHull.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 s x hx)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {x : E} (hx : Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s)), Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (Finset.toSet.{u2} E (Caratheodory.minCardFinsetOfMemConvexHull.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 s x hx)))
+Case conversion may be inaccurate. Consider using '#align caratheodory.mem_min_card_finset_of_mem_convex_hull Caratheodory.mem_minCardFinsetOfMemConvexHullₓ'. -/
 theorem mem_minCardFinsetOfMemConvexHull :
     x ∈ convexHull 𝕜 (minCardFinsetOfMemConvexHull hx : Set E) :=
   (Function.argminOn_mem _ _ { t : Finset E | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E) } _).2
 #align caratheodory.mem_min_card_finset_of_mem_convex_hull Caratheodory.mem_minCardFinsetOfMemConvexHull
 
+/- warning: caratheodory.min_card_finset_of_mem_convex_hull_nonempty -> Caratheodory.minCardFinsetOfMemConvexHull_nonempty is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E} {x : E} (hx : Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) s)), Finset.Nonempty.{u1} E (Caratheodory.minCardFinsetOfMemConvexHull.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 s x hx)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {x : E} (hx : Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s)), Finset.Nonempty.{u2} E (Caratheodory.minCardFinsetOfMemConvexHull.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 s x hx)
+Case conversion may be inaccurate. Consider using '#align caratheodory.min_card_finset_of_mem_convex_hull_nonempty Caratheodory.minCardFinsetOfMemConvexHull_nonemptyₓ'. -/
 theorem minCardFinsetOfMemConvexHull_nonempty : (minCardFinsetOfMemConvexHull hx).Nonempty :=
   by
   rw [← Finset.coe_nonempty, ← @convexHull_nonempty_iff 𝕜]
   exact ⟨x, mem_min_card_finset_of_mem_convex_hull hx⟩
 #align caratheodory.min_card_finset_of_mem_convex_hull_nonempty Caratheodory.minCardFinsetOfMemConvexHull_nonempty
 
+/- warning: caratheodory.min_card_finset_of_mem_convex_hull_card_le_card -> Caratheodory.minCardFinsetOfMemConvexHull_card_le_card is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E} {x : E} (hx : Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) s)) {t : Finset.{u1} E}, (HasSubset.Subset.{u1} (Set.{u1} E) (Set.hasSubset.{u1} E) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) t) s) -> (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) => (Set.{u1} E) -> (Set.{u1} E)) (ClosureOperator.hasCoeToFun.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (convexHull.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} E) (Set.{u1} E) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} E) (Set.{u1} E) (Finset.Set.hasCoeT.{u1} E))) t))) -> (LE.le.{0} Nat Nat.hasLe (Finset.card.{u1} E (Caratheodory.minCardFinsetOfMemConvexHull.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 s x hx)) (Finset.card.{u1} E t))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {x : E} (hx : Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s)) {t : Finset.{u2} E}, (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Finset.toSet.{u2} E t) s) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (Finset.toSet.{u2} E t))) -> (LE.le.{0} Nat instLENat (Finset.card.{u2} E (Caratheodory.minCardFinsetOfMemConvexHull.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 s x hx)) (Finset.card.{u2} E t))
+Case conversion may be inaccurate. Consider using '#align caratheodory.min_card_finset_of_mem_convex_hull_card_le_card Caratheodory.minCardFinsetOfMemConvexHull_card_le_cardₓ'. -/
 theorem minCardFinsetOfMemConvexHull_card_le_card {t : Finset E} (ht₁ : ↑t ⊆ s)
     (ht₂ : x ∈ convexHull 𝕜 (t : Set E)) : (minCardFinsetOfMemConvexHull hx).card ≤ t.card :=
   Function.argminOn_le _ _ _ ⟨ht₁, ht₂⟩
 #align caratheodory.min_card_finset_of_mem_convex_hull_card_le_card Caratheodory.minCardFinsetOfMemConvexHull_card_le_card
 
+/- warning: caratheodory.affine_independent_min_card_finset_of_mem_convex_hull -> Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align caratheodory.affine_independent_min_card_finset_of_mem_convex_hull Caratheodory.affineIndependent_minCardFinsetOfMemConvexHullₓ'. -/
 theorem affineIndependent_minCardFinsetOfMemConvexHull :
     AffineIndependent 𝕜 (coe : minCardFinsetOfMemConvexHull hx → E) :=
   by
@@ -167,6 +205,12 @@ end Caratheodory
 
 variable {s : Set E}
 
+/- warning: convex_hull_eq_union -> convexHull_eq_union is a dubious translation:
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+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, Eq.{succ u2} (Set.{u2} E) (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) 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(LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s) (Set.unionᵢ.{u2, succ u2} E (Finset.{u2} E) (fun (t : Finset.{u2} E) => Set.unionᵢ.{u2, 0} E (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Finset.toSet.{u2} E t) s) (fun (hss : HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Finset.toSet.{u2} E t) s) => Set.unionᵢ.{u2, 0} E (AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t))) (fun (hai : AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) (Subtype.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t)) (Subtype.val.{succ u2} E (fun (x : E) => Membership.mem.{u2, u2} E (Finset.{u2} E) (Finset.instMembershipFinset.{u2} E) x t))) => 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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) (Finset.toSet.{u2} E t)))))
+Case conversion may be inaccurate. Consider using '#align convex_hull_eq_union convexHull_eq_unionₓ'. -/
 /-- **Carathéodory's convexity theorem** -/
 theorem convexHull_eq_union :
     convexHull 𝕜 s =
@@ -184,6 +228,12 @@ theorem convexHull_eq_union :
     exact convexHull_mono ‹_›
 #align convex_hull_eq_union convexHull_eq_union
 
+/- warning: eq_pos_convex_span_of_mem_convex_hull -> eq_pos_convex_span_of_mem_convexHull is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u2} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E} {x : E}, (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x (coeFn.{succ u1, succ u1} (ClosureOperator.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))))) (fun (_x : ClosureOperator.{u1} (Set.{u1} E) 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+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {x : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (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 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)) s)) -> (Exists.{succ (succ u2)} Type.{u2} (fun (ι : Type.{u2}) => Exists.{succ u2} (Fintype.{u2} ι) (fun (_x : Fintype.{u2} ι) => Exists.{succ u2} (ι -> E) (fun (z : ι -> E) => Exists.{max (succ u2) (succ u1)} (ι -> 𝕜) (fun (w : ι -> 𝕜) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.range.{u2, succ u2} E ι z) s) (fun (hss : HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (Set.range.{u2, succ u2} E ι z) s) => Exists.{0} (AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) ι z) (fun (hai : AffineIndependent.{u1, u2, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) ι z) => Exists.{0} (forall (i : ι), LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (w i)) (fun (hw : forall (i : ι), LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (w i)) => And (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u2} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))) (Finset.univ.{u2} ι _x) (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (Eq.{succ u2} E (Finset.sum.{u2, u2} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (Finset.univ.{u2} ι _x) (fun (i : ι) => HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (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 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{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 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{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 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (w i) (z i))) x)))))))))
+Case conversion may be inaccurate. Consider using '#align eq_pos_convex_span_of_mem_convex_hull eq_pos_convex_span_of_mem_convexHullₓ'. -/
 /-- A more explicit version of `convex_hull_eq_union`. -/
 theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜 s) :
     ∃ (ι : Sort (u + 1))(_ : Fintype ι),

e6fab1dc

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -80,7 +80,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
       (∑ e in t.erase i₀, k e) = ∑ e in t, k e := by
         conv_rhs => rw [← insert_erase hi₀, sum_insert (not_mem_erase i₀ t), hk, zero_add]
       _ = ∑ e in t, f e - f i₀ / g i₀ * g e := rfl
-      _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, mul_zero, sub_zero]
+      _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, MulZeroClass.mul_zero, sub_zero]
       
   refine' ⟨⟨i₀, hi₀⟩, k, _, by convert ksum, _⟩
   · simp only [and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]

e6fab1dc

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

e6fab1dc

chore: avoid id.def (adaptation for nightly-2024-03-27) (#11829)

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

b8a0f589

Diff

@@ -97,7 +97,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
       _ = ∑ e in t, (f e - f i₀ / g i₀ * g e) • e := rfl
       _ = t.centerMass f id := by
         simp only [sub_smul, mul_smul, sum_sub_distrib, ← smul_sum, gcombo, smul_zero, sub_zero,
-          centerMass, fsum, inv_one, one_smul, id.def]
+          centerMass, fsum, inv_one, one_smul, id]
 #align caratheodory.mem_convex_hull_erase Caratheodory.mem_convexHull_erase
 
 variable {s : Set E} {x : E} (hx : x ∈ convexHull 𝕜 s)

e6fab1dc

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -77,7 +77,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
       _ = ∑ e in t, (f e - f i₀ / g i₀ * g e) := rfl
       _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, mul_zero, sub_zero]
   refine' ⟨⟨i₀, hi₀⟩, k, _, by convert ksum, _⟩
-  · simp only [k, and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]
+  · simp only [k, and_imp, sub_nonneg, mem_erase, Ne, Subtype.coe_mk]
     intro e _ het
     by_cases hes : e ∈ s
     · have hge : 0 < g e := by

e6fab1dc

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -69,7 +69,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
     exact mem.2
   have hi₀ : i₀ ∈ t := filter_subset _ _ mem
   let k : E → 𝕜 := fun z => f z - f i₀ / g i₀ * g z
-  have hk : k i₀ = 0 := by field_simp [ne_of_gt hg]
+  have hk : k i₀ = 0 := by field_simp [k, ne_of_gt hg]
   have ksum : ∑ e in t.erase i₀, k e = 1 := by
     calc
       ∑ e in t.erase i₀, k e = ∑ e in t, k e := by
@@ -77,7 +77,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
       _ = ∑ e in t, (f e - f i₀ / g i₀ * g e) := rfl
       _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, mul_zero, sub_zero]
   refine' ⟨⟨i₀, hi₀⟩, k, _, by convert ksum, _⟩
-  · simp only [and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]
+  · simp only [k, and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]
     intro e _ het
     by_cases hes : e ∈ s
     · have hge : 0 < g e := by
@@ -89,7 +89,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
         _ ≤ 0 := by
           apply mul_nonpos_of_nonneg_of_nonpos
           · apply div_nonneg (fpos i₀ (mem_of_subset (filter_subset _ t) mem)) (le_of_lt hg)
-          · simpa only [mem_filter, het, true_and_iff, not_lt] using hes
+          · simpa only [s, mem_filter, het, true_and_iff, not_lt] using hes
         _ ≤ f e := fpos e het
   · rw [Subtype.coe_mk, centerMass_eq_of_sum_1 _ id ksum]
     calc

e6fab1dc

chore(*): use ∃ x ∈ s, _ instead of ∃ (x) (_ : x ∈ s), _ (#9184)

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.

14c72960

Diff

@@ -166,8 +166,8 @@ theorem convexHull_eq_union : convexHull 𝕜 s =
 /-- A more explicit version of `convexHull_eq_union`. -/
 theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜 s) :
     ∃ (ι : Sort (u + 1)) (_ : Fintype ι),
-      ∃ (z : ι → E) (w : ι → 𝕜) (_ : Set.range z ⊆ s) (_ : AffineIndependent 𝕜 z)
-        (_ : ∀ i, 0 < w i), ∑ i, w i = 1 ∧ ∑ i, w i • z i = x := by
+      ∃ (z : ι → E) (w : ι → 𝕜), Set.range z ⊆ s ∧ AffineIndependent 𝕜 z ∧ (∀ i, 0 < w i) ∧
+        ∑ i, w i = 1 ∧ ∑ i, w i • z i = x := by
   rw [convexHull_eq_union] at hx
   simp only [exists_prop, Set.mem_iUnion] at hx
   obtain ⟨t, ht₁, ht₂, ht₃⟩ := hx

e6fab1dc

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

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

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

277dea95

Diff

@@ -75,7 +75,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
       ∑ e in t.erase i₀, k e = ∑ e in t, k e := by
         conv_rhs => rw [← insert_erase hi₀, sum_insert (not_mem_erase i₀ t), hk, zero_add]
       _ = ∑ e in t, (f e - f i₀ / g i₀ * g e) := rfl
-      _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, MulZeroClass.mul_zero, sub_zero]
+      _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, mul_zero, sub_zero]
   refine' ⟨⟨i₀, hi₀⟩, k, _, by convert ksum, _⟩
   · simp only [and_imp, sub_nonneg, mem_erase, Ne.def, Subtype.coe_mk]
     intro e _ het

e6fab1dc

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -45,7 +45,7 @@ open BigOperators
 
 universe u
 
-variable {𝕜 : Type _} {E : Type u} [LinearOrderedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
+variable {𝕜 : Type*} {E : Type u} [LinearOrderedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 namespace Caratheodory

e6fab1dc

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison
-
-! This file was ported from Lean 3 source module analysis.convex.caratheodory
-! leanprover-community/mathlib commit e6fab1dc073396d45da082c644642c4f8bff2264
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Convex.Combination
 import Mathlib.LinearAlgebra.AffineSpace.Independent
 import Mathlib.Tactic.FieldSimp
 
+#align_import analysis.convex.caratheodory from "leanprover-community/mathlib"@"e6fab1dc073396d45da082c644642c4f8bff2264"
+
 /-!
 # Carathéodory's convexity theorem

e6fab1dc

fix: ∑' precedence (#5615)

Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) $([∑∏][^()∑∏]*,[^()∑∏:]*)$ ([⊂⊆=<≤]) replaced by $1 $2 $3

03fc68aa

Diff

@@ -73,9 +73,9 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
   have hi₀ : i₀ ∈ t := filter_subset _ _ mem
   let k : E → 𝕜 := fun z => f z - f i₀ / g i₀ * g z
   have hk : k i₀ = 0 := by field_simp [ne_of_gt hg]
-  have ksum : (∑ e in t.erase i₀, k e) = 1 := by
+  have ksum : ∑ e in t.erase i₀, k e = 1 := by
     calc
-      (∑ e in t.erase i₀, k e) = ∑ e in t, k e := by
+      ∑ e in t.erase i₀, k e = ∑ e in t, k e := by
         conv_rhs => rw [← insert_erase hi₀, sum_insert (not_mem_erase i₀ t), hk, zero_add]
       _ = ∑ e in t, (f e - f i₀ / g i₀ * g e) := rfl
       _ = 1 := by rw [sum_sub_distrib, fsum, ← mul_sum, gsum, MulZeroClass.mul_zero, sub_zero]
@@ -96,7 +96,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
         _ ≤ f e := fpos e het
   · rw [Subtype.coe_mk, centerMass_eq_of_sum_1 _ id ksum]
     calc
-      (∑ e in t.erase i₀, k e • e) = ∑ e in t, k e • e := sum_erase _ (by rw [hk, zero_smul])
+      ∑ e in t.erase i₀, k e • e = ∑ e in t, k e • e := sum_erase _ (by rw [hk, zero_smul])
       _ = ∑ e in t, (f e - f i₀ / g i₀ * g e) • e := rfl
       _ = t.centerMass f id := by
         simp only [sub_smul, mul_smul, sum_sub_distrib, ← smul_sum, gcombo, smul_zero, sub_zero,
@@ -170,7 +170,7 @@ theorem convexHull_eq_union : convexHull 𝕜 s =
 theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜 s) :
     ∃ (ι : Sort (u + 1)) (_ : Fintype ι),
       ∃ (z : ι → E) (w : ι → 𝕜) (_ : Set.range z ⊆ s) (_ : AffineIndependent 𝕜 z)
-        (_ : ∀ i, 0 < w i), (∑ i, w i) = 1 ∧ (∑ i, w i • z i) = x := by
+        (_ : ∀ i, 0 < w i), ∑ i, w i = 1 ∧ ∑ i, w i • z i = x := by
   rw [convexHull_eq_union] at hx
   simp only [exists_prop, Set.mem_iUnion] at hx
   obtain ⟨t, ht₁, ht₂, ht₃⟩ := hx

e6fab1dc

chore: clean up spacing around at and goals (#5387)

Changes are of the form

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

2a870323

Diff

@@ -57,7 +57,7 @@ then it is in the convex hull of a strict subset of `t`. -/
 theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndependent 𝕜 ((↑) : t → E))
     {x : E} (m : x ∈ convexHull 𝕜 (↑t : Set E)) :
     ∃ y : (↑t : Set E), x ∈ convexHull 𝕜 (↑(t.erase y) : Set E) := by
-  simp only [Finset.convexHull_eq, mem_setOf_eq] at m⊢
+  simp only [Finset.convexHull_eq, mem_setOf_eq] at m ⊢
   obtain ⟨f, fpos, fsum, rfl⟩ := m
   obtain ⟨g, gcombo, gsum, gpos⟩ := exists_nontrivial_relation_sum_zero_of_not_affine_ind h
   replace gpos := exists_pos_of_sum_zero_of_exists_nonzero g gsum gpos

e6fab1dc

fix: correct names of LinearOrder decidable fields (#4006)

This renames

decidable_eq to decidableEq
decidable_lt to decidableLT
decidable_le to decidableLE
decidableLT_of_decidableLE to decidableLTOfDecidableLE
decidableEq_of_decidableLE to decidableEqOfDecidableLE

These fields are data not proofs, so they should be lowerCamelCased.

e7280432

Diff

@@ -62,7 +62,7 @@ theorem mem_convexHull_erase [DecidableEq E] {t : Finset E} (h : ¬AffineIndepen
   obtain ⟨g, gcombo, gsum, gpos⟩ := exists_nontrivial_relation_sum_zero_of_not_affine_ind h
   replace gpos := exists_pos_of_sum_zero_of_exists_nonzero g gsum gpos
   clear h
-  let s := @Finset.filter _ (fun z => 0 < g z) (fun _ => LinearOrder.decidable_lt _ _) t
+  let s := @Finset.filter _ (fun z => 0 < g z) (fun _ => LinearOrder.decidableLT _ _) t
   obtain ⟨i₀, mem, w⟩ : ∃ i₀ ∈ s, ∀ i ∈ s, f i₀ / g i₀ ≤ f i / g i := by
     apply s.exists_min_image fun z => f z / g z
     obtain ⟨x, hx, hgx⟩ : ∃ x ∈ t, 0 < g x := gpos

e6fab1dc

chore: Rename to sSup/iSup (#3938)

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>

d1eb6264

Diff

@@ -109,7 +109,7 @@ variable {s : Set E} {x : E} (hx : x ∈ convexHull 𝕜 s)
 cardinality, whose convex hull contains `x`. -/
 noncomputable def minCardFinsetOfMemConvexHull : Finset E :=
   Function.argminOn Finset.card Nat.lt_wfRel.2 { t | ↑t ⊆ s ∧ x ∈ convexHull 𝕜 (t : Set E) } <| by
-    simpa only [convexHull_eq_union_convexHull_finite_subsets s, exists_prop, mem_unionᵢ] using hx
+    simpa only [convexHull_eq_union_convexHull_finite_subsets s, exists_prop, mem_iUnion] using hx
 #align caratheodory.min_card_finset_of_mem_convex_hull Caratheodory.minCardFinsetOfMemConvexHull
 
 theorem minCardFinsetOfMemConvexHull_subseteq : ↑(minCardFinsetOfMemConvexHull hx) ⊆ s :=
@@ -157,12 +157,12 @@ theorem convexHull_eq_union : convexHull 𝕜 s =
     ⋃ (t : Finset E) (hss : ↑t ⊆ s) (hai : AffineIndependent 𝕜 ((↑) : t → E)), convexHull 𝕜 ↑t := by
   apply Set.Subset.antisymm
   · intro x hx
-    simp only [exists_prop, Set.mem_unionᵢ]
+    simp only [exists_prop, Set.mem_iUnion]
     exact ⟨Caratheodory.minCardFinsetOfMemConvexHull hx,
       Caratheodory.minCardFinsetOfMemConvexHull_subseteq hx,
       Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull hx,
       Caratheodory.mem_minCardFinsetOfMemConvexHull hx⟩
-  · iterate 3 convert Set.unionᵢ_subset _; intro
+  · iterate 3 convert Set.iUnion_subset _; intro
     exact convexHull_mono ‹_›
 #align convex_hull_eq_union convexHull_eq_union
 
@@ -172,7 +172,7 @@ theorem eq_pos_convex_span_of_mem_convexHull {x : E} (hx : x ∈ convexHull 𝕜
       ∃ (z : ι → E) (w : ι → 𝕜) (_ : Set.range z ⊆ s) (_ : AffineIndependent 𝕜 z)
         (_ : ∀ i, 0 < w i), (∑ i, w i) = 1 ∧ (∑ i, w i • z i) = x := by
   rw [convexHull_eq_union] at hx
-  simp only [exists_prop, Set.mem_unionᵢ] at hx
+  simp only [exists_prop, Set.mem_iUnion] at hx
   obtain ⟨t, ht₁, ht₂, ht₃⟩ := hx
   simp only [t.convexHull_eq, exists_prop, Set.mem_setOf_eq] at ht₃
   obtain ⟨w, hw₁, hw₂, hw₃⟩ := ht₃

e6fab1dc

feat: port Analysis.Convex.Caratheodory (#3639)

6b5a6157

`analysis.convex.caratheodory` ⟷ `Mathlib.Analysis.Convex.Caratheodory`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 9 + 445

analysis.convex.caratheodory ⟷ Mathlib.Analysis.Convex.Caratheodory

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 9 + 445

`analysis.convex.caratheodory` ⟷ `Mathlib.Analysis.Convex.Caratheodory`