analysis.convex.jensen | 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

bfad3f45

(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

@@ -123,7 +123,7 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
   by
   set y := t.center_mass w p
   rsuffices ⟨i, hi, hfi⟩ : ∃ i ∈ t.filter fun i => w i ≠ 0, w i • f y ≤ w i • (f ∘ p) i
-  · rw [mem_filter] at hi 
+  · rw [mem_filter] at hi
     exact ⟨i, hi.1, (smul_le_smul_iff_of_pos_left <| (hw₀ i hi.1).lt_of_ne hi.2.symm).1 hfi⟩
   have hw' : (0 : 𝕜) < ∑ i in Filter (fun i => w i ≠ 0) t, w i := by rwa [sum_filter_ne_zero]
   refine' exists_le_of_sum_le (nonempty_of_sum_ne_zero hw'.ne') _
@@ -149,7 +149,7 @@ then the eventual maximum of `f` on `convex_hull 𝕜 s` lies in `s`. -/
 theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 𝕜 s) f) {x}
     (hx : x ∈ convexHull 𝕜 s) : ∃ y ∈ s, f x ≤ f y :=
   by
-  rw [_root_.convex_hull_eq] at hx 
+  rw [_root_.convex_hull_eq] at hx
   obtain ⟨α, t, w, p, hw₀, hw₁, hp, rfl⟩ := hx
   rcases hf.exists_ge_of_center_mass hw₀ (hw₁.symm ▸ zero_lt_one) fun i hi =>
       subset_convexHull 𝕜 s (hp i hi) with

9d2f0748

bump to nightly-2023-12-25-06

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

c71f3cc2

Diff

@@ -124,10 +124,10 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
   set y := t.center_mass w p
   rsuffices ⟨i, hi, hfi⟩ : ∃ i ∈ t.filter fun i => w i ≠ 0, w i • f y ≤ w i • (f ∘ p) i
   · rw [mem_filter] at hi 
-    exact ⟨i, hi.1, (smul_le_smul_iff_of_pos <| (hw₀ i hi.1).lt_of_ne hi.2.symm).1 hfi⟩
+    exact ⟨i, hi.1, (smul_le_smul_iff_of_pos_left <| (hw₀ i hi.1).lt_of_ne hi.2.symm).1 hfi⟩
   have hw' : (0 : 𝕜) < ∑ i in Filter (fun i => w i ≠ 0) t, w i := by rwa [sum_filter_ne_zero]
   refine' exists_le_of_sum_le (nonempty_of_sum_ne_zero hw'.ne') _
-  rw [← sum_smul, ← smul_le_smul_iff_of_pos (inv_pos.2 hw'), inv_smul_smul₀ hw'.ne', ←
+  rw [← sum_smul, ← smul_le_smul_iff_of_pos_left (inv_pos.2 hw'), inv_smul_smul₀ hw'.ne', ←
     Finset.centerMass, Finset.centerMass_filter_ne_zero]
   exact h.map_center_mass_le hw₀ hw₁ hp
   infer_instance

9d2f0748

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp, Yury Kudriashov
 -/
-import Mathbin.Analysis.Convex.Combination
-import Mathbin.Analysis.Convex.Function
+import Analysis.Convex.Combination
+import Analysis.Convex.Function
 
 #align_import analysis.convex.jensen 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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp, Yury Kudriashov
-
-! This file was ported from Lean 3 source module analysis.convex.jensen
-! 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.Analysis.Convex.Function
 
+#align_import analysis.convex.jensen from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 # Jensen's inequality and maximum principle for convex functions

9d2f0748

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -48,6 +48,7 @@ section Jensen
 variable [LinearOrderedField 𝕜] [AddCommGroup E] [OrderedAddCommGroup β] [Module 𝕜 E] [Module 𝕜 β]
   [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E}
 
+#print ConvexOn.map_centerMass_le /-
 /-- Convex **Jensen's inequality**, `finset.center_mass` version. -/
 theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : 0 < ∑ i in t, w i) (hmem : ∀ i ∈ t, p i ∈ s) :
@@ -58,26 +59,33 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
   convert (hf.convex_epigraph.center_mass_mem h₀ h₁ hmem').2 <;>
     simp only [center_mass, Function.comp, Prod.smul_fst, Prod.fst_sum, Prod.smul_snd, Prod.snd_sum]
 #align convex_on.map_center_mass_le ConvexOn.map_centerMass_le
+-/
 
+#print ConcaveOn.le_map_centerMass /-
 /-- Concave **Jensen's inequality**, `finset.center_mass` version. -/
 theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : 0 < ∑ i in t, w i) (hmem : ∀ i ∈ t, p i ∈ s) :
     t.centerMass w (f ∘ p) ≤ f (t.centerMass w p) :=
   @ConvexOn.map_centerMass_le 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ hf h₀ h₁ hmem
 #align concave_on.le_map_center_mass ConcaveOn.le_map_centerMass
+-/
 
+#print ConvexOn.map_sum_le /-
 /-- Convex **Jensen's inequality**, `finset.sum` version. -/
 theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : ∑ i in t, w i = 1)
     (hmem : ∀ i ∈ t, p i ∈ s) : f (∑ i in t, w i • p i) ≤ ∑ i in t, w i • f (p i) := by
   simpa only [center_mass, h₁, inv_one, one_smul] using
     hf.map_center_mass_le h₀ (h₁.symm ▸ zero_lt_one) hmem
 #align convex_on.map_sum_le ConvexOn.map_sum_le
+-/
 
+#print ConcaveOn.le_map_sum /-
 /-- Concave **Jensen's inequality**, `finset.sum` version. -/
 theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : ∑ i in t, w i = 1)
     (hmem : ∀ i ∈ t, p i ∈ s) : ∑ i in t, w i • f (p i) ≤ f (∑ i in t, w i • p i) :=
   @ConvexOn.map_sum_le 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ hf h₀ h₁ hmem
 #align concave_on.le_map_sum ConcaveOn.le_map_sum
+-/
 
 end Jensen
 
@@ -90,6 +98,7 @@ variable [LinearOrderedField 𝕜] [AddCommGroup E] [LinearOrderedAddCommGroup 
   [Module 𝕜 β] [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E}
   {x : E}
 
+#print le_sup_of_mem_convexHull /-
 theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
     f x ≤ s.sup' (coe_nonempty.1 <| convexHull_nonempty_iff.1 ⟨x, hx⟩) f :=
@@ -99,13 +108,17 @@ theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull
     (hf.map_center_mass_le hw₀ (by positivity) <| subset_convexHull _ _).trans
       (center_mass_le_sup hw₀ <| by positivity)
 #align le_sup_of_mem_convex_hull le_sup_of_mem_convexHull
+-/
 
+#print inf_le_of_mem_convexHull /-
 theorem inf_le_of_mem_convexHull {s : Finset E} (hf : ConcaveOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
     s.inf' (coe_nonempty.1 <| convexHull_nonempty_iff.1 ⟨x, hx⟩) f ≤ f x :=
   le_sup_of_mem_convexHull hf.dual hx
 #align inf_le_of_mem_convex_hull inf_le_of_mem_convexHull
+-/
 
+#print ConvexOn.exists_ge_of_centerMass /-
 /-- If a function `f` is convex on `s`, then the value it takes at some center of mass of points of
 `s` is less than the value it takes on one of those points. -/
 theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i ∈ t, 0 ≤ w i)
@@ -122,14 +135,18 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
   exact h.map_center_mass_le hw₀ hw₁ hp
   infer_instance
 #align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMass
+-/
 
+#print ConcaveOn.exists_le_of_centerMass /-
 /-- If a function `f` is concave on `s`, then the value it takes at some center of mass of points of
 `s` is greater than the value it takes on one of those points. -/
 theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀ i ∈ t, 0 ≤ w i)
     (hw₁ : 0 < ∑ i in t, w i) (hp : ∀ i ∈ t, p i ∈ s) : ∃ i ∈ t, f (p i) ≤ f (t.centerMass w p) :=
   @ConvexOn.exists_ge_of_centerMass 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ h hw₀ hw₁ hp
 #align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMass
+-/
 
+#print ConvexOn.exists_ge_of_mem_convexHull /-
 /-- Maximum principle for convex functions. If a function `f` is convex on the convex hull of `s`,
 then the eventual maximum of `f` on `convex_hull 𝕜 s` lies in `s`. -/
 theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 𝕜 s) f) {x}
@@ -142,13 +159,16 @@ theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 
     ⟨i, hit, Hi⟩
   exact ⟨p i, hp i hit, Hi⟩
 #align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHull
+-/
 
+#print ConcaveOn.exists_le_of_mem_convexHull /-
 /-- Minimum principle for concave functions. If a function `f` is concave on the convex hull of `s`,
 then the eventual minimum of `f` on `convex_hull 𝕜 s` lies in `s`. -/
 theorem ConcaveOn.exists_le_of_mem_convexHull (hf : ConcaveOn 𝕜 (convexHull 𝕜 s) f) {x}
     (hx : x ∈ convexHull 𝕜 s) : ∃ y ∈ s, f y ≤ f x :=
   @ConvexOn.exists_ge_of_mem_convexHull 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ hf _ hx
 #align concave_on.exists_le_of_mem_convex_hull ConcaveOn.exists_le_of_mem_convexHull
+-/
 
 end MaximumPrinciple

9d2f0748

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -67,16 +67,15 @@ theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈
 #align concave_on.le_map_center_mass ConcaveOn.le_map_centerMass
 
 /-- Convex **Jensen's inequality**, `finset.sum` version. -/
-theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : (∑ i in t, w i) = 1)
+theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : ∑ i in t, w i = 1)
     (hmem : ∀ i ∈ t, p i ∈ s) : f (∑ i in t, w i • p i) ≤ ∑ i in t, w i • f (p i) := by
   simpa only [center_mass, h₁, inv_one, one_smul] using
     hf.map_center_mass_le h₀ (h₁.symm ▸ zero_lt_one) hmem
 #align convex_on.map_sum_le ConvexOn.map_sum_le
 
 /-- Concave **Jensen's inequality**, `finset.sum` version. -/
-theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
-    (h₁ : (∑ i in t, w i) = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
-    (∑ i in t, w i • f (p i)) ≤ f (∑ i in t, w i • p i) :=
+theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : ∑ i in t, w i = 1)
+    (hmem : ∀ i ∈ t, p i ∈ s) : ∑ i in t, w i • f (p i) ≤ f (∑ i in t, w i • p i) :=
   @ConvexOn.map_sum_le 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ hf h₀ h₁ hmem
 #align concave_on.le_map_sum ConcaveOn.le_map_sum

9d2f0748

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -53,9 +53,9 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
     (h₁ : 0 < ∑ i in t, w i) (hmem : ∀ i ∈ t, p i ∈ s) :
     f (t.centerMass w p) ≤ t.centerMass w (f ∘ p) :=
   by
-  have hmem' : ∀ i ∈ t, (p i, (f ∘ p) i) ∈ { p : E × β | p.1 ∈ s ∧ f p.1 ≤ p.2 } := fun i hi =>
+  have hmem' : ∀ i ∈ t, (p i, (f ∘ p) i) ∈ {p : E × β | p.1 ∈ s ∧ f p.1 ≤ p.2} := fun i hi =>
     ⟨hmem i hi, le_rfl⟩
-  convert(hf.convex_epigraph.center_mass_mem h₀ h₁ hmem').2 <;>
+  convert (hf.convex_epigraph.center_mass_mem h₀ h₁ hmem').2 <;>
     simp only [center_mass, Function.comp, Prod.smul_fst, Prod.fst_sum, Prod.smul_snd, Prod.snd_sum]
 #align convex_on.map_center_mass_le ConvexOn.map_centerMass_le

9d2f0748

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -114,7 +114,7 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
   by
   set y := t.center_mass w p
   rsuffices ⟨i, hi, hfi⟩ : ∃ i ∈ t.filter fun i => w i ≠ 0, w i • f y ≤ w i • (f ∘ p) i
-  · rw [mem_filter] at hi
+  · rw [mem_filter] at hi 
     exact ⟨i, hi.1, (smul_le_smul_iff_of_pos <| (hw₀ i hi.1).lt_of_ne hi.2.symm).1 hfi⟩
   have hw' : (0 : 𝕜) < ∑ i in Filter (fun i => w i ≠ 0) t, w i := by rwa [sum_filter_ne_zero]
   refine' exists_le_of_sum_le (nonempty_of_sum_ne_zero hw'.ne') _
@@ -136,7 +136,7 @@ then the eventual maximum of `f` on `convex_hull 𝕜 s` lies in `s`. -/
 theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 𝕜 s) f) {x}
     (hx : x ∈ convexHull 𝕜 s) : ∃ y ∈ s, f x ≤ f y :=
   by
-  rw [_root_.convex_hull_eq] at hx
+  rw [_root_.convex_hull_eq] at hx 
   obtain ⟨α, t, w, p, hw₀, hw₁, hp, rfl⟩ := hx
   rcases hf.exists_ge_of_center_mass hw₀ (hw₁.symm ▸ zero_lt_one) fun i hi =>
       subset_convexHull 𝕜 s (hp i hi) with

9d2f0748

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -36,7 +36,7 @@ As corollaries, we get:
 
 open Finset LinearMap Set
 
-open BigOperators Classical Convex Pointwise
+open scoped BigOperators Classical Convex Pointwise
 
 variable {𝕜 E F β ι : Type _}

9d2f0748

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -48,9 +48,6 @@ section Jensen
 variable [LinearOrderedField 𝕜] [AddCommGroup E] [OrderedAddCommGroup β] [Module 𝕜 E] [Module 𝕜 β]
   [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E}
 
-/- warning: convex_on.map_center_mass_le -> ConvexOn.map_centerMass_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align convex_on.map_center_mass_le ConvexOn.map_centerMass_leₓ'. -/
 /-- Convex **Jensen's inequality**, `finset.center_mass` version. -/
 theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : 0 < ∑ i in t, w i) (hmem : ∀ i ∈ t, p i ∈ s) :
@@ -62,9 +59,6 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
     simp only [center_mass, Function.comp, Prod.smul_fst, Prod.fst_sum, Prod.smul_snd, Prod.snd_sum]
 #align convex_on.map_center_mass_le ConvexOn.map_centerMass_le
 
-/- warning: concave_on.le_map_center_mass -> ConcaveOn.le_map_centerMass is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align concave_on.le_map_center_mass ConcaveOn.le_map_centerMassₓ'. -/
 /-- Concave **Jensen's inequality**, `finset.center_mass` version. -/
 theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : 0 < ∑ i in t, w i) (hmem : ∀ i ∈ t, p i ∈ s) :
@@ -72,9 +66,6 @@ theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈
   @ConvexOn.map_centerMass_le 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ hf h₀ h₁ hmem
 #align concave_on.le_map_center_mass ConcaveOn.le_map_centerMass
 
-/- warning: convex_on.map_sum_le -> ConvexOn.map_sum_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align convex_on.map_sum_le ConvexOn.map_sum_leₓ'. -/
 /-- Convex **Jensen's inequality**, `finset.sum` version. -/
 theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : (∑ i in t, w i) = 1)
     (hmem : ∀ i ∈ t, p i ∈ s) : f (∑ i in t, w i • p i) ≤ ∑ i in t, w i • f (p i) := by
@@ -82,9 +73,6 @@ theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤
     hf.map_center_mass_le h₀ (h₁.symm ▸ zero_lt_one) hmem
 #align convex_on.map_sum_le ConvexOn.map_sum_le
 
-/- warning: concave_on.le_map_sum -> ConcaveOn.le_map_sum is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align concave_on.le_map_sum ConcaveOn.le_map_sumₓ'. -/
 /-- Concave **Jensen's inequality**, `finset.sum` version. -/
 theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : (∑ i in t, w i) = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
@@ -103,9 +91,6 @@ variable [LinearOrderedField 𝕜] [AddCommGroup E] [LinearOrderedAddCommGroup 
   [Module 𝕜 β] [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E}
   {x : E}
 
-/- warning: le_sup_of_mem_convex_hull -> le_sup_of_mem_convexHull is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align le_sup_of_mem_convex_hull le_sup_of_mem_convexHullₓ'. -/
 theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
     f x ≤ s.sup' (coe_nonempty.1 <| convexHull_nonempty_iff.1 ⟨x, hx⟩) f :=
@@ -116,18 +101,12 @@ theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull
       (center_mass_le_sup hw₀ <| by positivity)
 #align le_sup_of_mem_convex_hull le_sup_of_mem_convexHull
 
-/- warning: inf_le_of_mem_convex_hull -> inf_le_of_mem_convexHull is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inf_le_of_mem_convex_hull inf_le_of_mem_convexHullₓ'. -/
 theorem inf_le_of_mem_convexHull {s : Finset E} (hf : ConcaveOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
     s.inf' (coe_nonempty.1 <| convexHull_nonempty_iff.1 ⟨x, hx⟩) f ≤ f x :=
   le_sup_of_mem_convexHull hf.dual hx
 #align inf_le_of_mem_convex_hull inf_le_of_mem_convexHull
 
-/- warning: convex_on.exists_ge_of_center_mass -> ConvexOn.exists_ge_of_centerMass is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMassₓ'. -/
 /-- If a function `f` is convex on `s`, then the value it takes at some center of mass of points of
 `s` is less than the value it takes on one of those points. -/
 theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i ∈ t, 0 ≤ w i)
@@ -145,9 +124,6 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
   infer_instance
 #align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMass
 
-/- warning: concave_on.exists_le_of_center_mass -> ConcaveOn.exists_le_of_centerMass is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMassₓ'. -/
 /-- If a function `f` is concave on `s`, then the value it takes at some center of mass of points of
 `s` is greater than the value it takes on one of those points. -/
 theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀ i ∈ t, 0 ≤ w i)
@@ -155,9 +131,6 @@ theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀
   @ConvexOn.exists_ge_of_centerMass 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ h hw₀ hw₁ hp
 #align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMass
 
-/- warning: convex_on.exists_ge_of_mem_convex_hull -> ConvexOn.exists_ge_of_mem_convexHull is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHullₓ'. -/
 /-- Maximum principle for convex functions. If a function `f` is convex on the convex hull of `s`,
 then the eventual maximum of `f` on `convex_hull 𝕜 s` lies in `s`. -/
 theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 𝕜 s) f) {x}
@@ -171,9 +144,6 @@ theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 
   exact ⟨p i, hp i hit, Hi⟩
 #align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHull
 
-/- warning: concave_on.exists_le_of_mem_convex_hull -> ConcaveOn.exists_le_of_mem_convexHull is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align concave_on.exists_le_of_mem_convex_hull ConcaveOn.exists_le_of_mem_convexHullₓ'. -/
 /-- Minimum principle for concave functions. If a function `f` is concave on the convex hull of `s`,
 then the eventual minimum of `f` on `convex_hull 𝕜 s` lies in `s`. -/
 theorem ConcaveOn.exists_le_of_mem_convexHull (hf : ConcaveOn 𝕜 (convexHull 𝕜 s) f) {x}

9d2f0748

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -49,10 +49,7 @@ variable [LinearOrderedField 𝕜] [AddCommGroup E] [OrderedAddCommGroup β] [Mo
   [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E}
 
 /- warning: convex_on.map_center_mass_le -> ConvexOn.map_centerMass_le is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (Finset.centerMass.{u1, u3, u4} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3) _inst_5 t w (Function.comp.{succ u4, succ u2, succ u3} ι E β f p)))
-but is expected to have type
-  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (Finset.centerMass.{u4, u2, u1} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3) _inst_5 t w (Function.comp.{succ u1, succ u3, succ u2} ι E β f p)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align convex_on.map_center_mass_le ConvexOn.map_centerMass_leₓ'. -/
 /-- Convex **Jensen's inequality**, `finset.center_mass` version. -/
 theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
@@ -66,10 +63,7 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
 #align convex_on.map_center_mass_le ConvexOn.map_centerMass_le
 
 /- warning: concave_on.le_map_center_mass -> ConcaveOn.le_map_centerMass is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (Finset.centerMass.{u1, u3, u4} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3) _inst_5 t w (Function.comp.{succ u4, succ u2, succ u3} ι E β f p)) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))
-but is expected to have type
-  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (Finset.centerMass.{u4, u2, u1} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3) _inst_5 t w (Function.comp.{succ u1, succ u3, succ u2} ι E β f p)) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align concave_on.le_map_center_mass ConcaveOn.le_map_centerMassₓ'. -/
 /-- Concave **Jensen's inequality**, `finset.center_mass` version. -/
 theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
@@ -79,10 +73,7 @@ theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈
 #align concave_on.le_map_center_mass ConcaveOn.le_map_centerMass
 
 /- warning: convex_on.map_sum_le -> ConvexOn.map_sum_le is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))))
-but is expected to have type
-  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (Semiring.toOne.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align convex_on.map_sum_le ConvexOn.map_sum_leₓ'. -/
 /-- Convex **Jensen's inequality**, `finset.sum` version. -/
 theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : (∑ i in t, w i) = 1)
@@ -92,10 +83,7 @@ theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤
 #align convex_on.map_sum_le ConvexOn.map_sum_le
 
 /- warning: concave_on.le_map_sum -> ConcaveOn.le_map_sum is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E 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(AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E 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(LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))))
-but is expected to have type
-  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (Semiring.toOne.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align concave_on.le_map_sum ConcaveOn.le_map_sumₓ'. -/
 /-- Concave **Jensen's inequality**, `finset.sum` version. -/
 theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
@@ -116,10 +104,7 @@ variable [LinearOrderedField 𝕜] [AddCommGroup E] [LinearOrderedAddCommGroup 
   {x : E}
 
 /- warning: le_sup_of_mem_convex_hull -> le_sup_of_mem_convexHull is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u2} E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 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(LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} 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(Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) x hx))) f))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u2, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u3} E}, (ConvexOn.{u2, u3, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 β (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s)) f) -> (forall (hx : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))), LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (f x) (Finset.sup'.{u1, u3} β E (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedAddCommGroup.toLinearOrder.{u1} β _inst_3)))) s (Iff.mp (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (Finset.Nonempty.{u3} E s) (Finset.coe_nonempty.{u3} E s) (Iff.mp (Set.Nonempty.{u3} E (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (convexHull_nonempty_iff.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4 (Finset.toSet.{u3} E s)) (Exists.intro.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) x hx))) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align le_sup_of_mem_convex_hull le_sup_of_mem_convexHullₓ'. -/
 theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
@@ -132,10 +117,7 @@ theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull
 #align le_sup_of_mem_convex_hull le_sup_of_mem_convexHull
 
 /- warning: inf_le_of_mem_convex_hull -> inf_le_of_mem_convexHull is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u2} E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 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(Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) x hx))) f) (f x))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u2, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u3} E}, (ConcaveOn.{u2, u3, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 β (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s)) f) -> (forall (hx : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))), LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (Finset.inf'.{u1, u3} β E (Lattice.toSemilatticeInf.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedAddCommGroup.toLinearOrder.{u1} β _inst_3)))) s (Iff.mp (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (Finset.Nonempty.{u3} E s) (Finset.coe_nonempty.{u3} E s) (Iff.mp (Set.Nonempty.{u3} E (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (convexHull_nonempty_iff.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4 (Finset.toSet.{u3} E s)) (Exists.intro.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) x hx))) f) (f x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align inf_le_of_mem_convex_hull inf_le_of_mem_convexHullₓ'. -/
 theorem inf_le_of_mem_convexHull {s : Finset E} (hf : ConcaveOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
@@ -144,10 +126,7 @@ theorem inf_le_of_mem_convexHull {s : Finset E} (hf : ConcaveOn 𝕜 (convexHull
 #align inf_le_of_mem_convex_hull inf_le_of_mem_convexHull
 
 /- warning: convex_on.exists_ge_of_center_mass -> ConvexOn.exists_ge_of_centerMass is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (Exists.{succ u4} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) (fun (H : Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) => LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (f (p i)))))
-but is expected to have type
-  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (Exists.{succ u1} ι (fun (i : ι) => And (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3)))) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (f (p i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMassₓ'. -/
 /-- If a function `f` is convex on `s`, then the value it takes at some center of mass of points of
 `s` is less than the value it takes on one of those points. -/
@@ -167,10 +146,7 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
 #align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMass
 
 /- warning: concave_on.exists_le_of_center_mass -> ConcaveOn.exists_le_of_centerMass is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (Exists.{succ u4} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) (fun (H : Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) => LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f (p i)) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))))
-but is expected to have type
-  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (Exists.{succ u1} ι (fun (i : ι) => And (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3)))) (f (p i)) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMassₓ'. -/
 /-- If a function `f` is concave on `s`, then the value it takes at some center of mass of points of
 `s` is greater than the value it takes on one of those points. -/
@@ -180,10 +156,7 @@ theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀
 #align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMass
 
 /- warning: convex_on.exists_ge_of_mem_convex_hull -> ConvexOn.exists_ge_of_mem_convexHull is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s) f) -> (forall {x : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s)) -> (Exists.{succ u2} E (fun (y : E) => Exists.{0} (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) => LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f x) (f y)))))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u3, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConvexOn.{u3, u2, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u3, 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.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜 β (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s) f) -> (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s)) -> (Exists.{succ u2} E (fun (y : E) => And (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) y s) (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (f x) (f y)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHullₓ'. -/
 /-- Maximum principle for convex functions. If a function `f` is convex on the convex hull of `s`,
 then the eventual maximum of `f` on `convex_hull 𝕜 s` lies in `s`. -/
@@ -199,10 +172,7 @@ theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 
 #align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHull
 
 /- warning: concave_on.exists_le_of_mem_convex_hull -> ConcaveOn.exists_le_of_mem_convexHull is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s) f) -> (forall {x : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s)) -> (Exists.{succ u2} E (fun (y : E) => Exists.{0} (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) => LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f y) (f x)))))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u3, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConcaveOn.{u3, u2, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u3, 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.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜 β (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s) f) -> (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s)) -> (Exists.{succ u2} E (fun (y : E) => And (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) y s) (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (f y) (f x)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align concave_on.exists_le_of_mem_convex_hull ConcaveOn.exists_le_of_mem_convexHullₓ'. -/
 /-- Minimum principle for concave functions. If a function `f` is concave on the convex hull of `s`,
 then the eventual minimum of `f` on `convex_hull 𝕜 s` lies in `s`. -/

9d2f0748

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -50,7 +50,7 @@ variable [LinearOrderedField 𝕜] [AddCommGroup E] [OrderedAddCommGroup β] [Mo
 
 /- warning: convex_on.map_center_mass_le -> ConvexOn.map_centerMass_le is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (Finset.centerMass.{u1, u3, u4} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3) _inst_5 t w (Function.comp.{succ u4, succ u2, succ u3} ι E β f p)))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (Finset.centerMass.{u1, u3, u4} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3) _inst_5 t w (Function.comp.{succ u4, succ u2, succ u3} ι E β f p)))
 but is expected to have type
   forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (Finset.centerMass.{u4, u2, u1} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3) _inst_5 t w (Function.comp.{succ u1, succ u3, succ u2} ι E β f p)))
 Case conversion may be inaccurate. Consider using '#align convex_on.map_center_mass_le ConvexOn.map_centerMass_leₓ'. -/
@@ -67,7 +67,7 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
 
 /- warning: concave_on.le_map_center_mass -> ConcaveOn.le_map_centerMass is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (Finset.centerMass.{u1, u3, u4} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3) _inst_5 t w (Function.comp.{succ u4, succ u2, succ u3} ι E β f p)) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (Finset.centerMass.{u1, u3, u4} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3) _inst_5 t w (Function.comp.{succ u4, succ u2, succ u3} ι E β f p)) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))
 but is expected to have type
   forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (Finset.centerMass.{u4, u2, u1} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3) _inst_5 t w (Function.comp.{succ u1, succ u3, succ u2} ι E β f p)) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))
 Case conversion may be inaccurate. Consider using '#align concave_on.le_map_center_mass ConcaveOn.le_map_centerMassₓ'. -/
@@ -80,7 +80,7 @@ theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈
 
 /- warning: convex_on.map_sum_le -> ConvexOn.map_sum_le is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))))
 but is expected to have type
   forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (Semiring.toOne.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))))
 Case conversion may be inaccurate. Consider using '#align convex_on.map_sum_le ConvexOn.map_sum_leₓ'. -/
@@ -93,7 +93,7 @@ theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤
 
 /- warning: concave_on.le_map_sum -> ConcaveOn.le_map_sum is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))))
 but is expected to have type
   forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (Semiring.toOne.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))))
 Case conversion may be inaccurate. Consider using '#align concave_on.le_map_sum ConcaveOn.le_map_sumₓ'. -/
@@ -117,7 +117,7 @@ variable [LinearOrderedField 𝕜] [AddCommGroup E] [LinearOrderedAddCommGroup 
 
 /- warning: le_sup_of_mem_convex_hull -> le_sup_of_mem_convexHull is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u2} E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) f) -> (forall (hx : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))), LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f x) (Finset.sup'.{u3, u2} β E (Lattice.toSemilatticeSup.{u3} β (LinearOrder.toLattice.{u3} β (LinearOrderedAddCommGroup.toLinearOrder.{u3} β _inst_3))) s (Iff.mp (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Finset.Nonempty.{u2} E s) (Finset.coe_nonempty.{u2} E s) (Iff.mp (Set.Nonempty.{u2} E (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (convexHull_nonempty_iff.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Exists.intro.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) x hx))) f))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u2} E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) f) -> (forall (hx : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))), LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f x) (Finset.sup'.{u3, u2} β E (Lattice.toSemilatticeSup.{u3} β (LinearOrder.toLattice.{u3} β (LinearOrderedAddCommGroup.toLinearOrder.{u3} β _inst_3))) s (Iff.mp (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Finset.Nonempty.{u2} E s) (Finset.coe_nonempty.{u2} E s) (Iff.mp (Set.Nonempty.{u2} E (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (convexHull_nonempty_iff.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Exists.intro.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) x hx))) f))
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u3}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u2, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u3} E}, (ConvexOn.{u2, u3, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 β (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s)) f) -> (forall (hx : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))), LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (f x) (Finset.sup'.{u1, u3} β E (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedAddCommGroup.toLinearOrder.{u1} β _inst_3)))) s (Iff.mp (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (Finset.Nonempty.{u3} E s) (Finset.coe_nonempty.{u3} E s) (Iff.mp (Set.Nonempty.{u3} E (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (convexHull_nonempty_iff.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4 (Finset.toSet.{u3} E s)) (Exists.intro.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) x hx))) f))
 Case conversion may be inaccurate. Consider using '#align le_sup_of_mem_convex_hull le_sup_of_mem_convexHullₓ'. -/
@@ -133,7 +133,7 @@ theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull
 
 /- warning: inf_le_of_mem_convex_hull -> inf_le_of_mem_convexHull is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u2} E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) f) -> (forall (hx : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))), LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (Finset.inf'.{u3, u2} β E (Lattice.toSemilatticeInf.{u3} β (LinearOrder.toLattice.{u3} β (LinearOrderedAddCommGroup.toLinearOrder.{u3} β _inst_3))) s (Iff.mp (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Finset.Nonempty.{u2} E s) (Finset.coe_nonempty.{u2} E s) (Iff.mp (Set.Nonempty.{u2} E (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (convexHull_nonempty_iff.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Exists.intro.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) x hx))) f) (f x))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u2} E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) f) -> (forall (hx : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))), LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (Finset.inf'.{u3, u2} β E (Lattice.toSemilatticeInf.{u3} β (LinearOrder.toLattice.{u3} β (LinearOrderedAddCommGroup.toLinearOrder.{u3} β _inst_3))) s (Iff.mp (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Finset.Nonempty.{u2} E s) (Finset.coe_nonempty.{u2} E s) (Iff.mp (Set.Nonempty.{u2} E (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (convexHull_nonempty_iff.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Exists.intro.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) x hx))) f) (f x))
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u3}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u2, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u3} E}, (ConcaveOn.{u2, u3, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 β (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s)) f) -> (forall (hx : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))), LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (Finset.inf'.{u1, u3} β E (Lattice.toSemilatticeInf.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedAddCommGroup.toLinearOrder.{u1} β _inst_3)))) s (Iff.mp (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (Finset.Nonempty.{u3} E s) (Finset.coe_nonempty.{u3} E s) (Iff.mp (Set.Nonempty.{u3} E (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (convexHull_nonempty_iff.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4 (Finset.toSet.{u3} E s)) (Exists.intro.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) x hx))) f) (f x))
 Case conversion may be inaccurate. Consider using '#align inf_le_of_mem_convex_hull inf_le_of_mem_convexHullₓ'. -/
@@ -145,7 +145,7 @@ theorem inf_le_of_mem_convexHull {s : Finset E} (hf : ConcaveOn 𝕜 (convexHull
 
 /- warning: convex_on.exists_ge_of_center_mass -> ConvexOn.exists_ge_of_centerMass is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (Exists.{succ u4} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) (fun (H : Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (f (p i)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (Exists.{succ u4} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) (fun (H : Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) => LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (f (p i)))))
 but is expected to have type
   forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (Exists.{succ u1} ι (fun (i : ι) => And (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3)))) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (f (p i)))))
 Case conversion may be inaccurate. Consider using '#align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMassₓ'. -/
@@ -168,7 +168,7 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
 
 /- warning: concave_on.exists_le_of_center_mass -> ConcaveOn.exists_le_of_centerMass is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (Exists.{succ u4} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) (fun (H : Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f (p i)) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (Exists.{succ u4} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) (fun (H : Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) => LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f (p i)) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))))
 but is expected to have type
   forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (Exists.{succ u1} ι (fun (i : ι) => And (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3)))) (f (p i)) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))))
 Case conversion may be inaccurate. Consider using '#align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMassₓ'. -/
@@ -181,7 +181,7 @@ theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀
 
 /- warning: convex_on.exists_ge_of_mem_convex_hull -> ConvexOn.exists_ge_of_mem_convexHull is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s) f) -> (forall {x : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s)) -> (Exists.{succ u2} E (fun (y : E) => Exists.{0} (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f x) (f y)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s) f) -> (forall {x : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s)) -> (Exists.{succ u2} E (fun (y : E) => Exists.{0} (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) => LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f x) (f y)))))
 but is expected to have type
   forall {𝕜 : Type.{u3}} {E : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u3, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConvexOn.{u3, u2, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u3, 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.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜 β (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s) f) -> (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s)) -> (Exists.{succ u2} E (fun (y : E) => And (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) y s) (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (f x) (f y)))))
 Case conversion may be inaccurate. Consider using '#align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHullₓ'. -/
@@ -200,7 +200,7 @@ theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 
 
 /- warning: concave_on.exists_le_of_mem_convex_hull -> ConcaveOn.exists_le_of_mem_convexHull is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s) f) -> (forall {x : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s)) -> (Exists.{succ u2} E (fun (y : E) => Exists.{0} (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f y) (f x)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s) f) -> (forall {x : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s)) -> (Exists.{succ u2} E (fun (y : E) => Exists.{0} (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) => LE.le.{u3} β (Preorder.toHasLe.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f y) (f x)))))
 but is expected to have type
   forall {𝕜 : Type.{u3}} {E : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u3, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConcaveOn.{u3, u2, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u3, 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.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜 β (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s) f) -> (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s)) -> (Exists.{succ u2} E (fun (y : E) => And (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) y s) (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (f y) (f x)))))
 Case conversion may be inaccurate. Consider using '#align concave_on.exists_le_of_mem_convex_hull ConcaveOn.exists_le_of_mem_convexHullₓ'. -/

9d2f0748

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -82,7 +82,7 @@ theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))))
 but is expected to have type
-  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (NonAssocRing.toOne.{u4} 𝕜 (Ring.toNonAssocRing.{u4} 𝕜 (StrictOrderedRing.toRing.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))))
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (Semiring.toOne.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))))
 Case conversion may be inaccurate. Consider using '#align convex_on.map_sum_le ConvexOn.map_sum_leₓ'. -/
 /-- Convex **Jensen's inequality**, `finset.sum` version. -/
 theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : (∑ i in t, w i) = 1)
@@ -95,7 +95,7 @@ theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))))
 but is expected to have type
-  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (NonAssocRing.toOne.{u4} 𝕜 (Ring.toNonAssocRing.{u4} 𝕜 (StrictOrderedRing.toRing.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))))
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (Semiring.toOne.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))))
 Case conversion may be inaccurate. Consider using '#align concave_on.le_map_sum ConcaveOn.le_map_sumₓ'. -/
 /-- Concave **Jensen's inequality**, `finset.sum` version. -/
 theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)

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: Alexander Bentkamp, Yury Kudriashov
 
 ! This file was ported from Lean 3 source module analysis.convex.jensen
-! leanprover-community/mathlib commit bfad3f455b388fbcc14c49d0cac884f774f14d20
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.Convex.Function
 /-!
 # Jensen's inequality and maximum principle for convex functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we prove the finite Jensen inequality and the finite maximum principle for convex
 functions. The integral versions are to be found in `analysis.convex.integral`.

bfad3f45

bump to nightly-2023-04-25-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

f51daedd

Diff

@@ -45,6 +45,12 @@ section Jensen
 variable [LinearOrderedField 𝕜] [AddCommGroup E] [OrderedAddCommGroup β] [Module 𝕜 E] [Module 𝕜 β]
   [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E}
 
+/- warning: convex_on.map_center_mass_le -> ConvexOn.map_centerMass_le is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (Finset.centerMass.{u1, u3, u4} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3) _inst_5 t w (Function.comp.{succ u4, succ u2, succ u3} ι E β f p)))
+but is expected to have type
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (Finset.centerMass.{u4, u2, u1} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3) _inst_5 t w (Function.comp.{succ u1, succ u3, succ u2} ι E β f p)))
+Case conversion may be inaccurate. Consider using '#align convex_on.map_center_mass_le ConvexOn.map_centerMass_leₓ'. -/
 /-- Convex **Jensen's inequality**, `finset.center_mass` version. -/
 theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : 0 < ∑ i in t, w i) (hmem : ∀ i ∈ t, p i ∈ s) :
@@ -56,6 +62,12 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
     simp only [center_mass, Function.comp, Prod.smul_fst, Prod.fst_sum, Prod.smul_snd, Prod.snd_sum]
 #align convex_on.map_center_mass_le ConvexOn.map_centerMass_le
 
+/- warning: concave_on.le_map_center_mass -> ConcaveOn.le_map_centerMass is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (Finset.centerMass.{u1, u3, u4} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3) _inst_5 t w (Function.comp.{succ u4, succ u2, succ u3} ι E β f p)) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))
+but is expected to have type
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (Finset.centerMass.{u4, u2, u1} 𝕜 β ι _inst_1 (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3) _inst_5 t w (Function.comp.{succ u1, succ u3, succ u2} ι E β f p)) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))
+Case conversion may be inaccurate. Consider using '#align concave_on.le_map_center_mass ConcaveOn.le_map_centerMassₓ'. -/
 /-- Concave **Jensen's inequality**, `finset.center_mass` version. -/
 theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : 0 < ∑ i in t, w i) (hmem : ∀ i ∈ t, p i ∈ s) :
@@ -63,6 +75,12 @@ theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈
   @ConvexOn.map_centerMass_le 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ hf h₀ h₁ hmem
 #align concave_on.le_map_center_mass ConcaveOn.le_map_centerMass
 
+/- warning: convex_on.map_sum_le -> ConvexOn.map_sum_le is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))))
+but is expected to have type
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (NonAssocRing.toOne.{u4} 𝕜 (Ring.toNonAssocRing.{u4} 𝕜 (StrictOrderedRing.toRing.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))))
+Case conversion may be inaccurate. Consider using '#align convex_on.map_sum_le ConvexOn.map_sum_leₓ'. -/
 /-- Convex **Jensen's inequality**, `finset.sum` version. -/
 theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : (∑ i in t, w i) = 1)
     (hmem : ∀ i ∈ t, p i ∈ s) : f (∑ i in t, w i • p i) ≤ ∑ i in t, w i • f (p i) := by
@@ -70,6 +88,12 @@ theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤
     hf.map_center_mass_le h₀ (h₁.symm ▸ zero_lt_one) hmem
 #align convex_on.map_sum_le ConvexOn.map_sum_le
 
+/- warning: concave_on.le_map_sum -> ConcaveOn.le_map_sum is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : OrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β _inst_3)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (Eq.{succ u1} 𝕜 (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β _inst_3))) (Finset.sum.{u3, u4} β ι (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) t (fun (i : ι) => SMul.smul.{u1, u3} 𝕜 β (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β _inst_3)) _inst_5)))) (w i) (f (p i)))) (f (Finset.sum.{u2, u4} E ι (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) t (fun (i : ι) => SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (w i) (p i)))))
+but is expected to have type
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : OrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (Eq.{succ u4} 𝕜 (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i)) (OfNat.ofNat.{u4} 𝕜 1 (One.toOfNat1.{u4} 𝕜 (NonAssocRing.toOne.{u4} 𝕜 (Ring.toNonAssocRing.{u4} 𝕜 (StrictOrderedRing.toRing.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1))))))))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β _inst_3))) (Finset.sum.{u2, u1} β ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) t (fun (i : ι) => HSMul.hSMul.{u4, u2, u2} 𝕜 β β (instHSMul.{u4, u2} 𝕜 β (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} β _inst_3)) _inst_5))))) (w i) (f (p i)))) (f (Finset.sum.{u3, u1} E ι (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) t (fun (i : ι) => HSMul.hSMul.{u4, u3, u3} 𝕜 E E (instHSMul.{u4, u3} 𝕜 E (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4))))) (w i) (p i)))))
+Case conversion may be inaccurate. Consider using '#align concave_on.le_map_sum ConcaveOn.le_map_sumₓ'. -/
 /-- Concave **Jensen's inequality**, `finset.sum` version. -/
 theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : (∑ i in t, w i) = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
@@ -88,6 +112,12 @@ variable [LinearOrderedField 𝕜] [AddCommGroup E] [LinearOrderedAddCommGroup 
   [Module 𝕜 β] [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E}
   {x : E}
 
+/- warning: le_sup_of_mem_convex_hull -> le_sup_of_mem_convexHull is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u2} E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 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(LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} 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(LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))), LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f x) (Finset.sup'.{u3, u2} β E (Lattice.toSemilatticeSup.{u3} β (LinearOrder.toLattice.{u3} β (LinearOrderedAddCommGroup.toLinearOrder.{u3} β _inst_3))) s (Iff.mp (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Finset.Nonempty.{u2} E s) (Finset.coe_nonempty.{u2} E s) (Iff.mp (Set.Nonempty.{u2} E (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (convexHull_nonempty_iff.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Exists.intro.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) x hx))) f))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u2, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u3} E}, (ConvexOn.{u2, u3, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 β (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s)) f) -> (forall (hx : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))), LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (f x) (Finset.sup'.{u1, u3} β E (Lattice.toSemilatticeSup.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedAddCommGroup.toLinearOrder.{u1} β _inst_3)))) s (Iff.mp (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (Finset.Nonempty.{u3} E s) (Finset.coe_nonempty.{u3} E s) (Iff.mp (Set.Nonempty.{u3} E (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (convexHull_nonempty_iff.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4 (Finset.toSet.{u3} E s)) (Exists.intro.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) x hx))) f))
+Case conversion may be inaccurate. Consider using '#align le_sup_of_mem_convex_hull le_sup_of_mem_convexHullₓ'. -/
 theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
     f x ≤ s.sup' (coe_nonempty.1 <| convexHull_nonempty_iff.1 ⟨x, hx⟩) f :=
@@ -98,12 +128,24 @@ theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull
       (center_mass_le_sup hw₀ <| by positivity)
 #align le_sup_of_mem_convex_hull le_sup_of_mem_convexHull
 
+/- warning: inf_le_of_mem_convex_hull -> inf_le_of_mem_convexHull is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u2} E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) 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(LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 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(LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))), LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (Finset.inf'.{u3, u2} β E (Lattice.toSemilatticeInf.{u3} β (LinearOrder.toLattice.{u3} β (LinearOrderedAddCommGroup.toLinearOrder.{u3} β _inst_3))) s (Iff.mp (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ 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(Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) (Set.Nonempty.{u2} E ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (convexHull_nonempty_iff.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s)) (Exists.intro.{succ u2} E (fun (x : E) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} E) (Set.{u2} E) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} E) (Set.{u2} E) (Finset.Set.hasCoeT.{u2} E))) s))) x hx))) f) (f x))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u2, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {f : E -> β} {x : E} {s : Finset.{u3} E}, (ConcaveOn.{u2, u3, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u2, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u2, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 β (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (LinearOrderedSemifield.toSemifield.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 β (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s)) f) -> (forall (hx : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))), LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (Finset.inf'.{u1, u3} β E (Lattice.toSemilatticeInf.{u1} β (DistribLattice.toLattice.{u1} β (instDistribLattice.{u1} β (LinearOrderedAddCommGroup.toLinearOrder.{u1} β _inst_3)))) s (Iff.mp (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (Finset.Nonempty.{u3} E s) (Finset.coe_nonempty.{u3} E s) (Iff.mp (Set.Nonempty.{u3} E (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) (Set.Nonempty.{u3} E (Finset.toSet.{u3} E s)) (convexHull_nonempty_iff.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4 (Finset.toSet.{u3} E s)) (Exists.intro.{succ u3} E (fun (x : E) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x (OrderHom.toFun.{u3, u3} (Set.{u3} E) (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (ClosureOperator.toOrderHom.{u3} (Set.{u3} E) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (convexHull.{u2, u3} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)) (Finset.toSet.{u3} E s))) x hx))) f) (f x))
+Case conversion may be inaccurate. Consider using '#align inf_le_of_mem_convex_hull inf_le_of_mem_convexHullₓ'. -/
 theorem inf_le_of_mem_convexHull {s : Finset E} (hf : ConcaveOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
     s.inf' (coe_nonempty.1 <| convexHull_nonempty_iff.1 ⟨x, hx⟩) f ≤ f x :=
   le_sup_of_mem_convexHull hf.dual hx
 #align inf_le_of_mem_convex_hull inf_le_of_mem_convexHull
 
+/- warning: convex_on.exists_ge_of_center_mass -> ConvexOn.exists_ge_of_centerMass is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (Exists.{succ u4} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) (fun (H : Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (f (p i)))))
+but is expected to have type
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConvexOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (Exists.{succ u1} ι (fun (i : ι) => And (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3)))) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)) (f (p i)))))
+Case conversion may be inaccurate. Consider using '#align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMassₓ'. -/
 /-- If a function `f` is convex on `s`, then the value it takes at some center of mass of points of
 `s` is less than the value it takes on one of those points. -/
 theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i ∈ t, 0 ≤ w i)
@@ -121,6 +163,12 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
   infer_instance
 #align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMass
 
+/- warning: concave_on.exists_le_of_center_mass -> ConcaveOn.exists_le_of_centerMass is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} {ι : Type.{u4}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β} {t : Finset.{u4} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (w i))) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Finset.sum.{u1, u4} 𝕜 ι (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (OrderedAddCommGroup.toAddCommGroup.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (p i) s)) -> (Exists.{succ u4} ι (fun (i : ι) => Exists.{0} (Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) (fun (H : Membership.Mem.{u4, u4} ι (Finset.{u4} ι) (Finset.hasMem.{u4} ι) i t) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f (p i)) (f (Finset.centerMass.{u1, u2, u4} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))))
+but is expected to have type
+  forall {𝕜 : Type.{u4}} {E : Type.{u3}} {β : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedField.{u4} 𝕜] [_inst_2 : AddCommGroup.{u3} E] [_inst_3 : LinearOrderedAddCommGroup.{u2} β] [_inst_4 : Module.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2)] [_inst_5 : Module.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))] [_inst_6 : OrderedSMul.{u4, u2} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u2} β (AddCommMonoid.toAddMonoid.{u2} β (OrderedAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3)))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5))] {s : Set.{u3} E} {f : E -> β} {t : Finset.{u1} ι} {w : ι -> 𝕜} {p : ι -> E}, (ConcaveOn.{u4, u3, u2} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u4} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) (SMulZeroClass.toSMul.{u4, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u4, u3} 𝕜 E (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u4, u3} 𝕜 E (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_2))))) (Module.toMulActionWithZero.{u4, u3} 𝕜 E (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u4, u2} 𝕜 β (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜 β (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜 β (Semiring.toMonoidWithZero.{u4} 𝕜 (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} β (SubNegZeroMonoid.toNegZeroClass.{u2} β (SubtractionMonoid.toSubNegZeroMonoid.{u2} β (SubtractionCommMonoid.toSubtractionMonoid.{u2} β (AddCommGroup.toDivisionAddCommMonoid.{u2} β (OrderedAddCommGroup.toAddCommGroup.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3))))))) (Module.toMulActionWithZero.{u4, u2} 𝕜 β (StrictOrderedSemiring.toSemiring.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u2} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u2} β _inst_3))) _inst_5)))) s f) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (LE.le.{u4} 𝕜 (Preorder.toLE.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (w i))) -> (LT.lt.{u4} 𝕜 (Preorder.toLT.{u4} 𝕜 (PartialOrder.toPreorder.{u4} 𝕜 (StrictOrderedRing.toPartialOrder.{u4} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u4} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u4} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u4} 𝕜 _inst_1)))))) (OfNat.ofNat.{u4} 𝕜 0 (Zero.toOfNat0.{u4} 𝕜 (CommMonoidWithZero.toZero.{u4} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u4} 𝕜 (Semifield.toCommGroupWithZero.{u4} 𝕜 (LinearOrderedSemifield.toSemifield.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1))))))) (Finset.sum.{u4, u1} 𝕜 ι (OrderedCancelAddCommMonoid.toAddCommMonoid.{u4} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u4} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u4} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u4} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u4} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u4} 𝕜 _inst_1)))))) t (fun (i : ι) => w i))) -> (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) -> (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (p i) s)) -> (Exists.{succ u1} ι (fun (i : ι) => And (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i t) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OrderedAddCommGroup.toPartialOrder.{u2} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u2} β _inst_3)))) (f (p i)) (f (Finset.centerMass.{u4, u3, u1} 𝕜 E ι _inst_1 _inst_2 _inst_4 t w p)))))
+Case conversion may be inaccurate. Consider using '#align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMassₓ'. -/
 /-- If a function `f` is concave on `s`, then the value it takes at some center of mass of points of
 `s` is greater than the value it takes on one of those points. -/
 theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀ i ∈ t, 0 ≤ w i)
@@ -128,6 +176,12 @@ theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀
   @ConvexOn.exists_ge_of_centerMass 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ h hw₀ hw₁ hp
 #align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMass
 
+/- warning: convex_on.exists_ge_of_mem_convex_hull -> ConvexOn.exists_ge_of_mem_convexHull is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConvexOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s) f) -> (forall {x : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s)) -> (Exists.{succ u2} E (fun (y : E) => Exists.{0} (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f x) (f y)))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u3, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConvexOn.{u3, u2, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u3, 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.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜 β (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s) f) -> (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s)) -> (Exists.{succ u2} E (fun (y : E) => And (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) y s) (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (f x) (f y)))))
+Case conversion may be inaccurate. Consider using '#align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHullₓ'. -/
 /-- Maximum principle for convex functions. If a function `f` is convex on the convex hull of `s`,
 then the eventual maximum of `f` on `convex_hull 𝕜 s` lies in `s`. -/
 theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 𝕜 s) f) {x}
@@ -141,6 +195,12 @@ theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 
   exact ⟨p i, hp i hit, Hi⟩
 #align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHull
 
+/- warning: concave_on.exists_le_of_mem_convex_hull -> ConcaveOn.exists_le_of_mem_convexHull is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {β : Type.{u3}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u3} β] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))] [_inst_6 : OrderedSMul.{u1, u3} 𝕜 β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (OrderedAddCommMonoid.toAddCommMonoid.{u3} β (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConcaveOn.{u1, u2, u3} 𝕜 E β (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u3} β (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 β (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 β (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 β (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u3} β (AddMonoid.toAddZeroClass.{u3} β (AddCommMonoid.toAddMonoid.{u3} β (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 β (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} β (OrderedAddCommGroup.toAddCommGroup.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3))) _inst_5)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s) f) -> (forall {x : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s)) -> (Exists.{succ u2} E (fun (y : E) => Exists.{0} (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y s) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (OrderedAddCommGroup.toPartialOrder.{u3} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u3} β _inst_3)))) (f y) (f x)))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrderedField.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : LinearOrderedAddCommGroup.{u1} β] [_inst_4 : Module.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : Module.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))] [_inst_6 : OrderedSMul.{u3, u1} 𝕜 β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (AddMonoid.toZero.{u1} β (AddCommMonoid.toAddMonoid.{u1} β (OrderedAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5))] {s : Set.{u2} E} {f : E -> β}, (ConcaveOn.{u3, u2, u1} 𝕜 E β (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toLinearOrderedAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) (SMulZeroClass.toSMul.{u3, 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.{u3, u2} 𝕜 E (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 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.{u3, u2} 𝕜 E (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (SMulZeroClass.toSMul.{u3, u1} 𝕜 β (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜 β (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (LinearOrderedSemifield.toSemifield.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 β (Semiring.toMonoidWithZero.{u3} 𝕜 (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u1} β (SubNegZeroMonoid.toNegZeroClass.{u1} β (SubtractionMonoid.toSubNegZeroMonoid.{u1} β (SubtractionCommMonoid.toSubtractionMonoid.{u1} β (AddCommGroup.toDivisionAddCommMonoid.{u1} β (OrderedAddCommGroup.toAddCommGroup.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3))))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 β (StrictOrderedSemiring.toSemiring.{u3} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} β (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} β (LinearOrderedAddCommGroup.toLinearOrderedAddCancelCommMonoid.{u1} β _inst_3))) _inst_5)))) (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s) f) -> (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.{u3, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u3} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u3} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u3} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u3} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u3} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)) s)) -> (Exists.{succ u2} E (fun (y : E) => And (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) y s) (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OrderedAddCommGroup.toPartialOrder.{u1} β (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} β _inst_3)))) (f y) (f x)))))
+Case conversion may be inaccurate. Consider using '#align concave_on.exists_le_of_mem_convex_hull ConcaveOn.exists_le_of_mem_convexHullₓ'. -/
 /-- Minimum principle for concave functions. If a function `f` is concave on the convex hull of `s`,
 then the eventual minimum of `f` on `convex_hull 𝕜 s` lies in `s`. -/
 theorem ConcaveOn.exists_le_of_mem_convexHull (hf : ConcaveOn 𝕜 (convexHull 𝕜 s) f) {x}

bfad3f45

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -52,7 +52,7 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
   by
   have hmem' : ∀ i ∈ t, (p i, (f ∘ p) i) ∈ { p : E × β | p.1 ∈ s ∧ f p.1 ≤ p.2 } := fun i hi =>
     ⟨hmem i hi, le_rfl⟩
-  convert (hf.convex_epigraph.center_mass_mem h₀ h₁ hmem').2 <;>
+  convert(hf.convex_epigraph.center_mass_mem h₀ h₁ hmem').2 <;>
     simp only [center_mass, Function.comp, Prod.smul_fst, Prod.fst_sum, Prod.smul_snd, Prod.snd_sum]
 #align convex_on.map_center_mass_le ConvexOn.map_centerMass_le

bfad3f45

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

bfad3f45

feat: Axiomatise b ≠ 0 → a * b / b = a (#12424)

This lets us unify a few lemmas between GroupWithZero and EuclideanDomain and two lemmas that were previously proved separately for Nat, Int, Polynomial.

ea608559

Diff

@@ -124,8 +124,8 @@ lemma StrictConvexOn.map_sum_lt (hf : StrictConvexOn 𝕜 s f) (h₀ : ∀ i ∈
   have := h₀ k <| by simp
   let c := w j + w k
   have hc : w j / c + w k / c = 1 := by field_simp
-  have hcj : c * (w j / c) = w j := by field_simp; ring
-  have hck : c * (w k / c) = w k := by field_simp; ring
+  have hcj : c * (w j / c) = w j := by field_simp
+  have hck : c * (w k / c) = w k := by field_simp
   calc f (w j • p j + (w k • p k + ∑ x in u, w x • p x))
     _ = f (c • ((w j / c) • p j + (w k / c) • p k) + ∑ x in u, w x • p x) := by
       rw [smul_add, ← mul_smul, ← mul_smul, hcj, hck, add_assoc]

bfad3f45

chore: scope open Classical (#11199)

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

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

c747be0a

Diff

@@ -35,7 +35,8 @@ As corollaries, we get:
 
 open Finset LinearMap Set
 
-open BigOperators Classical Convex Pointwise
+open scoped Classical
+open BigOperators Convex Pointwise
 
 variable {𝕜 E F β ι : Type*}

bfad3f45

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

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

38bce757

Diff

@@ -111,8 +111,8 @@ lemma StrictConvexOn.map_sum_lt (hf : StrictConvexOn 𝕜 s f) (h₀ : ∀ i ∈
   -- We replace `t` by `t \ {j, k}`
   have : k ∈ t.erase j := mem_erase.2 ⟨ne_of_apply_ne _ hjk.symm, hk⟩
   let u := (t.erase j).erase k
-  have hj : j ∉ u := by simp
-  have hk : k ∉ u := by simp
+  have hj : j ∉ u := by simp [u]
+  have hk : k ∉ u := by simp [u]
   have ht :
       t = (u.cons k hk).cons j (mem_cons.not.2 <| not_or_intro (ne_of_apply_ne _ hjk) hj) := by
     simp [insert_erase this, insert_erase ‹j ∈ t›, *]

bfad3f45

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

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

This follows on from #6964.

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

a13e8040

Diff

@@ -113,8 +113,9 @@ lemma StrictConvexOn.map_sum_lt (hf : StrictConvexOn 𝕜 s f) (h₀ : ∀ i ∈
   let u := (t.erase j).erase k
   have hj : j ∉ u := by simp
   have hk : k ∉ u := by simp
-  have ht : t = (u.cons k hk).cons j (mem_cons.not.2 <| not_or_intro (ne_of_apply_ne _ hjk) hj)
-  · simp [insert_erase this, insert_erase ‹j ∈ t›, *]
+  have ht :
+      t = (u.cons k hk).cons j (mem_cons.not.2 <| not_or_intro (ne_of_apply_ne _ hjk) hj) := by
+    simp [insert_erase this, insert_erase ‹j ∈ t›, *]
   clear_value u
   subst ht
   simp only [sum_cons]

bfad3f45

feat: Maximum principle for convex functions on an interval (#9364)

Corollaries of existing lemmas.

From LeanAPAP

d819f3c8

Diff

@@ -249,7 +249,7 @@ section MaximumPrinciple
 
 variable [LinearOrderedField 𝕜] [AddCommGroup E] [LinearOrderedAddCommGroup β] [Module 𝕜 E]
   [Module 𝕜 β] [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E}
-  {x : E}
+  {x y z : E}
 
 theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
@@ -289,8 +289,8 @@ theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀
   ConvexOn.exists_ge_of_centerMass (β := βᵒᵈ) h hw₀ hw₁ hp
 #align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMass
 
-/-- Maximum principle for convex functions. If a function `f` is convex on the convex hull of `s`,
-then the eventual maximum of `f` on `convexHull 𝕜 s` lies in `s`. -/
+/-- **Maximum principle** for convex functions. If a function `f` is convex on the convex hull of
+`s`, then the eventual maximum of `f` on `convexHull 𝕜 s` lies in `s`. -/
 theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 𝕜 s) f) {x}
     (hx : x ∈ convexHull 𝕜 s) : ∃ y ∈ s, f x ≤ f y := by
   rw [_root_.convexHull_eq] at hx
@@ -301,11 +301,35 @@ theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 
   exact ⟨p i, hp i hit, Hi⟩
 #align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHull
 
-/-- Minimum principle for concave functions. If a function `f` is concave on the convex hull of `s`,
-then the eventual minimum of `f` on `convexHull 𝕜 s` lies in `s`. -/
+/-- **Minimum principle** for concave functions. If a function `f` is concave on the convex hull of
+`s`, then the eventual minimum of `f` on `convexHull 𝕜 s` lies in `s`. -/
 theorem ConcaveOn.exists_le_of_mem_convexHull (hf : ConcaveOn 𝕜 (convexHull 𝕜 s) f) {x}
     (hx : x ∈ convexHull 𝕜 s) : ∃ y ∈ s, f y ≤ f x :=
   ConvexOn.exists_ge_of_mem_convexHull (β := βᵒᵈ) hf hx
 #align concave_on.exists_le_of_mem_convex_hull ConcaveOn.exists_le_of_mem_convexHull
 
+/-- **Maximum principle** for convex functions on a segment. If a function `f` is convex on the
+segment `[x, y]`, then the eventual maximum of `f` on `[x, y]` is at `x` or `y`. -/
+lemma ConvexOn.le_max_of_mem_segment (hf : ConvexOn 𝕜 [x -[𝕜] y] f) (hz : z ∈ [x -[𝕜] y]) :
+    f z ≤ max (f x) (f y) := by
+  rw [← convexHull_pair] at hf hz; simpa using hf.exists_ge_of_mem_convexHull hz
+
+/-- **Minimum principle** for concave functions on a segment. If a function `f` is concave on the
+segment `[x, y]`, then the eventual minimum of `f` on `[x, y]` is at `x` or `y`. -/
+lemma ConcaveOn.min_le_of_mem_segment (hf : ConcaveOn 𝕜 [x -[𝕜] y] f) (hz : z ∈ [x -[𝕜] y]) :
+    min (f x) (f y) ≤ f z := by
+  rw [← convexHull_pair] at hf hz; simpa using hf.exists_le_of_mem_convexHull hz
+
+/-- **Maximum principle** for convex functions on an interval. If a function `f` is convex on the
+interval `[x, y]`, then the eventual maximum of `f` on `[x, y]` is at `x` or `y`. -/
+lemma ConvexOn.le_max_of_mem_Icc {f : 𝕜 → β} {x y z : 𝕜} (hf : ConvexOn 𝕜 (Icc x y) f)
+    (hz : z ∈ Icc x y) : f z ≤ max (f x) (f y) := by
+  rw [← segment_eq_Icc (hz.1.trans hz.2)] at hf hz; exact hf.le_max_of_mem_segment hz
+
+/-- **Minimum principle** for concave functions on an interval. If a function `f` is concave on the
+interval `[x, y]`, then the eventual minimum of `f` on `[x, y]` is at `x` or `y`. -/
+lemma ConcaveOn.min_le_of_mem_Icc {f : 𝕜 → β} {x y z : 𝕜} (hf : ConcaveOn 𝕜 (Icc x y) f)
+    (hz : z ∈ Icc x y) : min (f x) (f y) ≤ f z := by
+  rw [← segment_eq_Icc (hz.1.trans hz.2)] at hf hz; exact hf.min_le_of_mem_segment hz
+
 end MaximumPrinciple

bfad3f45

chore(*): replace $ with <| (#9319)

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -113,13 +113,13 @@ lemma StrictConvexOn.map_sum_lt (hf : StrictConvexOn 𝕜 s f) (h₀ : ∀ i ∈
   let u := (t.erase j).erase k
   have hj : j ∉ u := by simp
   have hk : k ∉ u := by simp
-  have ht : t = (u.cons k hk).cons j (mem_cons.not.2 $ not_or_intro (ne_of_apply_ne _ hjk) hj)
+  have ht : t = (u.cons k hk).cons j (mem_cons.not.2 <| not_or_intro (ne_of_apply_ne _ hjk) hj)
   · simp [insert_erase this, insert_erase ‹j ∈ t›, *]
   clear_value u
   subst ht
   simp only [sum_cons]
-  have := h₀ j $ by simp
-  have := h₀ k $ by simp
+  have := h₀ j <| by simp
+  have := h₀ k <| by simp
   let c := w j + w k
   have hc : w j / c + w k / c = 1 := by field_simp
   have hcj : c * (w j / c) = w j := by field_simp; ring
@@ -130,13 +130,13 @@ lemma StrictConvexOn.map_sum_lt (hf : StrictConvexOn 𝕜 s f) (h₀ : ∀ i ∈
     _ ≤ c • f ((w j / c) • p j + (w k / c) • p k) + ∑ x in u, w x • f (p x) :=
       -- apply the usual Jensen's inequality wrt the weighted average of the two distinguished
       -- points and all the other points
-        hf.convexOn.map_add_sum_le (fun i hi ↦ (h₀ _ $ by simp [hi]).le)
+        hf.convexOn.map_add_sum_le (fun i hi ↦ (h₀ _ <| by simp [hi]).le)
           (by simpa [-cons_eq_insert, ← add_assoc] using h₁)
-          (forall_of_forall_cons $ forall_of_forall_cons hmem) (by positivity) $ by
-           refine hf.1 (hmem _ $ by simp) (hmem _ $ by simp) ?_ ?_ hc <;> positivity
+          (forall_of_forall_cons <| forall_of_forall_cons hmem) (by positivity) <| by
+           refine hf.1 (hmem _ <| by simp) (hmem _ <| by simp) ?_ ?_ hc <;> positivity
     _ < c • ((w j / c) • f (p j) + (w k / c) • f (p k)) + ∑ x in u, w x • f (p x) := by
       -- then apply the definition of strict convexity for the two distinguished points
-      gcongr; refine hf.2 (hmem _ $ by simp) (hmem _ $ by simp) hjk ?_ ?_ hc <;> positivity
+      gcongr; refine hf.2 (hmem _ <| by simp) (hmem _ <| by simp) hjk ?_ ?_ hc <;> positivity
     _ = (w j • f (p j) + w k • f (p k)) + ∑ x in u, w x • f (p x) := by
       rw [smul_add, ← mul_smul, ← mul_smul, hcj, hck]
     _ = w j • f (p j) + (w k • f (p k) + ∑ x in u, w x • f (p x)) := by abel_nf
@@ -163,7 +163,7 @@ lemma StrictConvexOn.eq_of_le_map_sum (hf : StrictConvexOn 𝕜 s f) (h₀ : ∀
     (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s)
     (h_eq : ∑ i in t, w i • f (p i) ≤ f (∑ i in t, w i • p i)) :
     ∀ ⦃j⦄, j ∈ t → ∀ ⦃k⦄, k ∈ t → p j = p k := by
-  by_contra!; exact h_eq.not_lt $ hf.map_sum_lt h₀ h₁ hmem this
+  by_contra!; exact h_eq.not_lt <| hf.map_sum_lt h₀ h₁ hmem this
 
 /-- A form of the **equality case of Jensen's equality**.
 
@@ -175,7 +175,7 @@ lemma StrictConcaveOn.eq_of_map_sum_eq (hf : StrictConcaveOn 𝕜 s f) (h₀ : 
     (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s)
     (h_eq : f (∑ i in t, w i • p i) ≤ ∑ i in t, w i • f (p i)) :
     ∀ ⦃j⦄, j ∈ t → ∀ ⦃k⦄, k ∈ t → p j = p k := by
-  by_contra!; exact h_eq.not_lt $ hf.lt_map_sum h₀ h₁ hmem this
+  by_contra!; exact h_eq.not_lt <| hf.lt_map_sum h₀ h₁ hmem this
 
 /-- Canonical form of the **equality case of Jensen's equality**.

bfad3f45

refactor: Deduplicate monotonicity of • lemmas (#9179)

Remove the duplicates introduced in #8869 by sorting the lemmas in Algebra.Order.SMul into three files:

Algebra.Order.Module.Defs for the order isomorphism induced by scalar multiplication by a positivity element
Algebra.Order.Module.Pointwise for the order properties of scalar multiplication of sets. This file is new. I credit myself for https://github.com/leanprover-community/mathlib/pull/9078
Algebra.Order.Module.OrderedSMul: The material about OrderedSMul per se. Inherits the copyright header from Algebra.Order.SMul. This file should eventually be deleted.

I move each #align to the correct file. On top of that, I delete unused redundant OrderedSMul instances (they were useful in Lean 3, but not anymore) and eq_of_smul_eq_smul_of_pos_of_le/eq_of_smul_eq_smul_of_neg_of_le since those lemmas are weird and unused.

ea70e843

Diff

@@ -274,10 +274,10 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
   obtain ⟨i, hi, hfi⟩ : ∃ i ∈ t.filter fun i => w i ≠ 0, w i • f y ≤ w i • (f ∘ p) i
   rotate_left
   · rw [mem_filter] at hi
-    exact ⟨i, hi.1, (smul_le_smul_iff_of_pos <| (hw₀ i hi.1).lt_of_ne hi.2.symm).1 hfi⟩
+    exact ⟨i, hi.1, (smul_le_smul_iff_of_pos_left <| (hw₀ i hi.1).lt_of_ne hi.2.symm).1 hfi⟩
   have hw' : (0 : 𝕜) < ∑ i in filter (fun i => w i ≠ 0) t, w i := by rwa [sum_filter_ne_zero]
   refine' exists_le_of_sum_le (nonempty_of_sum_ne_zero hw'.ne') _
-  rw [← sum_smul, ← smul_le_smul_iff_of_pos (inv_pos.2 hw'), inv_smul_smul₀ hw'.ne', ←
+  rw [← sum_smul, ← smul_le_smul_iff_of_pos_left (inv_pos.2 hw'), inv_smul_smul₀ hw'.ne', ←
     centerMass, centerMass_filter_ne_zero]
   exact h.map_centerMass_le hw₀ hw₁ hp
 #align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMass

bfad3f45

feat: Strict Jensen inequality (#8972)

and equality case

From PFR

Co-authored-by: Heather Macbeth <hrmacbeth@gmail.com>

5497c1ce

Diff

@@ -5,6 +5,7 @@ Authors: Alexander Bentkamp, Yury Kudriashov
 -/
 import Mathlib.Analysis.Convex.Combination
 import Mathlib.Analysis.Convex.Function
+import Mathlib.Tactic.FieldSimp
 
 #align_import analysis.convex.jensen from "leanprover-community/mathlib"@"bfad3f455b388fbcc14c49d0cac884f774f14d20"
 
@@ -21,8 +22,12 @@ Jensen's inequalities:
   convex combination of points under a convex function is less than the convex combination of the
   images.
 * `ConcaveOn.le_map_centerMass`, `ConcaveOn.le_map_sum`: Concave Jensen's inequality.
+* `StrictConvexOn.map_sum_lt`: Convex strict Jensen inequality.
+* `StrictConcaveOn.lt_map_sum`: Concave strict Jensen inequality.
 
 As corollaries, we get:
+* `StrictConvexOn.map_sum_eq_iff`: Equality case of the convex Jensen inequality.
+* `StrictConcaveOn.map_sum_eq_iff`: Equality case of the concave Jensen inequality.
 * `ConvexOn.exists_ge_of_mem_convexHull`: Maximum principle for convex functions.
 * `ConcaveOn.exists_le_of_mem_convexHull`: Minimum principle for concave functions.
 -/
@@ -40,7 +45,7 @@ variable {𝕜 E F β ι : Type*}
 section Jensen
 
 variable [LinearOrderedField 𝕜] [AddCommGroup E] [OrderedAddCommGroup β] [Module 𝕜 E] [Module 𝕜 β]
-  [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E}
+  [OrderedSMul 𝕜 β] {s : Set E} {f : E → β} {t : Finset ι} {w : ι → 𝕜} {p : ι → E} {v : 𝕜} {q : E}
 
 /-- Convex **Jensen's inequality**, `Finset.centerMass` version. -/
 theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
@@ -73,6 +78,168 @@ theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 
   ConvexOn.map_sum_le (β := βᵒᵈ) hf h₀ h₁ hmem
 #align concave_on.le_map_sum ConcaveOn.le_map_sum
 
+/-- Convex **Jensen's inequality** where an element plays a distinguished role. -/
+lemma ConvexOn.map_add_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
+    (h₁ : v + ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) (hv : 0 ≤ v) (hq : q ∈ s) :
+    f (v • q + ∑ i in t, w i • p i) ≤ v • f q + ∑ i in t, w i • f (p i) := by
+  let W j := Option.elim j v w
+  let P j := Option.elim j q p
+  have : f (∑ j in insertNone t, W j • P j) ≤ ∑ j in insertNone t, W j • f (P j) :=
+    hf.map_sum_le (forall_mem_insertNone.2 ⟨hv, h₀⟩) (by simpa using h₁)
+      (forall_mem_insertNone.2 ⟨hq, hmem⟩)
+  simpa using this
+
+/-- Concave **Jensen's inequality** where an element plays a distinguished role. -/
+lemma ConcaveOn.map_add_sum_le (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
+    (h₁ : v + ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) (hv : 0 ≤ v) (hq : q ∈ s) :
+    v • f q + ∑ i in t, w i • f (p i) ≤ f (v • q + ∑ i in t, w i • p i) :=
+  hf.dual.map_add_sum_le h₀ h₁ hmem hv hq
+
+/-! ### Strict Jensen inequality -/
+
+/-- Convex **strict Jensen inequality**.
+
+If the function is strictly convex, the weights are strictly positive and the indexed family of
+points is non-constant, then Jensen's inequality is strict.
+
+See also `StrictConvexOn.map_sum_eq_iff`. -/
+lemma StrictConvexOn.map_sum_lt (hf : StrictConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 < w i)
+    (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) (hp : ∃ j ∈ t, ∃ k ∈ t, p j ≠ p k) :
+    f (∑ i in t, w i • p i) < ∑ i in t, w i • f (p i) := by
+  classical
+  obtain ⟨j, hj, k, hk, hjk⟩ := hp
+  -- We replace `t` by `t \ {j, k}`
+  have : k ∈ t.erase j := mem_erase.2 ⟨ne_of_apply_ne _ hjk.symm, hk⟩
+  let u := (t.erase j).erase k
+  have hj : j ∉ u := by simp
+  have hk : k ∉ u := by simp
+  have ht : t = (u.cons k hk).cons j (mem_cons.not.2 $ not_or_intro (ne_of_apply_ne _ hjk) hj)
+  · simp [insert_erase this, insert_erase ‹j ∈ t›, *]
+  clear_value u
+  subst ht
+  simp only [sum_cons]
+  have := h₀ j $ by simp
+  have := h₀ k $ by simp
+  let c := w j + w k
+  have hc : w j / c + w k / c = 1 := by field_simp
+  have hcj : c * (w j / c) = w j := by field_simp; ring
+  have hck : c * (w k / c) = w k := by field_simp; ring
+  calc f (w j • p j + (w k • p k + ∑ x in u, w x • p x))
+    _ = f (c • ((w j / c) • p j + (w k / c) • p k) + ∑ x in u, w x • p x) := by
+      rw [smul_add, ← mul_smul, ← mul_smul, hcj, hck, add_assoc]
+    _ ≤ c • f ((w j / c) • p j + (w k / c) • p k) + ∑ x in u, w x • f (p x) :=
+      -- apply the usual Jensen's inequality wrt the weighted average of the two distinguished
+      -- points and all the other points
+        hf.convexOn.map_add_sum_le (fun i hi ↦ (h₀ _ $ by simp [hi]).le)
+          (by simpa [-cons_eq_insert, ← add_assoc] using h₁)
+          (forall_of_forall_cons $ forall_of_forall_cons hmem) (by positivity) $ by
+           refine hf.1 (hmem _ $ by simp) (hmem _ $ by simp) ?_ ?_ hc <;> positivity
+    _ < c • ((w j / c) • f (p j) + (w k / c) • f (p k)) + ∑ x in u, w x • f (p x) := by
+      -- then apply the definition of strict convexity for the two distinguished points
+      gcongr; refine hf.2 (hmem _ $ by simp) (hmem _ $ by simp) hjk ?_ ?_ hc <;> positivity
+    _ = (w j • f (p j) + w k • f (p k)) + ∑ x in u, w x • f (p x) := by
+      rw [smul_add, ← mul_smul, ← mul_smul, hcj, hck]
+    _ = w j • f (p j) + (w k • f (p k) + ∑ x in u, w x • f (p x)) := by abel_nf
+
+/-- Concave **strict Jensen inequality**.
+
+If the function is strictly concave, the weights are strictly positive and the indexed family of
+points is non-constant, then Jensen's inequality is strict.
+
+See also `StrictConcaveOn.map_sum_eq_iff`. -/
+lemma StrictConcaveOn.lt_map_sum (hf : StrictConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 < w i)
+    (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) (hp : ∃ j ∈ t, ∃ k ∈ t, p j ≠ p k) :
+    ∑ i in t, w i • f (p i) < f (∑ i in t, w i • p i) := hf.dual.map_sum_lt h₀ h₁ hmem hp
+
+/-! ### Equality case of Jensen's inequality -/
+
+/-- A form of the **equality case of Jensen's equality**.
+
+For a strictly convex function `f` and positive weights `w`, if
+`f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i)`, then the points `p` are all equal.
+
+See also `StrictConvexOn.map_sum_eq_iff`. -/
+lemma StrictConvexOn.eq_of_le_map_sum (hf : StrictConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 < w i)
+    (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s)
+    (h_eq : ∑ i in t, w i • f (p i) ≤ f (∑ i in t, w i • p i)) :
+    ∀ ⦃j⦄, j ∈ t → ∀ ⦃k⦄, k ∈ t → p j = p k := by
+  by_contra!; exact h_eq.not_lt $ hf.map_sum_lt h₀ h₁ hmem this
+
+/-- A form of the **equality case of Jensen's equality**.
+
+For a strictly concave function `f` and positive weights `w`, if
+`f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i)`, then the points `p` are all equal.
+
+See also `StrictConcaveOn.map_sum_eq_iff`. -/
+lemma StrictConcaveOn.eq_of_map_sum_eq (hf : StrictConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 < w i)
+    (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s)
+    (h_eq : f (∑ i in t, w i • p i) ≤ ∑ i in t, w i • f (p i)) :
+    ∀ ⦃j⦄, j ∈ t → ∀ ⦃k⦄, k ∈ t → p j = p k := by
+  by_contra!; exact h_eq.not_lt $ hf.lt_map_sum h₀ h₁ hmem this
+
+/-- Canonical form of the **equality case of Jensen's equality**.
+
+For a strictly convex function `f` and positive weights `w`, we have
+`f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i)` if and only if the points `p` are all equal
+(and in fact all equal to their center of mass wrt `w`). -/
+lemma StrictConvexOn.map_sum_eq_iff {w : ι → 𝕜} {p : ι → E} (hf : StrictConvexOn 𝕜 s f)
+    (h₀ : ∀ i ∈ t, 0 < w i) (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
+    f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i) ↔ ∀ j ∈ t, p j = ∑ i in t, w i • p i := by
+  constructor
+  · obtain rfl | ⟨i₀, hi₀⟩ := t.eq_empty_or_nonempty
+    · simp
+    intro h_eq i hi
+    have H : ∀ j ∈ t, p j = p i₀ := by
+      intro j hj
+      apply hf.eq_of_le_map_sum h₀ h₁ hmem h_eq.ge hj hi₀
+    calc p i = p i₀ := by rw [H _ hi]
+      _ = (1:𝕜) • p i₀ := by simp
+      _ = (∑ j in t, w j) • p i₀ := by rw [h₁]
+      _ = ∑ j in t, (w j • p i₀) := by rw [sum_smul]
+      _ = ∑ j in t, (w j • p j) := by congr! 2 with j hj; rw [← H _ hj]
+  · intro h
+    have H : ∀ j ∈ t, w j • f (p j) = w j • f (∑ i in t, w i • p i) := by
+      intro j hj
+      simp [h j hj]
+    rw [sum_congr rfl H, ← sum_smul, h₁, one_smul]
+
+/-- Canonical form of the **equality case of Jensen's equality**.
+
+For a strictly concave function `f` and positive weights `w`, we have
+`f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i)` if and only if the points `p` are all equal
+(and in fact all equal to their center of mass wrt `w`). -/
+lemma StrictConcaveOn.map_sum_eq_iff (hf : StrictConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 < w i)
+    (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
+    f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i) ↔ ∀ j ∈ t, p j = ∑ i in t, w i • p i := by
+  simpa using hf.neg.map_sum_eq_iff h₀ h₁ hmem
+
+/-- Canonical form of the **equality case of Jensen's equality**.
+
+For a strictly convex function `f` and nonnegative weights `w`, we have
+`f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i)` if and only if the points `p` with nonzero
+weight are all equal (and in fact all equal to their center of mass wrt `w`). -/
+lemma StrictConvexOn.map_sum_eq_iff' (hf : StrictConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
+    (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
+    f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i) ↔
+      ∀ j ∈ t, w j ≠ 0 → p j = ∑ i in t, w i • p i := by
+  have hw (i) (_ : i ∈ t) : w i • p i ≠ 0 → w i ≠ 0 := by aesop
+  have hw' (i) (_ : i ∈ t) : w i • f (p i) ≠ 0 → w i ≠ 0 := by aesop
+  rw [← sum_filter_of_ne hw, ← sum_filter_of_ne hw', hf.map_sum_eq_iff]
+  · simp
+  · simp (config := { contextual := true }) [(h₀ _ _).gt_iff_ne]
+  · rwa [sum_filter_ne_zero]
+  · simp (config := { contextual := true }) [hmem _ _]
+
+/-- Canonical form of the **equality case of Jensen's equality**.
+
+For a strictly concave function `f` and nonnegative weights `w`, we have
+`f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i)` if and only if the points `p` with nonzero
+weight are all equal (and in fact all equal to their center of mass wrt `w`). -/
+lemma StrictConcaveOn.map_sum_eq_iff' (hf : StrictConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
+    (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
+    f (∑ i in t, w i • p i) = ∑ i in t, w i • f (p i) ↔
+      ∀ j ∈ t, w j ≠ 0 → p j = ∑ i in t, w i • p i := hf.dual.map_sum_eq_iff' h₀ h₁ hmem
+
 end Jensen
 
 /-! ### Maximum principle -/
@@ -111,7 +278,7 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
   have hw' : (0 : 𝕜) < ∑ i in filter (fun i => w i ≠ 0) t, w i := by rwa [sum_filter_ne_zero]
   refine' exists_le_of_sum_le (nonempty_of_sum_ne_zero hw'.ne') _
   rw [← sum_smul, ← smul_le_smul_iff_of_pos (inv_pos.2 hw'), inv_smul_smul₀ hw'.ne', ←
-    Finset.centerMass, Finset.centerMass_filter_ne_zero]
+    centerMass, centerMass_filter_ne_zero]
   exact h.map_centerMass_le hw₀ hw₁ hp
 #align convex_on.exists_ge_of_center_mass ConvexOn.exists_ge_of_centerMass

bfad3f45

refactor: replace some [@foo](https://github.com/foo) _ _ _ _ _ ... by named arguments (#8702)

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

df634f2a

Diff

@@ -56,7 +56,7 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
 theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : 0 < ∑ i in t, w i) (hmem : ∀ i ∈ t, p i ∈ s) :
     t.centerMass w (f ∘ p) ≤ f (t.centerMass w p) :=
-  @ConvexOn.map_centerMass_le 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ hf h₀ h₁ hmem
+  ConvexOn.map_centerMass_le (β := βᵒᵈ) hf h₀ h₁ hmem
 #align concave_on.le_map_center_mass ConcaveOn.le_map_centerMass
 
 /-- Convex **Jensen's inequality**, `Finset.sum` version. -/
@@ -70,7 +70,7 @@ theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤
 theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
     (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
     (∑ i in t, w i • f (p i)) ≤ f (∑ i in t, w i • p i) :=
-  @ConvexOn.map_sum_le 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ hf h₀ h₁ hmem
+  ConvexOn.map_sum_le (β := βᵒᵈ) hf h₀ h₁ hmem
 #align concave_on.le_map_sum ConcaveOn.le_map_sum
 
 end Jensen
@@ -119,7 +119,7 @@ theorem ConvexOn.exists_ge_of_centerMass (h : ConvexOn 𝕜 s f) (hw₀ : ∀ i
 `s` is greater than the value it takes on one of those points. -/
 theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀ i ∈ t, 0 ≤ w i)
     (hw₁ : 0 < ∑ i in t, w i) (hp : ∀ i ∈ t, p i ∈ s) : ∃ i ∈ t, f (p i) ≤ f (t.centerMass w p) :=
-  @ConvexOn.exists_ge_of_centerMass 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ h hw₀ hw₁ hp
+  ConvexOn.exists_ge_of_centerMass (β := βᵒᵈ) h hw₀ hw₁ hp
 #align concave_on.exists_le_of_center_mass ConcaveOn.exists_le_of_centerMass
 
 /-- Maximum principle for convex functions. If a function `f` is convex on the convex hull of `s`,
@@ -138,7 +138,7 @@ theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 
 then the eventual minimum of `f` on `convexHull 𝕜 s` lies in `s`. -/
 theorem ConcaveOn.exists_le_of_mem_convexHull (hf : ConcaveOn 𝕜 (convexHull 𝕜 s) f) {x}
     (hx : x ∈ convexHull 𝕜 s) : ∃ y ∈ s, f y ≤ f x :=
-  @ConvexOn.exists_ge_of_mem_convexHull 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ hf _ hx
+  ConvexOn.exists_ge_of_mem_convexHull (β := βᵒᵈ) hf hx
 #align concave_on.exists_le_of_mem_convex_hull ConcaveOn.exists_le_of_mem_convexHull
 
 end MaximumPrinciple

bfad3f45

chore: missing spaces after rcases, convert and congrm (#7725)

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

c5594244

Diff

@@ -48,7 +48,7 @@ theorem ConvexOn.map_centerMass_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t,
     f (t.centerMass w p) ≤ t.centerMass w (f ∘ p) := by
   have hmem' : ∀ i ∈ t, (p i, (f ∘ p) i) ∈ { p : E × β | p.1 ∈ s ∧ f p.1 ≤ p.2 } := fun i hi =>
     ⟨hmem i hi, le_rfl⟩
-  convert(hf.convex_epigraph.centerMass_mem h₀ h₁ hmem').2 <;>
+  convert (hf.convex_epigraph.centerMass_mem h₀ h₁ hmem').2 <;>
     simp only [centerMass, Function.comp, Prod.smul_fst, Prod.fst_sum, Prod.smul_snd, Prod.snd_sum]
 #align convex_on.map_center_mass_le ConvexOn.map_centerMass_le

bfad3f45

chore: remove many Type _ before the colon (#7718)

We have turned to Type* instead of Type _, but many of them remained in mathlib because the straight replacement did not work. In general, having Type _ before the colon is a code smell, though, as it hides which types should be in the same universe and which shouldn't, and is not very robust.

This PR replaces most of the remaining Type _ before the colon (except those in category theory) by Type* or Type u. This has uncovered a few bugs (where declarations were not as polymorphic as they should be).

I had to increase heartbeats at two places when replacing Type _ by Type*, but I think it's worth it as it's really more robust.

fe9572d2

Diff

@@ -32,7 +32,7 @@ open Finset LinearMap Set
 
 open BigOperators Classical Convex Pointwise
 
-variable {𝕜 E F β ι : Type _}
+variable {𝕜 E F β ι : Type*}
 
 /-! ### Jensen's inequality -/

bfad3f45

chore: remove trailing space in backticks (#7617)

This will improve spaces in the mathlib4 docs.

9106dcf8

Diff

@@ -23,7 +23,7 @@ Jensen's inequalities:
 * `ConcaveOn.le_map_centerMass`, `ConcaveOn.le_map_sum`: Concave Jensen's inequality.
 
 As corollaries, we get:
-* `ConvexOn.exists_ge_of_mem_convexHull `: Maximum principle for convex functions.
+* `ConvexOn.exists_ge_of_mem_convexHull`: Maximum principle for convex functions.
 * `ConcaveOn.exists_le_of_mem_convexHull`: Minimum principle for concave functions.
 -/

bfad3f45

chore: no need for universe polymorphism in convexHull_eq (#3634)

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

df08e0d6

Diff

@@ -125,9 +125,8 @@ theorem ConcaveOn.exists_le_of_centerMass (h : ConcaveOn 𝕜 s f) (hw₀ : ∀
 /-- Maximum principle for convex functions. If a function `f` is convex on the convex hull of `s`,
 then the eventual maximum of `f` on `convexHull 𝕜 s` lies in `s`. -/
 theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 𝕜 s) f) {x}
-    (hx : x ∈ convexHull.{u, v} 𝕜 s) : ∃ y ∈ s, f x ≤ f y := by
-  -- Porting note: `convexHull_eq` has an unspecified universe value that we need to pick.
-  rw [_root_.convexHull_eq.{u, v, 0}] at hx
+    (hx : x ∈ convexHull 𝕜 s) : ∃ y ∈ s, f x ≤ f y := by
+  rw [_root_.convexHull_eq] at hx
   obtain ⟨α, t, w, p, hw₀, hw₁, hp, rfl⟩ := hx
   rcases hf.exists_ge_of_centerMass hw₀ (hw₁.symm ▸ zero_lt_one) fun i hi =>
       subset_convexHull 𝕜 s (hp i hi) with

bfad3f45

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp, Yury Kudriashov
-
-! This file was ported from Lean 3 source module analysis.convex.jensen
-! leanprover-community/mathlib commit bfad3f455b388fbcc14c49d0cac884f774f14d20
-! 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.Analysis.Convex.Function
 
+#align_import analysis.convex.jensen from "leanprover-community/mathlib"@"bfad3f455b388fbcc14c49d0cac884f774f14d20"
+
 /-!
 # Jensen's inequality and maximum principle for convex functions

bfad3f45

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

@@ -63,7 +63,7 @@ theorem ConcaveOn.le_map_centerMass (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈
 #align concave_on.le_map_center_mass ConcaveOn.le_map_centerMass
 
 /-- Convex **Jensen's inequality**, `Finset.sum` version. -/
-theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : (∑ i in t, w i) = 1)
+theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i) (h₁ : ∑ i in t, w i = 1)
     (hmem : ∀ i ∈ t, p i ∈ s) : f (∑ i in t, w i • p i) ≤ ∑ i in t, w i • f (p i) := by
   simpa only [centerMass, h₁, inv_one, one_smul] using
     hf.map_centerMass_le h₀ (h₁.symm ▸ zero_lt_one) hmem
@@ -71,7 +71,7 @@ theorem ConvexOn.map_sum_le (hf : ConvexOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤
 
 /-- Concave **Jensen's inequality**, `Finset.sum` version. -/
 theorem ConcaveOn.le_map_sum (hf : ConcaveOn 𝕜 s f) (h₀ : ∀ i ∈ t, 0 ≤ w i)
-    (h₁ : (∑ i in t, w i) = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
+    (h₁ : ∑ i in t, w i = 1) (hmem : ∀ i ∈ t, p i ∈ s) :
     (∑ i in t, w i • f (p i)) ≤ f (∑ i in t, w i • p i) :=
   @ConvexOn.map_sum_le 𝕜 E βᵒᵈ _ _ _ _ _ _ _ _ _ _ _ _ hf h₀ h₁ hmem
 #align concave_on.le_map_sum ConcaveOn.le_map_sum

bfad3f45

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -95,7 +95,6 @@ theorem le_sup_of_mem_convexHull {s : Finset E} (hf : ConvexOn 𝕜 (convexHull
     (centerMass_le_sup hw₀ <| by positivity)
 #align le_sup_of_mem_convex_hull le_sup_of_mem_convexHull
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem inf_le_of_mem_convexHull {s : Finset E} (hf : ConcaveOn 𝕜 (convexHull 𝕜 (s : Set E)) f)
     (hx : x ∈ convexHull 𝕜 (s : Set E)) :
     s.inf' (coe_nonempty.1 <| convexHull_nonempty_iff.1 ⟨x, hx⟩) f ≤ f x :=
@@ -139,7 +138,6 @@ theorem ConvexOn.exists_ge_of_mem_convexHull (hf : ConvexOn 𝕜 (convexHull 
   exact ⟨p i, hp i hit, Hi⟩
 #align convex_on.exists_ge_of_mem_convex_hull ConvexOn.exists_ge_of_mem_convexHull
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Minimum principle for concave functions. If a function `f` is concave on the convex hull of `s`,
 then the eventual minimum of `f` on `convexHull 𝕜 s` lies in `s`. -/
 theorem ConcaveOn.exists_le_of_mem_convexHull (hf : ConcaveOn 𝕜 (convexHull 𝕜 s) f) {x}

bfad3f45

feat: port Analysis.Convex.Jensen (#3622)

Co-authored-by: Moritz Doll <moritz.doll@googlemail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

4929c76a

`analysis.convex.jensen` ⟷ `Mathlib.Analysis.Convex.Jensen`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 9 + 446

analysis.convex.jensen ⟷ Mathlib.Analysis.Convex.Jensen

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 9 + 446

`analysis.convex.jensen` ⟷ `Mathlib.Analysis.Convex.Jensen`