analysis.normed_space.hahn_banach.separation ⟷ Mathlib.Analysis.NormedSpace.HahnBanach.Separation

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

@@ -103,7 +103,7 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
   have : Convex ℝ C := (hs₁.sub ht).vadd _
   have : x₀ ∉ C := by
     intro hx₀
-    rw [← add_zero x₀] at hx₀ 
+    rw [← add_zero x₀] at hx₀
     exact disj.zero_not_mem_sub_set (vadd_mem_vadd_set_iff.1 hx₀)
   obtain ⟨f, hf₁, hf₂⟩ := separate_convex_open_set ‹0 ∈ C› ‹_› (hs₂.sub_right.vadd _) ‹x₀ ∉ C›
   have : f b₀ = f a₀ + 1 := by simp [← hf₁]
@@ -111,7 +111,7 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
     by
     intro a ha b hb
     have := hf₂ (x₀ + (a - b)) (vadd_mem_vadd_set <| sub_mem_sub ha hb)
-    simp only [f.map_add, f.map_sub, hf₁] at this 
+    simp only [f.map_add, f.map_sub, hf₁] at this
     linarith
   refine' ⟨f, Inf (f '' t), image_subset_iff.1 (_ : f '' s ⊆ Iio (Inf (f '' t))), fun b hb => _⟩
   · rw [← interior_Iic]

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

@@ -60,7 +60,7 @@ theorem separate_convex_open_set [TopologicalSpace E] [AddCommGroup E] [Topologi
     rw [← Submodule.coe_mk x₀ (Submodule.mem_span_singleton_self _), hφ₁,
       LinearPMap.mkSpanSingleton'_apply_self]
   have hφ₄ : ∀ x ∈ s, φ x < 1 := fun x hx =>
-    (hφ₂ x).trans_lt (gauge_lt_one_of_mem_of_open hs₁ hs₀ hs₂ hx)
+    (hφ₂ x).trans_lt (gauge_lt_one_of_mem_of_isOpen hs₁ hs₀ hs₂ hx)
   · refine' ⟨⟨φ, _⟩, hφ₃, hφ₄⟩
     refine'
       φ.continuous_of_nonzero_on_open _ (hs₂.vadd (-x₀)) (nonempty.vadd_set ⟨0, hs₀⟩)

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

@@ -3,10 +3,10 @@ Copyright (c) 2022 Bhavik Mehta All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Yaël Dillies
 -/
-import Mathbin.Analysis.Convex.Cone.Basic
-import Mathbin.Analysis.Convex.Gauge
-import Mathbin.Topology.Algebra.Module.FiniteDimension
-import Mathbin.Topology.Algebra.Module.LocallyConvex
+import Analysis.Convex.Cone.Basic
+import Analysis.Convex.Gauge
+import Topology.Algebra.Module.FiniteDimension
+import Topology.Algebra.Module.LocallyConvex
 
 #align_import analysis.normed_space.hahn_banach.separation from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Bhavik Mehta All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Yaël Dillies
-
-! This file was ported from Lean 3 source module analysis.normed_space.hahn_banach.separation
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Cone.Basic
 import Mathbin.Analysis.Convex.Gauge
 import Mathbin.Topology.Algebra.Module.FiniteDimension
 import Mathbin.Topology.Algebra.Module.LocallyConvex
 
+#align_import analysis.normed_space.hahn_banach.separation from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Separation Hahn-Banach theorem
 

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

@@ -47,6 +47,7 @@ open scoped Pointwise
 
 variable {𝕜 E : Type _}
 
+#print separate_convex_open_set /-
 /-- Given a set `s` which is a convex neighbourhood of `0` and a point `x₀` outside of it, there is
 a continuous linear functional `f` separating `x₀` and `s`, in the sense that it sends `x₀` to 1 and
 all of `s` to values strictly below `1`. -/
@@ -83,10 +84,12 @@ theorem separate_convex_open_set [TopologicalSpace E] [AddCommGroup E] [Topologi
         (absorbent_nhds_zero <| hs₂.mem_nhds hs₀).Absorbs hx₀
     infer_instance
 #align separate_convex_open_set separate_convex_open_set
+-/
 
 variable [TopologicalSpace E] [AddCommGroup E] [TopologicalAddGroup E] [Module ℝ E]
   [ContinuousSMul ℝ E] {s t : Set E} {x y : E}
 
+#print geometric_hahn_banach_open /-
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is open,
 there is a continuous linear functional which separates them. -/
 theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht : Convex ℝ t)
@@ -121,20 +124,26 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
       simpa using hf₁
   · exact csInf_le ⟨f a₀, ball_image_of_ball <| forall_le _ ha₀⟩ (mem_image_of_mem _ hb)
 #align geometric_hahn_banach_open geometric_hahn_banach_open
+-/
 
+#print geometric_hahn_banach_open_point /-
 theorem geometric_hahn_banach_open_point (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (disj : x ∉ s) :
     ∃ f : E →L[ℝ] ℝ, ∀ a ∈ s, f a < f x :=
   let ⟨f, s, hs, hx⟩ :=
     geometric_hahn_banach_open hs₁ hs₂ (convex_singleton x) (disjoint_singleton_right.2 disj)
   ⟨f, fun a ha => lt_of_lt_of_le (hs a ha) (hx x (mem_singleton _))⟩
 #align geometric_hahn_banach_open_point geometric_hahn_banach_open_point
+-/
 
+#print geometric_hahn_banach_point_open /-
 theorem geometric_hahn_banach_point_open (ht₁ : Convex ℝ t) (ht₂ : IsOpen t) (disj : x ∉ t) :
     ∃ f : E →L[ℝ] ℝ, ∀ b ∈ t, f x < f b :=
   let ⟨f, hf⟩ := geometric_hahn_banach_open_point ht₁ ht₂ disj
   ⟨-f, by simpa⟩
 #align geometric_hahn_banach_point_open geometric_hahn_banach_point_open
+-/
 
+#print geometric_hahn_banach_open_open /-
 theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht₁ : Convex ℝ t)
     (ht₃ : IsOpen t) (disj : Disjoint s t) :
     ∃ (f : E →L[ℝ] ℝ) (u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u < f b :=
@@ -154,9 +163,11 @@ theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s
   rintro rfl
   exact (hf₁ _ ha₀).not_le (hf₂ _ hb₀)
 #align geometric_hahn_banach_open_open geometric_hahn_banach_open_open
+-/
 
 variable [LocallyConvexSpace ℝ E]
 
+#print geometric_hahn_banach_compact_closed /-
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is
 compact and `t` is closed, there is a continuous linear functional which strongly separates them. -/
 theorem geometric_hahn_banach_compact_closed (hs₁ : Convex ℝ s) (hs₂ : IsCompact s)
@@ -175,7 +186,9 @@ theorem geometric_hahn_banach_compact_closed (hs₁ : Convex ℝ s) (hs₂ : IsC
     ⟨f, (f x + u) / 2, u, fun a ha => by linarith [hx₂ a ha], by linarith, fun b hb =>
       hf₂ b (tV hb)⟩
 #align geometric_hahn_banach_compact_closed geometric_hahn_banach_compact_closed
+-/
 
+#print geometric_hahn_banach_closed_compact /-
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is
 closed, and `t` is compact, there is a continuous linear functional which strongly separates them.
 -/
@@ -185,7 +198,9 @@ theorem geometric_hahn_banach_closed_compact (hs₁ : Convex ℝ s) (hs₂ : IsC
   let ⟨f, s, t, hs, st, ht⟩ := geometric_hahn_banach_compact_closed ht₁ ht₂ hs₁ hs₂ disj.symm
   ⟨-f, -t, -s, by simpa using ht, by simpa using st, by simpa using hs⟩
 #align geometric_hahn_banach_closed_compact geometric_hahn_banach_closed_compact
+-/
 
+#print geometric_hahn_banach_point_closed /-
 theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClosed t) (disj : x ∉ t) :
     ∃ (f : E →L[ℝ] ℝ) (u : ℝ), f x < u ∧ ∀ b ∈ t, u < f b :=
   let ⟨f, u, v, ha, hst, hb⟩ :=
@@ -193,7 +208,9 @@ theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClo
       (disjoint_singleton_left.2 disj)
   ⟨f, v, hst.trans' <| ha x <| mem_singleton _, hb⟩
 #align geometric_hahn_banach_point_closed geometric_hahn_banach_point_closed
+-/
 
+#print geometric_hahn_banach_closed_point /-
 theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) (disj : x ∉ s) :
     ∃ (f : E →L[ℝ] ℝ) (u : ℝ), (∀ a ∈ s, f a < u) ∧ u < f x :=
   let ⟨f, s, t, ha, hst, hb⟩ :=
@@ -201,7 +218,9 @@ theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClo
       (disjoint_singleton_right.2 disj)
   ⟨f, s, ha, hst.trans <| hb x <| mem_singleton _⟩
 #align geometric_hahn_banach_closed_point geometric_hahn_banach_closed_point
+-/
 
+#print geometric_hahn_banach_point_point /-
 /-- See also `normed_space.eq_iff_forall_dual_eq`. -/
 theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f : E →L[ℝ] ℝ, f x < f y :=
   by
@@ -210,7 +229,9 @@ theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f :
       (convex_singleton y) isClosed_singleton (disjoint_singleton.2 hxy)
   exact ⟨f, by linarith [hs x rfl, ht y rfl]⟩
 #align geometric_hahn_banach_point_point geometric_hahn_banach_point_point
+-/
 
+#print iInter_halfspaces_eq /-
 /-- A closed convex set is the intersection of the halfspaces containing it. -/
 theorem iInter_halfspaces_eq (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) :
     (⋂ l : E →L[ℝ] ℝ, {x | ∃ y ∈ s, l x ≤ l y}) = s :=
@@ -222,4 +243,5 @@ theorem iInter_halfspaces_eq (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) :
   obtain ⟨y, hy, hxy⟩ := hx l
   exact ((hxy.trans_lt (hlA y hy)).trans hl).not_le le_rfl
 #align Inter_halfspaces_eq iInter_halfspaces_eq
+-/
 

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

@@ -213,7 +213,7 @@ theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f :
 
 /-- A closed convex set is the intersection of the halfspaces containing it. -/
 theorem iInter_halfspaces_eq (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) :
-    (⋂ l : E →L[ℝ] ℝ, { x | ∃ y ∈ s, l x ≤ l y }) = s :=
+    (⋂ l : E →L[ℝ] ℝ, {x | ∃ y ∈ s, l x ≤ l y}) = s :=
   by
   rw [Set.iInter_setOf]
   refine' Set.Subset.antisymm (fun x hx => _) fun x hx l => ⟨x, hx, le_rfl⟩

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

@@ -90,7 +90,7 @@ variable [TopologicalSpace E] [AddCommGroup E] [TopologicalAddGroup E] [Module 
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is open,
 there is a continuous linear functional which separates them. -/
 theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht : Convex ℝ t)
-    (disj : Disjoint s t) : ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u ≤ f b :=
+    (disj : Disjoint s t) : ∃ (f : E →L[ℝ] ℝ) (u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u ≤ f b :=
   by
   obtain rfl | ⟨a₀, ha₀⟩ := s.eq_empty_or_nonempty
   · exact ⟨0, 0, by simp, fun b hb => le_rfl⟩
@@ -103,7 +103,7 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
   have : Convex ℝ C := (hs₁.sub ht).vadd _
   have : x₀ ∉ C := by
     intro hx₀
-    rw [← add_zero x₀] at hx₀
+    rw [← add_zero x₀] at hx₀ 
     exact disj.zero_not_mem_sub_set (vadd_mem_vadd_set_iff.1 hx₀)
   obtain ⟨f, hf₁, hf₂⟩ := separate_convex_open_set ‹0 ∈ C› ‹_› (hs₂.sub_right.vadd _) ‹x₀ ∉ C›
   have : f b₀ = f a₀ + 1 := by simp [← hf₁]
@@ -111,7 +111,7 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
     by
     intro a ha b hb
     have := hf₂ (x₀ + (a - b)) (vadd_mem_vadd_set <| sub_mem_sub ha hb)
-    simp only [f.map_add, f.map_sub, hf₁] at this
+    simp only [f.map_add, f.map_sub, hf₁] at this 
     linarith
   refine' ⟨f, Inf (f '' t), image_subset_iff.1 (_ : f '' s ⊆ Iio (Inf (f '' t))), fun b hb => _⟩
   · rw [← interior_Iic]
@@ -137,7 +137,7 @@ theorem geometric_hahn_banach_point_open (ht₁ : Convex ℝ t) (ht₂ : IsOpen
 
 theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht₁ : Convex ℝ t)
     (ht₃ : IsOpen t) (disj : Disjoint s t) :
-    ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u < f b :=
+    ∃ (f : E →L[ℝ] ℝ) (u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u < f b :=
   by
   obtain rfl | ⟨a₀, ha₀⟩ := s.eq_empty_or_nonempty
   · exact ⟨0, -1, by simp, fun b hb => by norm_num⟩
@@ -161,7 +161,7 @@ variable [LocallyConvexSpace ℝ E]
 compact and `t` is closed, there is a continuous linear functional which strongly separates them. -/
 theorem geometric_hahn_banach_compact_closed (hs₁ : Convex ℝ s) (hs₂ : IsCompact s)
     (ht₁ : Convex ℝ t) (ht₂ : IsClosed t) (disj : Disjoint s t) :
-    ∃ (f : E →L[ℝ] ℝ)(u v : ℝ), (∀ a ∈ s, f a < u) ∧ u < v ∧ ∀ b ∈ t, v < f b :=
+    ∃ (f : E →L[ℝ] ℝ) (u v : ℝ), (∀ a ∈ s, f a < u) ∧ u < v ∧ ∀ b ∈ t, v < f b :=
   by
   obtain rfl | hs := s.eq_empty_or_nonempty
   · exact ⟨0, -2, -1, by simp, by norm_num, fun b hb => by norm_num⟩
@@ -181,13 +181,13 @@ closed, and `t` is compact, there is a continuous linear functional which strong
 -/
 theorem geometric_hahn_banach_closed_compact (hs₁ : Convex ℝ s) (hs₂ : IsClosed s)
     (ht₁ : Convex ℝ t) (ht₂ : IsCompact t) (disj : Disjoint s t) :
-    ∃ (f : E →L[ℝ] ℝ)(u v : ℝ), (∀ a ∈ s, f a < u) ∧ u < v ∧ ∀ b ∈ t, v < f b :=
+    ∃ (f : E →L[ℝ] ℝ) (u v : ℝ), (∀ a ∈ s, f a < u) ∧ u < v ∧ ∀ b ∈ t, v < f b :=
   let ⟨f, s, t, hs, st, ht⟩ := geometric_hahn_banach_compact_closed ht₁ ht₂ hs₁ hs₂ disj.symm
   ⟨-f, -t, -s, by simpa using ht, by simpa using st, by simpa using hs⟩
 #align geometric_hahn_banach_closed_compact geometric_hahn_banach_closed_compact
 
 theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClosed t) (disj : x ∉ t) :
-    ∃ (f : E →L[ℝ] ℝ)(u : ℝ), f x < u ∧ ∀ b ∈ t, u < f b :=
+    ∃ (f : E →L[ℝ] ℝ) (u : ℝ), f x < u ∧ ∀ b ∈ t, u < f b :=
   let ⟨f, u, v, ha, hst, hb⟩ :=
     geometric_hahn_banach_compact_closed (convex_singleton x) isCompact_singleton ht₁ ht₂
       (disjoint_singleton_left.2 disj)
@@ -195,7 +195,7 @@ theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClo
 #align geometric_hahn_banach_point_closed geometric_hahn_banach_point_closed
 
 theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) (disj : x ∉ s) :
-    ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ u < f x :=
+    ∃ (f : E →L[ℝ] ℝ) (u : ℝ), (∀ a ∈ s, f a < u) ∧ u < f x :=
   let ⟨f, s, t, ha, hst, hb⟩ :=
     geometric_hahn_banach_closed_compact hs₁ hs₂ (convex_singleton x) isCompact_singleton
       (disjoint_singleton_right.2 disj)

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

@@ -43,7 +43,7 @@ We provide many variations to stricten the result under more assumptions on the
 
 open Set
 
-open Pointwise
+open scoped Pointwise
 
 variable {𝕜 E : Type _}
 

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

@@ -47,9 +47,6 @@ open Pointwise
 
 variable {𝕜 E : Type _}
 
-/- warning: separate_convex_open_set -> separate_convex_open_set is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align separate_convex_open_set separate_convex_open_setₓ'. -/
 /-- Given a set `s` which is a convex neighbourhood of `0` and a point `x₀` outside of it, there is
 a continuous linear functional `f` separating `x₀` and `s`, in the sense that it sends `x₀` to 1 and
 all of `s` to values strictly below `1`. -/
@@ -90,9 +87,6 @@ theorem separate_convex_open_set [TopologicalSpace E] [AddCommGroup E] [Topologi
 variable [TopologicalSpace E] [AddCommGroup E] [TopologicalAddGroup E] [Module ℝ E]
   [ContinuousSMul ℝ E] {s t : Set E} {x y : E}
 
-/- warning: geometric_hahn_banach_open -> geometric_hahn_banach_open is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_open geometric_hahn_banach_openₓ'. -/
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is open,
 there is a continuous linear functional which separates them. -/
 theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht : Convex ℝ t)
@@ -128,9 +122,6 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
   · exact csInf_le ⟨f a₀, ball_image_of_ball <| forall_le _ ha₀⟩ (mem_image_of_mem _ hb)
 #align geometric_hahn_banach_open geometric_hahn_banach_open
 
-/- warning: geometric_hahn_banach_open_point -> geometric_hahn_banach_open_point is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_open_point geometric_hahn_banach_open_pointₓ'. -/
 theorem geometric_hahn_banach_open_point (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (disj : x ∉ s) :
     ∃ f : E →L[ℝ] ℝ, ∀ a ∈ s, f a < f x :=
   let ⟨f, s, hs, hx⟩ :=
@@ -138,18 +129,12 @@ theorem geometric_hahn_banach_open_point (hs₁ : Convex ℝ s) (hs₂ : IsOpen
   ⟨f, fun a ha => lt_of_lt_of_le (hs a ha) (hx x (mem_singleton _))⟩
 #align geometric_hahn_banach_open_point geometric_hahn_banach_open_point
 
-/- warning: geometric_hahn_banach_point_open -> geometric_hahn_banach_point_open is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_point_open geometric_hahn_banach_point_openₓ'. -/
 theorem geometric_hahn_banach_point_open (ht₁ : Convex ℝ t) (ht₂ : IsOpen t) (disj : x ∉ t) :
     ∃ f : E →L[ℝ] ℝ, ∀ b ∈ t, f x < f b :=
   let ⟨f, hf⟩ := geometric_hahn_banach_open_point ht₁ ht₂ disj
   ⟨-f, by simpa⟩
 #align geometric_hahn_banach_point_open geometric_hahn_banach_point_open
 
-/- warning: geometric_hahn_banach_open_open -> geometric_hahn_banach_open_open is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_open_open geometric_hahn_banach_open_openₓ'. -/
 theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht₁ : Convex ℝ t)
     (ht₃ : IsOpen t) (disj : Disjoint s t) :
     ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u < f b :=
@@ -172,9 +157,6 @@ theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s
 
 variable [LocallyConvexSpace ℝ E]
 
-/- warning: geometric_hahn_banach_compact_closed -> geometric_hahn_banach_compact_closed is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_compact_closed geometric_hahn_banach_compact_closedₓ'. -/
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is
 compact and `t` is closed, there is a continuous linear functional which strongly separates them. -/
 theorem geometric_hahn_banach_compact_closed (hs₁ : Convex ℝ s) (hs₂ : IsCompact s)
@@ -194,9 +176,6 @@ theorem geometric_hahn_banach_compact_closed (hs₁ : Convex ℝ s) (hs₂ : IsC
       hf₂ b (tV hb)⟩
 #align geometric_hahn_banach_compact_closed geometric_hahn_banach_compact_closed
 
-/- warning: geometric_hahn_banach_closed_compact -> geometric_hahn_banach_closed_compact is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_closed_compact geometric_hahn_banach_closed_compactₓ'. -/
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is
 closed, and `t` is compact, there is a continuous linear functional which strongly separates them.
 -/
@@ -207,9 +186,6 @@ theorem geometric_hahn_banach_closed_compact (hs₁ : Convex ℝ s) (hs₂ : IsC
   ⟨-f, -t, -s, by simpa using ht, by simpa using st, by simpa using hs⟩
 #align geometric_hahn_banach_closed_compact geometric_hahn_banach_closed_compact
 
-/- warning: geometric_hahn_banach_point_closed -> geometric_hahn_banach_point_closed is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_point_closed geometric_hahn_banach_point_closedₓ'. -/
 theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClosed t) (disj : x ∉ t) :
     ∃ (f : E →L[ℝ] ℝ)(u : ℝ), f x < u ∧ ∀ b ∈ t, u < f b :=
   let ⟨f, u, v, ha, hst, hb⟩ :=
@@ -218,9 +194,6 @@ theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClo
   ⟨f, v, hst.trans' <| ha x <| mem_singleton _, hb⟩
 #align geometric_hahn_banach_point_closed geometric_hahn_banach_point_closed
 
-/- warning: geometric_hahn_banach_closed_point -> geometric_hahn_banach_closed_point is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_closed_point geometric_hahn_banach_closed_pointₓ'. -/
 theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) (disj : x ∉ s) :
     ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ u < f x :=
   let ⟨f, s, t, ha, hst, hb⟩ :=
@@ -229,9 +202,6 @@ theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClo
   ⟨f, s, ha, hst.trans <| hb x <| mem_singleton _⟩
 #align geometric_hahn_banach_closed_point geometric_hahn_banach_closed_point
 
-/- warning: geometric_hahn_banach_point_point -> geometric_hahn_banach_point_point is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_point_point geometric_hahn_banach_point_pointₓ'. -/
 /-- See also `normed_space.eq_iff_forall_dual_eq`. -/
 theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f : E →L[ℝ] ℝ, f x < f y :=
   by
@@ -241,9 +211,6 @@ theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f :
   exact ⟨f, by linarith [hs x rfl, ht y rfl]⟩
 #align geometric_hahn_banach_point_point geometric_hahn_banach_point_point
 
-/- warning: Inter_halfspaces_eq -> iInter_halfspaces_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Inter_halfspaces_eq iInter_halfspaces_eqₓ'. -/
 /-- A closed convex set is the intersection of the halfspaces containing it. -/
 theorem iInter_halfspaces_eq (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) :
     (⋂ l : E →L[ℝ] ℝ, { x | ∃ y ∈ s, l x ≤ l y }) = s :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.normed_space.hahn_banach.separation
-! leanprover-community/mathlib commit 915591b2bb3ea303648db07284a161a7f2a9e3d4
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Algebra.Module.LocallyConvex
 /-!
 # Separation Hahn-Banach theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove the geometric Hahn-Banach theorem. For any two disjoint convex sets, there
 exists a continuous linear functional separating them, geometrically meaning that we can intercalate
 a plane between them.
@@ -45,10 +48,7 @@ open Pointwise
 variable {𝕜 E : Type _}
 
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(AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) Real.instOneReal)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align separate_convex_open_set separate_convex_open_setₓ'. -/
 /-- Given a set `s` which is a convex neighbourhood of `0` and a point `x₀` outside of it, there is
 a continuous linear functional `f` separating `x₀` and `s`, in the sense that it sends `x₀` to 1 and
@@ -91,10 +91,7 @@ variable [TopologicalSpace E] [AddCommGroup E] [TopologicalAddGroup E] [Module 
   [ContinuousSMul ℝ E] {s t : Set E} {x y : E}
 
 /- warning: geometric_hahn_banach_open -> geometric_hahn_banach_open is a dubious translation:
-lean 3 declaration is
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(AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (Disjoint.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => And (forall (a : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) a s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f a) u)) (forall (b : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) b t) -> (LE.le.{0} Real Real.hasLe u (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f b))))))
-but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (Disjoint.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} E) (Preorder.toLE.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real 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+<too large>
 Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_open geometric_hahn_banach_openₓ'. -/
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is open,
 there is a continuous linear functional which separates them. -/
@@ -132,10 +129,7 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
 #align geometric_hahn_banach_open geometric_hahn_banach_open
 
 /- warning: geometric_hahn_banach_open_point -> geometric_hahn_banach_open_point is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_open_point geometric_hahn_banach_open_pointₓ'. -/
 theorem geometric_hahn_banach_open_point (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (disj : x ∉ s) :
     ∃ f : E →L[ℝ] ℝ, ∀ a ∈ s, f a < f x :=
@@ -145,10 +139,7 @@ theorem geometric_hahn_banach_open_point (hs₁ : Convex ℝ s) (hs₂ : IsOpen
 #align geometric_hahn_banach_open_point geometric_hahn_banach_open_point
 
 /- warning: geometric_hahn_banach_point_open -> geometric_hahn_banach_point_open is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_point_open geometric_hahn_banach_point_openₓ'. -/
 theorem geometric_hahn_banach_point_open (ht₁ : Convex ℝ t) (ht₂ : IsOpen t) (disj : x ∉ t) :
     ∃ f : E →L[ℝ] ℝ, ∀ b ∈ t, f x < f b :=
@@ -157,10 +148,7 @@ theorem geometric_hahn_banach_point_open (ht₁ : Convex ℝ t) (ht₂ : IsOpen
 #align geometric_hahn_banach_point_open geometric_hahn_banach_point_open
 
 /- warning: geometric_hahn_banach_open_open -> geometric_hahn_banach_open_open is a dubious translation:
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_inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real 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(NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real 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0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f a) u)) (forall (b : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) b t) -> (LT.lt.{0} Real Real.instLTReal u (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_open_open geometric_hahn_banach_open_openₓ'. -/
 theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht₁ : Convex ℝ t)
     (ht₃ : IsOpen t) (disj : Disjoint s t) :
@@ -185,10 +173,7 @@ theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s
 variable [LocallyConvexSpace ℝ E]
 
 /- warning: geometric_hahn_banach_compact_closed -> geometric_hahn_banach_compact_closed is a dubious translation:
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(AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real 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(NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real 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Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_compact_closed geometric_hahn_banach_compact_closedₓ'. -/
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is
 compact and `t` is closed, there is a continuous linear functional which strongly separates them. -/
@@ -210,10 +195,7 @@ theorem geometric_hahn_banach_compact_closed (hs₁ : Convex ℝ s) (hs₂ : IsC
 #align geometric_hahn_banach_compact_closed geometric_hahn_banach_compact_closed
 
 /- warning: geometric_hahn_banach_closed_compact -> geometric_hahn_banach_closed_compact is a dubious translation:
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(AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real 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(GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => Exists.{1} Real (fun (v : Real) => And (forall (a : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) a s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real 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-but is expected to have type
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(RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 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(NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real 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_inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_closed_compact geometric_hahn_banach_closed_compactₓ'. -/
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is
 closed, and `t` is compact, there is a continuous linear functional which strongly separates them.
@@ -226,10 +208,7 @@ theorem geometric_hahn_banach_closed_compact (hs₁ : Convex ℝ s) (hs₂ : IsC
 #align geometric_hahn_banach_closed_compact geometric_hahn_banach_closed_compact
 
 /- warning: geometric_hahn_banach_point_closed -> geometric_hahn_banach_point_closed is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {t : Set.{u1} E} {x : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsClosed.{u1} E _inst_1 t) -> (Not (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x t)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => And (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f x) u) (forall (b : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) b t) -> (LT.lt.{0} Real Real.hasLt u (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f b))))))
-but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {t : Set.{u1} E} {x : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsClosed.{u1} E _inst_1 t) -> (Not (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x t)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => Exists.{1} Real (fun (u : Real) => And (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x) u) (forall (b : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) b t) -> (LT.lt.{0} Real Real.instLTReal u (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_point_closed geometric_hahn_banach_point_closedₓ'. -/
 theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClosed t) (disj : x ∉ t) :
     ∃ (f : E →L[ℝ] ℝ)(u : ℝ), f x < u ∧ ∀ b ∈ t, u < f b :=
@@ -240,10 +219,7 @@ theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClo
 #align geometric_hahn_banach_point_closed geometric_hahn_banach_point_closed
 
 /- warning: geometric_hahn_banach_closed_point -> geometric_hahn_banach_closed_point is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {x : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsClosed.{u1} E _inst_1 s) -> (Not (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => And (forall (a : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) a s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring 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(PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f x)))))
-but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {x : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsClosed.{u1} E _inst_1 s) -> (Not (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => Exists.{1} Real (fun (u : Real) => And (forall (a : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) a s) -> (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f a) u)) (LT.lt.{0} Real Real.instLTReal u (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real 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(PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_closed_point geometric_hahn_banach_closed_pointₓ'. -/
 theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) (disj : x ∉ s) :
     ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ u < f x :=
@@ -254,10 +230,7 @@ theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClo
 #align geometric_hahn_banach_closed_point geometric_hahn_banach_closed_point
 
 /- warning: geometric_hahn_banach_point_point -> geometric_hahn_banach_point_point is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_point_point geometric_hahn_banach_point_pointₓ'. -/
 /-- See also `normed_space.eq_iff_forall_dual_eq`. -/
 theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f : E →L[ℝ] ℝ, f x < f y :=
@@ -269,10 +242,7 @@ theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f :
 #align geometric_hahn_banach_point_point geometric_hahn_banach_point_point
 
 /- warning: Inter_halfspaces_eq -> iInter_halfspaces_eq is a dubious translation:
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(PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) l y)))))) s)
-but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsClosed.{u1} E _inst_1 s) -> (Eq.{succ u1} (Set.{u1} E) (Set.iInter.{u1, succ u1} E (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (l : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => setOf.{u1} E (fun (x : E) => Exists.{succ u1} E (fun (y : E) => And (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) y s) (LE.le.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) Real.instLEReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (a : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) l x) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (a : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) l y)))))) s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align Inter_halfspaces_eq iInter_halfspaces_eqₓ'. -/
 /-- A closed convex set is the intersection of the halfspaces containing it. -/
 theorem iInter_halfspaces_eq (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) :

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

@@ -44,6 +44,12 @@ open Pointwise
 
 variable {𝕜 E : Type _}
 
+/- warning: separate_convex_open_set -> separate_convex_open_set is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E}, (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))))) s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (forall {x₀ : E}, (Not (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x₀ s)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => And (Eq.{1} Real (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f x₀) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (forall (x : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E}, (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))))) s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (forall {x₀ : E}, (Not (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x₀ s)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => And (Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x₀) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x₀) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x₀) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x₀) Real.instOneReal))) (forall (x : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s) -> (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) Real.instOneReal)))))))
+Case conversion may be inaccurate. Consider using '#align separate_convex_open_set separate_convex_open_setₓ'. -/
 /-- Given a set `s` which is a convex neighbourhood of `0` and a point `x₀` outside of it, there is
 a continuous linear functional `f` separating `x₀` and `s`, in the sense that it sends `x₀` to 1 and
 all of `s` to values strictly below `1`. -/
@@ -84,6 +90,12 @@ theorem separate_convex_open_set [TopologicalSpace E] [AddCommGroup E] [Topologi
 variable [TopologicalSpace E] [AddCommGroup E] [TopologicalAddGroup E] [Module ℝ E]
   [ContinuousSMul ℝ E] {s t : Set E} {x y : E}
 
+/- warning: geometric_hahn_banach_open -> geometric_hahn_banach_open is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (Disjoint.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => And (forall (a : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) a s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f a) u)) (forall (b : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) b t) -> (LE.le.{0} Real Real.hasLe u (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f b))))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (Disjoint.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} E) (Preorder.toLE.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => Exists.{1} Real (fun (u : Real) => And (forall (a : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) a s) -> (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f a) u)) (forall (b : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) b t) -> (LE.le.{0} Real Real.instLEReal u (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))))
+Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_open geometric_hahn_banach_openₓ'. -/
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is open,
 there is a continuous linear functional which separates them. -/
 theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht : Convex ℝ t)
@@ -119,6 +131,12 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
   · exact csInf_le ⟨f a₀, ball_image_of_ball <| forall_le _ ha₀⟩ (mem_image_of_mem _ hb)
 #align geometric_hahn_banach_open geometric_hahn_banach_open
 
+/- warning: geometric_hahn_banach_open_point -> geometric_hahn_banach_open_point is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {x : E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (Not (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => forall (a : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) a s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f a) (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f x))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {x : E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (Not (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => forall (a : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) a s) -> (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f a) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x))))
+Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_open_point geometric_hahn_banach_open_pointₓ'. -/
 theorem geometric_hahn_banach_open_point (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (disj : x ∉ s) :
     ∃ f : E →L[ℝ] ℝ, ∀ a ∈ s, f a < f x :=
   let ⟨f, s, hs, hx⟩ :=
@@ -126,12 +144,24 @@ theorem geometric_hahn_banach_open_point (hs₁ : Convex ℝ s) (hs₂ : IsOpen
   ⟨f, fun a ha => lt_of_lt_of_le (hs a ha) (hx x (mem_singleton _))⟩
 #align geometric_hahn_banach_open_point geometric_hahn_banach_open_point
 
+/- warning: geometric_hahn_banach_point_open -> geometric_hahn_banach_point_open is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {t : Set.{u1} E} {x : E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsOpen.{u1} E _inst_1 t) -> (Not (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x t)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => forall (b : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) b t) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f x) (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f b))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {t : Set.{u1} E} {x : E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsOpen.{u1} E _inst_1 t) -> (Not (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x t)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => forall (b : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) b t) -> (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))
+Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_point_open geometric_hahn_banach_point_openₓ'. -/
 theorem geometric_hahn_banach_point_open (ht₁ : Convex ℝ t) (ht₂ : IsOpen t) (disj : x ∉ t) :
     ∃ f : E →L[ℝ] ℝ, ∀ b ∈ t, f x < f b :=
   let ⟨f, hf⟩ := geometric_hahn_banach_open_point ht₁ ht₂ disj
   ⟨-f, by simpa⟩
 #align geometric_hahn_banach_point_open geometric_hahn_banach_point_open
 
+/- warning: geometric_hahn_banach_open_open -> geometric_hahn_banach_open_open is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsOpen.{u1} E _inst_1 t) -> (Disjoint.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => And (forall (a : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) a s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f a) u)) (forall (b : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) b t) -> (LT.lt.{0} Real Real.hasLt u (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f b))))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsOpen.{u1} E _inst_1 s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsOpen.{u1} E _inst_1 t) -> (Disjoint.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} E) (Preorder.toLE.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => Exists.{1} Real (fun (u : Real) => And (forall (a : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) a s) -> (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f a) u)) (forall (b : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) b t) -> (LT.lt.{0} Real Real.instLTReal u (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))))
+Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_open_open geometric_hahn_banach_open_openₓ'. -/
 theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht₁ : Convex ℝ t)
     (ht₃ : IsOpen t) (disj : Disjoint s t) :
     ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u < f b :=
@@ -154,6 +184,12 @@ theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s
 
 variable [LocallyConvexSpace ℝ E]
 
+/- warning: geometric_hahn_banach_compact_closed -> geometric_hahn_banach_compact_closed is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsCompact.{u1} E _inst_1 s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsClosed.{u1} E _inst_1 t) -> (Disjoint.{u1} (Set.{u1} E) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.completeBooleanAlgebra.{u1} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => Exists.{1} Real (fun (v : Real) => And (forall (a : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) a s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f a) u)) (And (LT.lt.{0} Real Real.hasLt u v) (forall (b : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) b t) -> (LT.lt.{0} Real Real.hasLt v (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f b))))))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsCompact.{u1} E _inst_1 s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsClosed.{u1} E _inst_1 t) -> (Disjoint.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} E) (Preorder.toLE.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => Exists.{1} Real (fun (u : Real) => Exists.{1} Real (fun (v : Real) => And (forall (a : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) a s) -> (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f a) u)) (And (LT.lt.{0} Real Real.instLTReal u v) (forall (b : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) b t) -> (LT.lt.{0} Real Real.instLTReal v (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))))))
+Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_compact_closed geometric_hahn_banach_compact_closedₓ'. -/
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is
 compact and `t` is closed, there is a continuous linear functional which strongly separates them. -/
 theorem geometric_hahn_banach_compact_closed (hs₁ : Convex ℝ s) (hs₂ : IsCompact s)
@@ -173,6 +209,12 @@ theorem geometric_hahn_banach_compact_closed (hs₁ : Convex ℝ s) (hs₂ : IsC
       hf₂ b (tV hb)⟩
 #align geometric_hahn_banach_compact_closed geometric_hahn_banach_compact_closed
 
+/- warning: geometric_hahn_banach_closed_compact -> geometric_hahn_banach_closed_compact is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real 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(GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} E) (Set.booleanAlgebra.{u1} E))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => Exists.{1} Real (fun (v : Real) => And (forall (a : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) a s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f a) u)) (And (LT.lt.{0} Real Real.hasLt u v) (forall (b : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) b t) -> (LT.lt.{0} Real Real.hasLt v (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f b))))))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {t : Set.{u1} E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsClosed.{u1} E _inst_1 s) -> (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsCompact.{u1} E _inst_1 t) -> (Disjoint.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} E) (Preorder.toLE.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E)))))) s t) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => Exists.{1} Real (fun (u : Real) => Exists.{1} Real (fun (v : Real) => And (forall (a : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) a s) -> (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f a) u)) (And (LT.lt.{0} Real Real.instLTReal u v) (forall (b : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) b t) -> (LT.lt.{0} Real Real.instLTReal v (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))))))
+Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_closed_compact geometric_hahn_banach_closed_compactₓ'. -/
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is
 closed, and `t` is compact, there is a continuous linear functional which strongly separates them.
 -/
@@ -183,6 +225,12 @@ theorem geometric_hahn_banach_closed_compact (hs₁ : Convex ℝ s) (hs₂ : IsC
   ⟨-f, -t, -s, by simpa using ht, by simpa using st, by simpa using hs⟩
 #align geometric_hahn_banach_closed_compact geometric_hahn_banach_closed_compact
 
+/- warning: geometric_hahn_banach_point_closed -> geometric_hahn_banach_point_closed is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {t : Set.{u1} E} {x : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsClosed.{u1} E _inst_1 t) -> (Not (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x t)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => And (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f x) u) (forall (b : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) b t) -> (LT.lt.{0} Real Real.hasLt u (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f b))))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {t : Set.{u1} E} {x : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) t) -> (IsClosed.{u1} E _inst_1 t) -> (Not (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x t)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => Exists.{1} Real (fun (u : Real) => And (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x) u) (forall (b : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) b t) -> (LT.lt.{0} Real Real.instLTReal u (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f b))))))
+Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_point_closed geometric_hahn_banach_point_closedₓ'. -/
 theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClosed t) (disj : x ∉ t) :
     ∃ (f : E →L[ℝ] ℝ)(u : ℝ), f x < u ∧ ∀ b ∈ t, u < f b :=
   let ⟨f, u, v, ha, hst, hb⟩ :=
@@ -191,6 +239,12 @@ theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClo
   ⟨f, v, hst.trans' <| ha x <| mem_singleton _, hb⟩
 #align geometric_hahn_banach_point_closed geometric_hahn_banach_point_closed
 
+/- warning: geometric_hahn_banach_closed_point -> geometric_hahn_banach_closed_point is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {x : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsClosed.{u1} E _inst_1 s) -> (Not (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => Exists.{1} Real (fun (u : Real) => And (forall (a : E), (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) a s) -> (LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f a) u)) (LT.lt.{0} Real Real.hasLt u (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f x)))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} {x : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsClosed.{u1} E _inst_1 s) -> (Not (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s)) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => Exists.{1} Real (fun (u : Real) => And (forall (a : E), (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) a s) -> (LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f a) u)) (LT.lt.{0} Real Real.instLTReal u (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x)))))
+Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_closed_point geometric_hahn_banach_closed_pointₓ'. -/
 theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) (disj : x ∉ s) :
     ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ u < f x :=
   let ⟨f, s, t, ha, hst, hb⟩ :=
@@ -199,6 +253,12 @@ theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClo
   ⟨f, s, ha, hst.trans <| hb x <| mem_singleton _⟩
 #align geometric_hahn_banach_closed_point geometric_hahn_banach_closed_point
 
+/- warning: geometric_hahn_banach_point_point -> geometric_hahn_banach_point_point is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {x : E} {y : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1] [_inst_7 : T1Space.{u1} E _inst_1], (Ne.{succ u1} E x y) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => LT.lt.{0} Real Real.hasLt (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f x) (coeFn.{succ u1, succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) f y)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {x : E} {y : E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1] [_inst_7 : T1Space.{u1} E _inst_1], (Ne.{succ u1} E x y) -> (Exists.{succ u1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (f : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => LT.lt.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) Real.instLTReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f x) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) _x) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) f y)))
+Case conversion may be inaccurate. Consider using '#align geometric_hahn_banach_point_point geometric_hahn_banach_point_pointₓ'. -/
 /-- See also `normed_space.eq_iff_forall_dual_eq`. -/
 theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f : E →L[ℝ] ℝ, f x < f y :=
   by
@@ -208,6 +268,12 @@ theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f :
   exact ⟨f, by linarith [hs x rfl, ht y rfl]⟩
 #align geometric_hahn_banach_point_point geometric_hahn_banach_point_point
 
+/- warning: Inter_halfspaces_eq -> iInter_halfspaces_eq is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) 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(PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) (fun (_x : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) => E -> Real) (ContinuousLinearMap.toFun.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.addCommMonoid _inst_4 Real.module) l y)))))) s)
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} E] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : TopologicalAddGroup.{u1} E _inst_1 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : ContinuousSMul.{0, u1} Real E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) _inst_1] {s : Set.{u1} E} [_inst_6 : LocallyConvexSpace.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4 _inst_1], (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) s) -> (IsClosed.{u1} E _inst_1 s) -> (Eq.{succ u1} (Set.{u1} E) (Set.iInter.{u1, succ u1} E (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) (fun (l : ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) => setOf.{u1} E (fun (x : E) => Exists.{succ u1} E (fun (y : E) => And (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) y s) (LE.le.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) x) Real.instLEReal (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (a : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) l x) (FunLike.coe.{succ u1, succ u1, 1} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E (fun (a : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => Real) a) (ContinuousMapClass.toFunLike.{u1, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) E Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, 0, 0, u1, 0} (ContinuousLinearMap.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))) Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField)) (ContinuousLinearMap.continuousSemilinearMapClass.{0, 0, u1, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.instAddCommMonoidReal _inst_4 (NormedSpace.toModule.{0, 0} Real Real Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (NormedField.toNormedSpace.{0} Real Real.normedField))))) l y)))))) s)
+Case conversion may be inaccurate. Consider using '#align Inter_halfspaces_eq iInter_halfspaces_eqₓ'. -/
 /-- A closed convex set is the intersection of the halfspaces containing it. -/
 theorem iInter_halfspaces_eq (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) :
     (⋂ l : E →L[ℝ] ℝ, { x | ∃ y ∈ s, l x ≤ l y }) = s :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

@@ -4,12 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.normed_space.hahn_banach.separation
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 915591b2bb3ea303648db07284a161a7f2a9e3d4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Cone.Basic
 import Mathbin.Analysis.Convex.Gauge
+import Mathbin.Topology.Algebra.Module.FiniteDimension
 import Mathbin.Topology.Algebra.Module.LocallyConvex
 
 /-!

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

@@ -112,10 +112,10 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
   refine' ⟨f, Inf (f '' t), image_subset_iff.1 (_ : f '' s ⊆ Iio (Inf (f '' t))), fun b hb => _⟩
   · rw [← interior_Iic]
     refine' interior_maximal (image_subset_iff.2 fun a ha => _) (f.is_open_map_of_ne_zero _ _ hs₂)
-    · exact le_cinfₛ (nonempty.image _ ⟨_, hb₀⟩) (ball_image_of_ball <| forall_le _ ha)
+    · exact le_csInf (nonempty.image _ ⟨_, hb₀⟩) (ball_image_of_ball <| forall_le _ ha)
     · rintro rfl
       simpa using hf₁
-  · exact cinfₛ_le ⟨f a₀, ball_image_of_ball <| forall_le _ ha₀⟩ (mem_image_of_mem _ hb)
+  · exact csInf_le ⟨f a₀, ball_image_of_ball <| forall_le _ ha₀⟩ (mem_image_of_mem _ hb)
 #align geometric_hahn_banach_open geometric_hahn_banach_open
 
 theorem geometric_hahn_banach_open_point (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (disj : x ∉ s) :
@@ -208,14 +208,14 @@ theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) : ∃ f :
 #align geometric_hahn_banach_point_point geometric_hahn_banach_point_point
 
 /-- A closed convex set is the intersection of the halfspaces containing it. -/
-theorem interᵢ_halfspaces_eq (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) :
+theorem iInter_halfspaces_eq (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) :
     (⋂ l : E →L[ℝ] ℝ, { x | ∃ y ∈ s, l x ≤ l y }) = s :=
   by
-  rw [Set.interᵢ_setOf]
+  rw [Set.iInter_setOf]
   refine' Set.Subset.antisymm (fun x hx => _) fun x hx l => ⟨x, hx, le_rfl⟩
   by_contra
   obtain ⟨l, s, hlA, hl⟩ := geometric_hahn_banach_closed_point hs₁ hs₂ h
   obtain ⟨y, hy, hxy⟩ := hx l
   exact ((hxy.trans_lt (hlA y hy)).trans hl).not_le le_rfl
-#align Inter_halfspaces_eq interᵢ_halfspaces_eq
+#align Inter_halfspaces_eq iInter_halfspaces_eq
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

@@ -50,13 +50,13 @@ theorem separate_convex_open_set [TopologicalSpace E] [AddCommGroup E] [Topologi
     [Module ℝ E] [ContinuousSMul ℝ E] {s : Set E} (hs₀ : (0 : E) ∈ s) (hs₁ : Convex ℝ s)
     (hs₂ : IsOpen s) {x₀ : E} (hx₀ : x₀ ∉ s) : ∃ f : E →L[ℝ] ℝ, f x₀ = 1 ∧ ∀ x ∈ s, f x < 1 :=
   by
-  let f : E →ₗ.[ℝ] ℝ := LinearPmap.mkSpanSingleton x₀ 1 (ne_of_mem_of_not_mem hs₀ hx₀).symm
+  let f : E →ₗ.[ℝ] ℝ := LinearPMap.mkSpanSingleton x₀ 1 (ne_of_mem_of_not_mem hs₀ hx₀).symm
   obtain ⟨φ, hφ₁, hφ₂⟩ :=
     exists_extension_of_le_sublinear f (gauge s) (fun c hc => gauge_smul_of_nonneg hc.le)
       (gauge_add_le hs₁ <| absorbent_nhds_zero <| hs₂.mem_nhds hs₀) _
   have hφ₃ : φ x₀ = 1 := by
     rw [← Submodule.coe_mk x₀ (Submodule.mem_span_singleton_self _), hφ₁,
-      LinearPmap.mkSpanSingleton'_apply_self]
+      LinearPMap.mkSpanSingleton'_apply_self]
   have hφ₄ : ∀ x ∈ s, φ x < 1 := fun x hx =>
     (hφ₂ x).trans_lt (gauge_lt_one_of_mem_of_open hs₁ hs₀ hs₂ hx)
   · refine' ⟨⟨φ, _⟩, hφ₃, hφ₄⟩
@@ -69,7 +69,7 @@ theorem separate_convex_open_set [TopologicalSpace E] [AddCommGroup E] [Topologi
     linarith
   rintro ⟨x, hx⟩
   obtain ⟨y, rfl⟩ := Submodule.mem_span_singleton.1 hx
-  rw [LinearPmap.mkSpanSingleton'_apply]
+  rw [LinearPMap.mkSpanSingleton'_apply]
   simp only [mul_one, Algebra.id.smul_eq_mul, Submodule.coe_mk]
   obtain h | h := le_or_lt y 0
   · exact h.trans (gauge_nonneg _)

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

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

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

@@ -106,10 +106,10 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
   refine' ⟨f, sInf (f '' t), image_subset_iff.1 (_ : f '' s ⊆ Iio (sInf (f '' t))), fun b hb => _⟩
   · rw [← interior_Iic]
     refine' interior_maximal (image_subset_iff.2 fun a ha => _) (f.isOpenMap_of_ne_zero _ _ hs₂)
-    · exact le_csInf (Nonempty.image _ ⟨_, hb₀⟩) (ball_image_of_ball <| forall_le _ ha)
+    · exact le_csInf (Nonempty.image _ ⟨_, hb₀⟩) (forall_mem_image.2 <| forall_le _ ha)
     · rintro rfl
       simp at hf₁
-  · exact csInf_le ⟨f a₀, ball_image_of_ball <| forall_le _ ha₀⟩ (mem_image_of_mem _ hb)
+  · exact csInf_le ⟨f a₀, forall_mem_image.2 <| forall_le _ ha₀⟩ (mem_image_of_mem _ hb)
 #align geometric_hahn_banach_open geometric_hahn_banach_open
 
 theorem geometric_hahn_banach_open_point (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (disj : x ∉ s) :

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

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

@@ -90,7 +90,7 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
   let x₀ := b₀ - a₀
   let C := x₀ +ᵥ (s - t)
   have : (0 : E) ∈ C :=
-    ⟨a₀ - b₀, sub_mem_sub ha₀ hb₀, by simp_rw [vadd_eq_add, sub_add_sub_cancel', sub_self]⟩
+    ⟨a₀ - b₀, sub_mem_sub ha₀ hb₀, by simp_rw [x₀, vadd_eq_add, sub_add_sub_cancel', sub_self]⟩
   have : Convex ℝ C := (hs₁.sub ht).vadd _
   have : x₀ ∉ C := by
     intro hx₀

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

@@ -97,7 +97,7 @@ theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht
     rw [← add_zero x₀] at hx₀
     exact disj.zero_not_mem_sub_set (vadd_mem_vadd_set_iff.1 hx₀)
   obtain ⟨f, hf₁, hf₂⟩ := separate_convex_open_set ‹0 ∈ C› ‹_› (hs₂.sub_right.vadd _) ‹x₀ ∉ C›
-  have : f b₀ = f a₀ + 1 := by simp [← hf₁]
+  have : f b₀ = f a₀ + 1 := by simp [x₀, ← hf₁]
   have forall_le : ∀ a ∈ s, ∀ b ∈ t, f a ≤ f b := by
     intro a ha b hb
     have := hf₂ (x₀ + (a - b)) (vadd_mem_vadd_set <| sub_mem_sub ha hb)

Mostly, this means replacing "of_open" by "of_isOpen". A few lemmas names were misleading and are corrected differently. Zulip discussion.

@@ -55,7 +55,7 @@ theorem separate_convex_open_set [TopologicalSpace E] [AddCommGroup E] [Topologi
     rw [← f.domain.coe_mk x₀ (Submodule.mem_span_singleton_self _), hφ₁,
       LinearPMap.mkSpanSingleton'_apply_self]
   have hφ₄ : ∀ x ∈ s, φ x < 1 := fun x hx =>
-    (hφ₂ x).trans_lt (gauge_lt_one_of_mem_of_open hs₂ hx)
+    (hφ₂ x).trans_lt (gauge_lt_one_of_mem_of_isOpen hs₂ hx)
   · refine' ⟨⟨φ, _⟩, hφ₃, hφ₄⟩
     refine'
       φ.continuous_of_nonzero_on_open _ (hs₂.vadd (-x₀)) (Nonempty.vadd_set ⟨0, hs₀⟩)

Splits Mathlib.Analysis.Convex.Cone.Basic, to move Riesz extension and Hahn-Banach out of the basic file about definitions.

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Bhavik Mehta All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Yaël Dillies
 -/
-import Mathlib.Analysis.Convex.Cone.Basic
+import Mathlib.Analysis.Convex.Cone.Extension
 import Mathlib.Analysis.Convex.Gauge
 import Mathlib.Topology.Algebra.Module.FiniteDimension
 import Mathlib.Topology.Algebra.Module.LocallyConvex

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

This has nice performance benefits.

@@ -39,7 +39,7 @@ open Set
 
 open Pointwise
 
-variable {𝕜 E : Type _}
+variable {𝕜 E : Type*}
 
 /-- Given a set `s` which is a convex neighbourhood of `0` and a point `x₀` outside of it, there is
 a continuous linear functional `f` separating `x₀` and `s`, in the sense that it sends `x₀` to 1 and

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Bhavik Mehta All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Yaël Dillies
-
-! This file was ported from Lean 3 source module analysis.normed_space.hahn_banach.separation
-! leanprover-community/mathlib commit 915591b2bb3ea303648db07284a161a7f2a9e3d4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Convex.Cone.Basic
 import Mathlib.Analysis.Convex.Gauge
 import Mathlib.Topology.Algebra.Module.FiniteDimension
 import Mathlib.Topology.Algebra.Module.LocallyConvex
 
+#align_import analysis.normed_space.hahn_banach.separation from "leanprover-community/mathlib"@"915591b2bb3ea303648db07284a161a7f2a9e3d4"
+
 /-!
 # Separation Hahn-Banach theorem
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -51,7 +51,7 @@ theorem separate_convex_open_set [TopologicalSpace E] [AddCommGroup E] [Topologi
     [Module ℝ E] [ContinuousSMul ℝ E] {s : Set E} (hs₀ : (0 : E) ∈ s) (hs₁ : Convex ℝ s)
     (hs₂ : IsOpen s) {x₀ : E} (hx₀ : x₀ ∉ s) : ∃ f : E →L[ℝ] ℝ, f x₀ = 1 ∧ ∀ x ∈ s, f x < 1 := by
   let f : E →ₗ.[ℝ] ℝ := LinearPMap.mkSpanSingleton x₀ 1 (ne_of_mem_of_not_mem hs₀ hx₀).symm
-  have :=  exists_extension_of_le_sublinear f (gauge s) (fun c hc => gauge_smul_of_nonneg hc.le)
+  have := exists_extension_of_le_sublinear f (gauge s) (fun c hc => gauge_smul_of_nonneg hc.le)
     (gauge_add_le hs₁ <| absorbent_nhds_zero <| hs₂.mem_nhds hs₀) ?_
   obtain ⟨φ, hφ₁, hφ₂⟩ := this
   have hφ₃ : φ x₀ = 1 := by

@@ -206,7 +206,7 @@ theorem geometric_hahn_banach_point_point [T1Space E] (hxy : x ≠ y) :
 
 /-- A closed convex set is the intersection of the halfspaces containing it. -/
 theorem iInter_halfspaces_eq (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) :
-    (⋂ l : E →L[ℝ] ℝ, { x | ∃ y ∈ s, l x ≤ l y }) = s := by
+    ⋂ l : E →L[ℝ] ℝ, { x | ∃ y ∈ s, l x ≤ l y } = s := by
   rw [Set.iInter_setOf]
   refine' Set.Subset.antisymm (fun x hx => _) fun x hx l => ⟨x, hx, le_rfl⟩
   by_contra h

Drop unneeded assumptions in gauge_lt_one_of_mem_of_open and gauge_lt_of_mem_smul

@@ -58,7 +58,7 @@ theorem separate_convex_open_set [TopologicalSpace E] [AddCommGroup E] [Topologi
     rw [← f.domain.coe_mk x₀ (Submodule.mem_span_singleton_self _), hφ₁,
       LinearPMap.mkSpanSingleton'_apply_self]
   have hφ₄ : ∀ x ∈ s, φ x < 1 := fun x hx =>
-    (hφ₂ x).trans_lt (gauge_lt_one_of_mem_of_open hs₁ hs₀ hs₂ hx)
+    (hφ₂ x).trans_lt (gauge_lt_one_of_mem_of_open hs₂ hx)
   · refine' ⟨⟨φ, _⟩, hφ₃, hφ₄⟩
     refine'
       φ.continuous_of_nonzero_on_open _ (hs₂.vadd (-x₀)) (Nonempty.vadd_set ⟨0, hs₀⟩)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -85,7 +85,7 @@ variable [TopologicalSpace E] [AddCommGroup E] [TopologicalAddGroup E] [Module 
 /-- A version of the **Hahn-Banach theorem**: given disjoint convex sets `s`, `t` where `s` is open,
 there is a continuous linear functional which separates them. -/
 theorem geometric_hahn_banach_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht : Convex ℝ t)
-    (disj : Disjoint s t) : ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u ≤ f b := by
+    (disj : Disjoint s t) : ∃ (f : E →L[ℝ] ℝ) (u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u ≤ f b := by
   obtain rfl | ⟨a₀, ha₀⟩ := s.eq_empty_or_nonempty
   · exact ⟨0, 0, by simp, fun b _hb => le_rfl⟩
   obtain rfl | ⟨b₀, hb₀⟩ := t.eq_empty_or_nonempty
@@ -130,7 +130,7 @@ theorem geometric_hahn_banach_point_open (ht₁ : Convex ℝ t) (ht₂ : IsOpen
 
 theorem geometric_hahn_banach_open_open (hs₁ : Convex ℝ s) (hs₂ : IsOpen s) (ht₁ : Convex ℝ t)
     (ht₃ : IsOpen t) (disj : Disjoint s t) :
-    ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u < f b := by
+    ∃ (f : E →L[ℝ] ℝ) (u : ℝ), (∀ a ∈ s, f a < u) ∧ ∀ b ∈ t, u < f b := by
   obtain rfl | ⟨a₀, ha₀⟩ := s.eq_empty_or_nonempty
   · exact ⟨0, -1, by simp, fun b _hb => by norm_num⟩
   obtain rfl | ⟨b₀, hb₀⟩ := t.eq_empty_or_nonempty
@@ -155,7 +155,7 @@ variable [LocallyConvexSpace ℝ E]
 compact and `t` is closed, there is a continuous linear functional which strongly separates them. -/
 theorem geometric_hahn_banach_compact_closed (hs₁ : Convex ℝ s) (hs₂ : IsCompact s)
     (ht₁ : Convex ℝ t) (ht₂ : IsClosed t) (disj : Disjoint s t) :
-    ∃ (f : E →L[ℝ] ℝ)(u v : ℝ), (∀ a ∈ s, f a < u) ∧ u < v ∧ ∀ b ∈ t, v < f b := by
+    ∃ (f : E →L[ℝ] ℝ) (u v : ℝ), (∀ a ∈ s, f a < u) ∧ u < v ∧ ∀ b ∈ t, v < f b := by
   obtain rfl | hs := s.eq_empty_or_nonempty
   · exact ⟨0, -2, -1, by simp, by norm_num, fun b _hb => by norm_num⟩
   obtain rfl | _ht := t.eq_empty_or_nonempty
@@ -174,13 +174,13 @@ closed, and `t` is compact, there is a continuous linear functional which strong
 -/
 theorem geometric_hahn_banach_closed_compact (hs₁ : Convex ℝ s) (hs₂ : IsClosed s)
     (ht₁ : Convex ℝ t) (ht₂ : IsCompact t) (disj : Disjoint s t) :
-    ∃ (f : E →L[ℝ] ℝ)(u v : ℝ), (∀ a ∈ s, f a < u) ∧ u < v ∧ ∀ b ∈ t, v < f b :=
+    ∃ (f : E →L[ℝ] ℝ) (u v : ℝ), (∀ a ∈ s, f a < u) ∧ u < v ∧ ∀ b ∈ t, v < f b :=
   let ⟨f, s, t, hs, st, ht⟩ := geometric_hahn_banach_compact_closed ht₁ ht₂ hs₁ hs₂ disj.symm
   ⟨-f, -t, -s, by simpa using ht, by simpa using st, by simpa using hs⟩
 #align geometric_hahn_banach_closed_compact geometric_hahn_banach_closed_compact
 
 theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClosed t) (disj : x ∉ t) :
-    ∃ (f : E →L[ℝ] ℝ)(u : ℝ), f x < u ∧ ∀ b ∈ t, u < f b :=
+    ∃ (f : E →L[ℝ] ℝ) (u : ℝ), f x < u ∧ ∀ b ∈ t, u < f b :=
   let ⟨f, _u, v, ha, hst, hb⟩ :=
     geometric_hahn_banach_compact_closed (convex_singleton x) isCompact_singleton ht₁ ht₂
       (disjoint_singleton_left.2 disj)
@@ -188,7 +188,7 @@ theorem geometric_hahn_banach_point_closed (ht₁ : Convex ℝ t) (ht₂ : IsClo
 #align geometric_hahn_banach_point_closed geometric_hahn_banach_point_closed
 
 theorem geometric_hahn_banach_closed_point (hs₁ : Convex ℝ s) (hs₂ : IsClosed s) (disj : x ∉ s) :
-    ∃ (f : E →L[ℝ] ℝ)(u : ℝ), (∀ a ∈ s, f a < u) ∧ u < f x :=
+    ∃ (f : E →L[ℝ] ℝ) (u : ℝ), (∀ a ∈ s, f a < u) ∧ u < f x :=
   let ⟨f, s, _t, ha, hst, hb⟩ :=
     geometric_hahn_banach_closed_compact hs₁ hs₂ (convex_singleton x) isCompact_singleton
       (disjoint_singleton_right.2 disj)