topology.algebra.module.locally_convex ⟷ Mathlib.Topology.Algebra.Module.LocallyConvex

This file has been ported!

Changes since the initial port

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

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -158,13 +158,13 @@ theorem Disjoint.exists_open_convexes [LocallyConvexSpace π•œ E] {s t : Set E}
   letI : UniformSpace E := TopologicalAddGroup.toUniformSpace E
   haveI : UniformAddGroup E := comm_topologicalAddGroup_is_uniform
   have := (LocallyConvexSpace.convex_open_basis_zero π•œ E).comap fun x : E Γ— E => x.2 - x.1
-  rw [← uniformity_eq_comap_nhds_zero] at this 
+  rw [← uniformity_eq_comap_nhds_zero] at this
   rcases disj.exists_uniform_thickening_of_basis this hsβ‚‚ htβ‚‚ with ⟨V, ⟨hV0, hVopen, hVconvex⟩, hV⟩
   refine'
     ⟨s + V, t + V, hVopen.add_left, hVopen.add_left, hs₁.add hVconvex, ht₁.add hVconvex,
       subset_add_left _ hV0, subset_add_left _ hV0, _⟩
   simp_rw [← Union_add_left_image, image_add_left]
-  simp_rw [UniformSpace.ball, ← preimage_comp, sub_eq_neg_add] at hV 
+  simp_rw [UniformSpace.ball, ← preimage_comp, sub_eq_neg_add] at hV
   exact hV
 #align disjoint.exists_open_convexes Disjoint.exists_open_convexes
 -/
Diff
@@ -3,7 +3,7 @@ Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 -/
-import Mathbin.Analysis.Convex.Topology
+import Analysis.Convex.Topology
 
 #align_import topology.algebra.module.locally_convex from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 
Diff
@@ -2,14 +2,11 @@
 Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module topology.algebra.module.locally_convex
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Topology
 
+#align_import topology.algebra.module.locally_convex from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 # Locally convex topological modules
 
Diff
@@ -54,10 +54,12 @@ class LocallyConvexSpace (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommMonoid
 
 variable (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E] [TopologicalSpace E]
 
+#print locallyConvexSpace_iff /-
 theorem locallyConvexSpace_iff :
     LocallyConvexSpace π•œ E ↔ βˆ€ x : E, (𝓝 x).HasBasis (fun s : Set E => s ∈ 𝓝 x ∧ Convex π•œ s) id :=
   ⟨@LocallyConvexSpace.convex_basis _ _ _ _ _ _, LocallyConvexSpace.mk⟩
 #align locally_convex_space_iff locallyConvexSpace_iff
+-/
 
 #print LocallyConvexSpace.ofBases /-
 theorem LocallyConvexSpace.ofBases {ΞΉ : Type _} (b : E β†’ ΞΉ β†’ Set E) (p : E β†’ ΞΉ β†’ Prop)
@@ -71,15 +73,19 @@ theorem LocallyConvexSpace.ofBases {ΞΉ : Type _} (b : E β†’ ΞΉ β†’ Set E) (p : E
 #align locally_convex_space.of_bases LocallyConvexSpace.ofBases
 -/
 
+#print LocallyConvexSpace.convex_basis_zero /-
 theorem LocallyConvexSpace.convex_basis_zero [LocallyConvexSpace π•œ E] :
     (𝓝 0 : Filter E).HasBasis (fun s => s ∈ (𝓝 0 : Filter E) ∧ Convex π•œ s) id :=
   LocallyConvexSpace.convex_basis 0
 #align locally_convex_space.convex_basis_zero LocallyConvexSpace.convex_basis_zero
+-/
 
+#print locallyConvexSpace_iff_exists_convex_subset /-
 theorem locallyConvexSpace_iff_exists_convex_subset :
     LocallyConvexSpace π•œ E ↔ βˆ€ x : E, βˆ€ U ∈ 𝓝 x, βˆƒ S ∈ 𝓝 x, Convex π•œ S ∧ S βŠ† U :=
   (locallyConvexSpace_iff π•œ E).trans (forall_congr' fun x => hasBasis_self)
 #align locally_convex_space_iff_exists_convex_subset locallyConvexSpace_iff_exists_convex_subset
+-/
 
 end Semimodule
 
@@ -88,6 +94,7 @@ section Module
 variable (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
   [TopologicalAddGroup E]
 
+#print LocallyConvexSpace.ofBasisZero /-
 theorem LocallyConvexSpace.ofBasisZero {ΞΉ : Type _} (b : ΞΉ β†’ Set E) (p : ΞΉ β†’ Prop)
     (hbasis : (𝓝 0).HasBasis p b) (hconvex : βˆ€ i, p i β†’ Convex π•œ (b i)) : LocallyConvexSpace π•œ E :=
   by
@@ -97,18 +104,23 @@ theorem LocallyConvexSpace.ofBasisZero {ΞΉ : Type _} (b : ΞΉ β†’ Set E) (p : ΞΉ
   rw [← map_add_left_nhds_zero]
   exact hbasis.map _
 #align locally_convex_space.of_basis_zero LocallyConvexSpace.ofBasisZero
+-/
 
+#print locallyConvexSpace_iff_zero /-
 theorem locallyConvexSpace_iff_zero :
     LocallyConvexSpace π•œ E ↔
       (𝓝 0 : Filter E).HasBasis (fun s : Set E => s ∈ (𝓝 0 : Filter E) ∧ Convex π•œ s) id :=
   ⟨fun h => @LocallyConvexSpace.convex_basis _ _ _ _ _ _ h 0, fun h =>
     LocallyConvexSpace.ofBasisZero π•œ E _ _ h fun s => And.right⟩
 #align locally_convex_space_iff_zero locallyConvexSpace_iff_zero
+-/
 
+#print locallyConvexSpace_iff_exists_convex_subset_zero /-
 theorem locallyConvexSpace_iff_exists_convex_subset_zero :
     LocallyConvexSpace π•œ E ↔ βˆ€ U ∈ (𝓝 0 : Filter E), βˆƒ S ∈ (𝓝 0 : Filter E), Convex π•œ S ∧ S βŠ† U :=
   (locallyConvexSpace_iff_zero π•œ E).trans hasBasis_self
 #align locally_convex_space_iff_exists_convex_subset_zero locallyConvexSpace_iff_exists_convex_subset_zero
+-/
 
 #print LocallyConvexSpace.toLocallyConnectedSpace /-
 -- see Note [lower instance priority]
@@ -126,6 +138,7 @@ section LinearOrderedField
 variable (π•œ E : Type _) [LinearOrderedField π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
   [TopologicalAddGroup E] [ContinuousConstSMul π•œ E]
 
+#print LocallyConvexSpace.convex_open_basis_zero /-
 theorem LocallyConvexSpace.convex_open_basis_zero [LocallyConvexSpace π•œ E] :
     (𝓝 0 : Filter E).HasBasis (fun s => (0 : E) ∈ s ∧ IsOpen s ∧ Convex π•œ s) id :=
   (LocallyConvexSpace.convex_basis_zero π•œ E).to_hasBasis
@@ -134,9 +147,11 @@ theorem LocallyConvexSpace.convex_open_basis_zero [LocallyConvexSpace π•œ E] :
         interior_subset⟩)
     fun s hs => ⟨s, ⟨hs.2.1.mem_nhds hs.1, hs.2.2⟩, subset_rfl⟩
 #align locally_convex_space.convex_open_basis_zero LocallyConvexSpace.convex_open_basis_zero
+-/
 
 variable {π•œ E}
 
+#print Disjoint.exists_open_convexes /-
 /-- In a locally convex space, if `s`, `t` are disjoint convex sets, `s` is compact and `t` is
 closed, then we can find open disjoint convex sets containing them. -/
 theorem Disjoint.exists_open_convexes [LocallyConvexSpace π•œ E] {s t : Set E} (disj : Disjoint s t)
@@ -155,6 +170,7 @@ theorem Disjoint.exists_open_convexes [LocallyConvexSpace π•œ E] {s t : Set E}
   simp_rw [UniformSpace.ball, ← preimage_comp, sub_eq_neg_add] at hV 
   exact hV
 #align disjoint.exists_open_convexes Disjoint.exists_open_convexes
+-/
 
 end LinearOrderedField
 
@@ -163,6 +179,7 @@ section LatticeOps
 variable {ΞΉ : Sort _} {π•œ E F : Type _} [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E]
   [AddCommMonoid F] [Module π•œ F]
 
+#print locallyConvexSpace_sInf /-
 theorem locallyConvexSpace_sInf {ts : Set (TopologicalSpace E)}
     (h : βˆ€ t ∈ ts, @LocallyConvexSpace π•œ E _ _ _ t) : @LocallyConvexSpace π•œ E _ _ _ (sInf ts) :=
   by
@@ -175,7 +192,9 @@ theorem locallyConvexSpace_sInf {ts : Set (TopologicalSpace E)}
   rw [nhds_sInf, ← iInf_subtype'']
   exact has_basis_infi' fun i : ts => (@locallyConvexSpace_iff π•œ E _ _ _ ↑i).mp (h (↑i) i.2) x
 #align locally_convex_space_Inf locallyConvexSpace_sInf
+-/
 
+#print locallyConvexSpace_iInf /-
 theorem locallyConvexSpace_iInf {ts' : ΞΉ β†’ TopologicalSpace E}
     (h' : βˆ€ i, @LocallyConvexSpace π•œ E _ _ _ (ts' i)) :
     @LocallyConvexSpace π•œ E _ _ _ (β¨… i, ts' i) :=
@@ -183,12 +202,16 @@ theorem locallyConvexSpace_iInf {ts' : ΞΉ β†’ TopologicalSpace E}
   refine' locallyConvexSpace_sInf _
   rwa [forall_range_iff]
 #align locally_convex_space_infi locallyConvexSpace_iInf
+-/
 
+#print locallyConvexSpace_inf /-
 theorem locallyConvexSpace_inf {t₁ tβ‚‚ : TopologicalSpace E} (h₁ : @LocallyConvexSpace π•œ E _ _ _ t₁)
     (hβ‚‚ : @LocallyConvexSpace π•œ E _ _ _ tβ‚‚) : @LocallyConvexSpace π•œ E _ _ _ (t₁ βŠ“ tβ‚‚) := by
   rw [inf_eq_iInf]; refine' locallyConvexSpace_iInf fun b => _; cases b <;> assumption
 #align locally_convex_space_inf locallyConvexSpace_inf
+-/
 
+#print locallyConvexSpace_induced /-
 theorem locallyConvexSpace_induced {t : TopologicalSpace F} [LocallyConvexSpace π•œ F]
     (f : E β†’β‚—[π•œ] F) : @LocallyConvexSpace π•œ E _ _ _ (t.induced f) :=
   by
@@ -200,6 +223,7 @@ theorem locallyConvexSpace_induced {t : TopologicalSpace F} [LocallyConvexSpace
   rw [nhds_induced]
   exact (LocallyConvexSpace.convex_basis <| f x).comap f
 #align locally_convex_space_induced locallyConvexSpace_induced
+-/
 
 instance {ΞΉ : Type _} {X : ΞΉ β†’ Type _} [βˆ€ i, AddCommMonoid (X i)] [βˆ€ i, TopologicalSpace (X i)]
     [βˆ€ i, Module π•œ (X i)] [βˆ€ i, LocallyConvexSpace π•œ (X i)] : LocallyConvexSpace π•œ (βˆ€ i, X i) :=
Diff
@@ -47,7 +47,7 @@ section Semimodule
 /-- A `locally_convex_space` is a topological semimodule over an ordered semiring in which convex
 neighborhoods of a point form a neighborhood basis at that point. -/
 class LocallyConvexSpace (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E]
-  [TopologicalSpace E] : Prop where
+    [TopologicalSpace E] : Prop where
   convex_basis : βˆ€ x : E, (𝓝 x).HasBasis (fun s : Set E => s ∈ 𝓝 x ∧ Convex π•œ s) id
 #align locally_convex_space LocallyConvexSpace
 -/
@@ -146,13 +146,13 @@ theorem Disjoint.exists_open_convexes [LocallyConvexSpace π•œ E] {s t : Set E}
   letI : UniformSpace E := TopologicalAddGroup.toUniformSpace E
   haveI : UniformAddGroup E := comm_topologicalAddGroup_is_uniform
   have := (LocallyConvexSpace.convex_open_basis_zero π•œ E).comap fun x : E Γ— E => x.2 - x.1
-  rw [← uniformity_eq_comap_nhds_zero] at this
+  rw [← uniformity_eq_comap_nhds_zero] at this 
   rcases disj.exists_uniform_thickening_of_basis this hsβ‚‚ htβ‚‚ with ⟨V, ⟨hV0, hVopen, hVconvex⟩, hV⟩
   refine'
     ⟨s + V, t + V, hVopen.add_left, hVopen.add_left, hs₁.add hVconvex, ht₁.add hVconvex,
       subset_add_left _ hV0, subset_add_left _ hV0, _⟩
   simp_rw [← Union_add_left_image, image_add_left]
-  simp_rw [UniformSpace.ball, ← preimage_comp, sub_eq_neg_add] at hV
+  simp_rw [UniformSpace.ball, ← preimage_comp, sub_eq_neg_add] at hV 
   exact hV
 #align disjoint.exists_open_convexes Disjoint.exists_open_convexes
 
Diff
@@ -39,7 +39,7 @@ In a module, this is equivalent to `0` satisfying such properties.
 
 open TopologicalSpace Filter Set
 
-open Topology Pointwise
+open scoped Topology Pointwise
 
 section Semimodule
 
Diff
@@ -54,12 +54,6 @@ class LocallyConvexSpace (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommMonoid
 
 variable (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E] [TopologicalSpace E]
 
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space_iff locallyConvexSpace_iffβ‚“'. -/
 theorem locallyConvexSpace_iff :
     LocallyConvexSpace π•œ E ↔ βˆ€ x : E, (𝓝 x).HasBasis (fun s : Set E => s ∈ 𝓝 x ∧ Convex π•œ s) id :=
   ⟨@LocallyConvexSpace.convex_basis _ _ _ _ _ _, LocallyConvexSpace.mk⟩
@@ -77,23 +71,11 @@ theorem LocallyConvexSpace.ofBases {ΞΉ : Type _} (b : E β†’ ΞΉ β†’ Set E) (p : E
 #align locally_convex_space.of_bases LocallyConvexSpace.ofBases
 -/
 
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space.convex_basis_zero LocallyConvexSpace.convex_basis_zeroβ‚“'. -/
 theorem LocallyConvexSpace.convex_basis_zero [LocallyConvexSpace π•œ E] :
     (𝓝 0 : Filter E).HasBasis (fun s => s ∈ (𝓝 0 : Filter E) ∧ Convex π•œ s) id :=
   LocallyConvexSpace.convex_basis 0
 #align locally_convex_space.convex_basis_zero LocallyConvexSpace.convex_basis_zero
 
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space_iff_exists_convex_subset locallyConvexSpace_iff_exists_convex_subsetβ‚“'. -/
 theorem locallyConvexSpace_iff_exists_convex_subset :
     LocallyConvexSpace π•œ E ↔ βˆ€ x : E, βˆ€ U ∈ 𝓝 x, βˆƒ S ∈ 𝓝 x, Convex π•œ S ∧ S βŠ† U :=
   (locallyConvexSpace_iff π•œ E).trans (forall_congr' fun x => hasBasis_self)
@@ -106,12 +88,6 @@ section Module
 variable (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
   [TopologicalAddGroup E]
 
-/- warning: locally_convex_space.of_basis_zero -> LocallyConvexSpace.ofBasisZero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space.of_basis_zero LocallyConvexSpace.ofBasisZeroβ‚“'. -/
 theorem LocallyConvexSpace.ofBasisZero {ΞΉ : Type _} (b : ΞΉ β†’ Set E) (p : ΞΉ β†’ Prop)
     (hbasis : (𝓝 0).HasBasis p b) (hconvex : βˆ€ i, p i β†’ Convex π•œ (b i)) : LocallyConvexSpace π•œ E :=
   by
@@ -122,12 +98,6 @@ theorem LocallyConvexSpace.ofBasisZero {ΞΉ : Type _} (b : ΞΉ β†’ Set E) (p : ΞΉ
   exact hbasis.map _
 #align locally_convex_space.of_basis_zero LocallyConvexSpace.ofBasisZero
 
-/- warning: locally_convex_space_iff_zero -> locallyConvexSpace_iff_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space_iff_zero locallyConvexSpace_iff_zeroβ‚“'. -/
 theorem locallyConvexSpace_iff_zero :
     LocallyConvexSpace π•œ E ↔
       (𝓝 0 : Filter E).HasBasis (fun s : Set E => s ∈ (𝓝 0 : Filter E) ∧ Convex π•œ s) id :=
@@ -135,12 +105,6 @@ theorem locallyConvexSpace_iff_zero :
     LocallyConvexSpace.ofBasisZero π•œ E _ _ h fun s => And.right⟩
 #align locally_convex_space_iff_zero locallyConvexSpace_iff_zero
 
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space_iff_exists_convex_subset_zero locallyConvexSpace_iff_exists_convex_subset_zeroβ‚“'. -/
 theorem locallyConvexSpace_iff_exists_convex_subset_zero :
     LocallyConvexSpace π•œ E ↔ βˆ€ U ∈ (𝓝 0 : Filter E), βˆƒ S ∈ (𝓝 0 : Filter E), Convex π•œ S ∧ S βŠ† U :=
   (locallyConvexSpace_iff_zero π•œ E).trans hasBasis_self
@@ -162,9 +126,6 @@ section LinearOrderedField
 variable (π•œ E : Type _) [LinearOrderedField π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
   [TopologicalAddGroup E] [ContinuousConstSMul π•œ E]
 
-/- warning: locally_convex_space.convex_open_basis_zero -> LocallyConvexSpace.convex_open_basis_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align locally_convex_space.convex_open_basis_zero LocallyConvexSpace.convex_open_basis_zeroβ‚“'. -/
 theorem LocallyConvexSpace.convex_open_basis_zero [LocallyConvexSpace π•œ E] :
     (𝓝 0 : Filter E).HasBasis (fun s => (0 : E) ∈ s ∧ IsOpen s ∧ Convex π•œ s) id :=
   (LocallyConvexSpace.convex_basis_zero π•œ E).to_hasBasis
@@ -176,9 +137,6 @@ theorem LocallyConvexSpace.convex_open_basis_zero [LocallyConvexSpace π•œ E] :
 
 variable {π•œ E}
 
-/- warning: disjoint.exists_open_convexes -> Disjoint.exists_open_convexes is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align disjoint.exists_open_convexes Disjoint.exists_open_convexesβ‚“'. -/
 /-- In a locally convex space, if `s`, `t` are disjoint convex sets, `s` is compact and `t` is
 closed, then we can find open disjoint convex sets containing them. -/
 theorem Disjoint.exists_open_convexes [LocallyConvexSpace π•œ E] {s t : Set E} (disj : Disjoint s t)
@@ -205,12 +163,6 @@ section LatticeOps
 variable {ΞΉ : Sort _} {π•œ E F : Type _} [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E]
   [AddCommMonoid F] [Module π•œ F]
 
-/- warning: locally_convex_space_Inf -> locallyConvexSpace_sInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space_Inf locallyConvexSpace_sInfβ‚“'. -/
 theorem locallyConvexSpace_sInf {ts : Set (TopologicalSpace E)}
     (h : βˆ€ t ∈ ts, @LocallyConvexSpace π•œ E _ _ _ t) : @LocallyConvexSpace π•œ E _ _ _ (sInf ts) :=
   by
@@ -224,12 +176,6 @@ theorem locallyConvexSpace_sInf {ts : Set (TopologicalSpace E)}
   exact has_basis_infi' fun i : ts => (@locallyConvexSpace_iff π•œ E _ _ _ ↑i).mp (h (↑i) i.2) x
 #align locally_convex_space_Inf locallyConvexSpace_sInf
 
-/- warning: locally_convex_space_infi -> locallyConvexSpace_iInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space_infi locallyConvexSpace_iInfβ‚“'. -/
 theorem locallyConvexSpace_iInf {ts' : ΞΉ β†’ TopologicalSpace E}
     (h' : βˆ€ i, @LocallyConvexSpace π•œ E _ _ _ (ts' i)) :
     @LocallyConvexSpace π•œ E _ _ _ (β¨… i, ts' i) :=
@@ -238,23 +184,11 @@ theorem locallyConvexSpace_iInf {ts' : ΞΉ β†’ TopologicalSpace E}
   rwa [forall_range_iff]
 #align locally_convex_space_infi locallyConvexSpace_iInf
 
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space_inf locallyConvexSpace_infβ‚“'. -/
 theorem locallyConvexSpace_inf {t₁ tβ‚‚ : TopologicalSpace E} (h₁ : @LocallyConvexSpace π•œ E _ _ _ t₁)
     (hβ‚‚ : @LocallyConvexSpace π•œ E _ _ _ tβ‚‚) : @LocallyConvexSpace π•œ E _ _ _ (t₁ βŠ“ tβ‚‚) := by
   rw [inf_eq_iInf]; refine' locallyConvexSpace_iInf fun b => _; cases b <;> assumption
 #align locally_convex_space_inf locallyConvexSpace_inf
 
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-Case conversion may be inaccurate. Consider using '#align locally_convex_space_induced locallyConvexSpace_inducedβ‚“'. -/
 theorem locallyConvexSpace_induced {t : TopologicalSpace F} [LocallyConvexSpace π•œ F]
     (f : E β†’β‚—[π•œ] F) : @LocallyConvexSpace π•œ E _ _ _ (t.induced f) :=
   by
Diff
@@ -245,11 +245,8 @@ but is expected to have type
   forall {π•œ : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] {t₁ : TopologicalSpace.{u2} E} {tβ‚‚ : TopologicalSpace.{u2} E}, (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 t₁) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 tβ‚‚) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 (Inf.inf.{u2} (TopologicalSpace.{u2} E) (Lattice.toInf.{u2} (TopologicalSpace.{u2} E) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.instCompleteLatticeTopologicalSpace.{u2} E)))) t₁ tβ‚‚))
 Case conversion may be inaccurate. Consider using '#align locally_convex_space_inf locallyConvexSpace_infβ‚“'. -/
 theorem locallyConvexSpace_inf {t₁ tβ‚‚ : TopologicalSpace E} (h₁ : @LocallyConvexSpace π•œ E _ _ _ t₁)
-    (hβ‚‚ : @LocallyConvexSpace π•œ E _ _ _ tβ‚‚) : @LocallyConvexSpace π•œ E _ _ _ (t₁ βŠ“ tβ‚‚) :=
-  by
-  rw [inf_eq_iInf]
-  refine' locallyConvexSpace_iInf fun b => _
-  cases b <;> assumption
+    (hβ‚‚ : @LocallyConvexSpace π•œ E _ _ _ tβ‚‚) : @LocallyConvexSpace π•œ E _ _ _ (t₁ βŠ“ tβ‚‚) := by
+  rw [inf_eq_iInf]; refine' locallyConvexSpace_iInf fun b => _; cases b <;> assumption
 #align locally_convex_space_inf locallyConvexSpace_inf
 
 /- warning: locally_convex_space_induced -> locallyConvexSpace_induced is a dubious translation:
Diff
@@ -163,10 +163,7 @@ variable (π•œ E : Type _) [LinearOrderedField π•œ] [AddCommGroup E] [Module 
   [TopologicalAddGroup E] [ContinuousConstSMul π•œ E]
 
 /- warning: locally_convex_space.convex_open_basis_zero -> LocallyConvexSpace.convex_open_basis_zero is a dubious translation:
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(Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} 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(LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))) (id.{succ u2} (Set.{u2} E))
-but is expected to have type
-  forall (π•œ : Type.{u2}) (E : Type.{u1}) [_inst_1 : LinearOrderedField.{u2} π•œ] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : TopologicalSpace.{u1} E] [_inst_5 : TopologicalAddGroup.{u1} E _inst_4 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_6 : ContinuousConstSMul.{u2, u1} π•œ E _inst_4 (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] [_inst_7 : LocallyConvexSpace.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_4], Filter.HasBasis.{u1, succ u1} E (Set.{u1} E) (nhds.{u1} E _inst_4 (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)))))))) (fun (s : Set.{u1} E) => And (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) (And (IsOpen.{u1} E _inst_4 s) (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s))) (id.{succ u1} (Set.{u1} E))
+<too large>
 Case conversion may be inaccurate. Consider using '#align locally_convex_space.convex_open_basis_zero LocallyConvexSpace.convex_open_basis_zeroβ‚“'. -/
 theorem LocallyConvexSpace.convex_open_basis_zero [LocallyConvexSpace π•œ E] :
     (𝓝 0 : Filter E).HasBasis (fun s => (0 : E) ∈ s ∧ IsOpen s ∧ Convex π•œ s) id :=
@@ -180,10 +177,7 @@ theorem LocallyConvexSpace.convex_open_basis_zero [LocallyConvexSpace π•œ E] :
 variable {π•œ E}
 
 /- warning: disjoint.exists_open_convexes -> Disjoint.exists_open_convexes is a dubious translation:
-lean 3 declaration is
-  forall {π•œ : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} π•œ] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_6 : ContinuousConstSMul.{u1, u2} π•œ E _inst_4 (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] [_inst_7 : LocallyConvexSpace.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_4] {s : Set.{u2} E} {t : Set.{u2} E}, (Disjoint.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E))) s t) -> (Convex.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s) -> (IsCompact.{u2} E _inst_4 s) -> (Convex.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) t) -> (IsClosed.{u2} E _inst_4 t) -> (Exists.{succ u2} (Set.{u2} E) (fun (u : Set.{u2} E) => Exists.{succ u2} (Set.{u2} E) (fun (v : Set.{u2} E) => And (IsOpen.{u2} E _inst_4 u) (And (IsOpen.{u2} E _inst_4 v) (And (Convex.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) u) (And (Convex.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) v) (And (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s u) (And (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) t v) (Disjoint.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E))) u v)))))))))
-but is expected to have type
-  forall {π•œ : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} π•œ] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : TopologicalSpace.{u1} E] [_inst_5 : TopologicalAddGroup.{u1} E _inst_4 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_6 : ContinuousConstSMul.{u2, u1} π•œ E _inst_4 (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] [_inst_7 : LocallyConvexSpace.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_4] {s : Set.{u1} E} {t : Set.{u1} E}, (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) -> (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s) -> (IsCompact.{u1} E _inst_4 s) -> (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) t) -> (IsClosed.{u1} E _inst_4 t) -> (Exists.{succ u1} (Set.{u1} E) (fun (u : Set.{u1} E) => Exists.{succ u1} (Set.{u1} E) (fun (v : Set.{u1} E) => And (IsOpen.{u1} E _inst_4 u) (And (IsOpen.{u1} E _inst_4 v) (And (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) u) (And (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) v) (And (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s u) (And (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) t v) (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)))))) u v)))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align disjoint.exists_open_convexes Disjoint.exists_open_convexesβ‚“'. -/
 /-- In a locally convex space, if `s`, `t` are disjoint convex sets, `s` is compact and `t` is
 closed, then we can find open disjoint convex sets containing them. -/
Diff
@@ -262,7 +262,7 @@ theorem locallyConvexSpace_inf {t₁ tβ‚‚ : TopologicalSpace E} (h₁ : @Locally
 lean 3 declaration is
   forall {π•œ : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} F] [_inst_5 : Module.{u1, u3} π•œ F (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_4] {t : TopologicalSpace.{u3} F} [_inst_6 : LocallyConvexSpace.{u1, u3} π•œ F _inst_1 _inst_4 _inst_5 t] (f : LinearMap.{u1, u1, u2, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (RingHom.id.{u1} π•œ (Semiring.toNonAssocSemiring.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5), LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 (TopologicalSpace.induced.{u2, u3} E F (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (RingHom.id.{u1} π•œ (Semiring.toNonAssocSemiring.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (RingHom.id.{u1} π•œ (Semiring.toNonAssocSemiring.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5) => E -> F) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} π•œ π•œ E F (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} π•œ (Semiring.toNonAssocSemiring.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1)))) f) t)
 but is expected to have type
-  forall {π•œ : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} F] [_inst_5 : Module.{u2, u3} π•œ F (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_4] {t : TopologicalSpace.{u3} F} [_inst_6 : LocallyConvexSpace.{u2, u3} π•œ F _inst_1 _inst_4 _inst_5 t] (f : LinearMap.{u2, u2, u1, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (RingHom.id.{u2} π•œ (Semiring.toNonAssocSemiring.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5), LocallyConvexSpace.{u2, u1} π•œ E _inst_1 _inst_2 _inst_3 (TopologicalSpace.induced.{u1, u3} E F (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u2, u1, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (RingHom.id.{u2} π•œ (Semiring.toNonAssocSemiring.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} π•œ π•œ E F (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u2} π•œ (Semiring.toNonAssocSemiring.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1)))) f) t)
+  forall {π•œ : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} F] [_inst_5 : Module.{u2, u3} π•œ F (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_4] {t : TopologicalSpace.{u3} F} [_inst_6 : LocallyConvexSpace.{u2, u3} π•œ F _inst_1 _inst_4 _inst_5 t] (f : LinearMap.{u2, u2, u1, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (RingHom.id.{u2} π•œ (Semiring.toNonAssocSemiring.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5), LocallyConvexSpace.{u2, u1} π•œ E _inst_1 _inst_2 _inst_3 (TopologicalSpace.induced.{u1, u3} E F (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u2, u1, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (RingHom.id.{u2} π•œ (Semiring.toNonAssocSemiring.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} π•œ π•œ E F (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u2} π•œ (Semiring.toNonAssocSemiring.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1)))) f) t)
 Case conversion may be inaccurate. Consider using '#align locally_convex_space_induced locallyConvexSpace_inducedβ‚“'. -/
 theorem locallyConvexSpace_induced {t : TopologicalSpace F} [LocallyConvexSpace π•œ F]
     (f : E β†’β‚—[π•œ] F) : @LocallyConvexSpace π•œ E _ _ _ (t.induced f) :=
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 
 ! This file was ported from Lean 3 source module topology.algebra.module.locally_convex
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.Convex.Topology
 /-!
 # Locally convex topological modules
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A `locally_convex_space` is a topological semimodule over an ordered semiring in which any point
 admits a neighborhood basis made of convex sets, or equivalently, in which convex neighborhoods of
 a point form a neighborhood basis at that point.
Diff
@@ -40,20 +40,29 @@ open Topology Pointwise
 
 section Semimodule
 
+#print LocallyConvexSpace /-
 /-- A `locally_convex_space` is a topological semimodule over an ordered semiring in which convex
 neighborhoods of a point form a neighborhood basis at that point. -/
 class LocallyConvexSpace (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E]
   [TopologicalSpace E] : Prop where
   convex_basis : βˆ€ x : E, (𝓝 x).HasBasis (fun s : Set E => s ∈ 𝓝 x ∧ Convex π•œ s) id
 #align locally_convex_space LocallyConvexSpace
+-/
 
 variable (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E] [TopologicalSpace E]
 
+/- warning: locally_convex_space_iff -> locallyConvexSpace_iff is a dubious translation:
+lean 3 declaration is
+  forall (π•œ : Type.{u1}) (E : Type.{u2}) [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] [_inst_4 : TopologicalSpace.{u2} E], Iff (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 _inst_4) (forall (x : E), Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (nhds.{u2} E _inst_4 x) (fun (s : Set.{u2} E) => And (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) s (nhds.{u2} E _inst_4 x)) (Convex.{u1, u2} π•œ E _inst_1 _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2 _inst_3)))) s)) (id.{succ u2} (Set.{u2} E)))
+but is expected to have type
+  forall (π•œ : Type.{u2}) (E : Type.{u1}) [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2] [_inst_4 : TopologicalSpace.{u1} E], Iff (LocallyConvexSpace.{u2, u1} π•œ E _inst_1 _inst_2 _inst_3 _inst_4) (forall (x : E), Filter.HasBasis.{u1, succ u1} E (Set.{u1} E) (nhds.{u1} E _inst_4 x) (fun (s : Set.{u1} E) => And (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) s (nhds.{u1} E _inst_4 x)) (Convex.{u2, u1} π•œ E _inst_1 _inst_2 (SMulZeroClass.toSMul.{u2, u1} π•œ E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (MonoidWithZero.toZero.{u2} π•œ (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)) (Module.toMulActionWithZero.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2 _inst_3)))) s)) (id.{succ u1} (Set.{u1} E)))
+Case conversion may be inaccurate. Consider using '#align locally_convex_space_iff locallyConvexSpace_iffβ‚“'. -/
 theorem locallyConvexSpace_iff :
     LocallyConvexSpace π•œ E ↔ βˆ€ x : E, (𝓝 x).HasBasis (fun s : Set E => s ∈ 𝓝 x ∧ Convex π•œ s) id :=
   ⟨@LocallyConvexSpace.convex_basis _ _ _ _ _ _, LocallyConvexSpace.mk⟩
 #align locally_convex_space_iff locallyConvexSpace_iff
 
+#print LocallyConvexSpace.ofBases /-
 theorem LocallyConvexSpace.ofBases {ΞΉ : Type _} (b : E β†’ ΞΉ β†’ Set E) (p : E β†’ ΞΉ β†’ Prop)
     (hbasis : βˆ€ x : E, (𝓝 x).HasBasis (p x) (b x)) (hconvex : βˆ€ x i, p x i β†’ Convex π•œ (b x i)) :
     LocallyConvexSpace π•œ E :=
@@ -63,12 +72,25 @@ theorem LocallyConvexSpace.ofBases {ΞΉ : Type _} (b : E β†’ ΞΉ β†’ Set E) (p : E
       fun s hs =>
       ⟨(hbasis x).index s hs.1, ⟨(hbasis x).property_index hs.1, (hbasis x).set_index_subset hs.1⟩⟩⟩
 #align locally_convex_space.of_bases LocallyConvexSpace.ofBases
+-/
 
+/- warning: locally_convex_space.convex_basis_zero -> LocallyConvexSpace.convex_basis_zero is a dubious translation:
+lean 3 declaration is
+  forall (π•œ : Type.{u1}) (E : Type.{u2}) [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 _inst_4], Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))))))) (fun (s : Set.{u2} E) => And (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) s (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))))))) (Convex.{u1, u2} π•œ E _inst_1 _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2 _inst_3)))) s)) (id.{succ u2} (Set.{u2} E))
+but is expected to have type
+  forall (π•œ : Type.{u2}) (E : Type.{u1}) [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2] [_inst_4 : TopologicalSpace.{u1} E] [_inst_5 : LocallyConvexSpace.{u2, u1} π•œ E _inst_1 _inst_2 _inst_3 _inst_4], Filter.HasBasis.{u1, succ u1} E (Set.{u1} E) (nhds.{u1} E _inst_4 (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2))))) (fun (s : Set.{u1} E) => And (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) s (nhds.{u1} E _inst_4 (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)))))) (Convex.{u2, u1} π•œ E _inst_1 _inst_2 (SMulZeroClass.toSMul.{u2, u1} π•œ E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (MonoidWithZero.toZero.{u2} π•œ (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)) (Module.toMulActionWithZero.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2 _inst_3)))) s)) (id.{succ u1} (Set.{u1} E))
+Case conversion may be inaccurate. Consider using '#align locally_convex_space.convex_basis_zero LocallyConvexSpace.convex_basis_zeroβ‚“'. -/
 theorem LocallyConvexSpace.convex_basis_zero [LocallyConvexSpace π•œ E] :
     (𝓝 0 : Filter E).HasBasis (fun s => s ∈ (𝓝 0 : Filter E) ∧ Convex π•œ s) id :=
   LocallyConvexSpace.convex_basis 0
 #align locally_convex_space.convex_basis_zero LocallyConvexSpace.convex_basis_zero
 
+/- warning: locally_convex_space_iff_exists_convex_subset -> locallyConvexSpace_iff_exists_convex_subset is a dubious translation:
+lean 3 declaration is
+  forall (π•œ : Type.{u1}) (E : Type.{u2}) [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] [_inst_4 : TopologicalSpace.{u2} E], Iff (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 _inst_4) (forall (x : E) (U : Set.{u2} E), (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) U (nhds.{u2} E _inst_4 x)) -> (Exists.{succ u2} (Set.{u2} E) (fun (S : Set.{u2} E) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) S (nhds.{u2} E _inst_4 x)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) S (nhds.{u2} E _inst_4 x)) => And (Convex.{u1, u2} π•œ E _inst_1 _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2 _inst_3)))) S) (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) S U)))))
+but is expected to have type
+  forall (π•œ : Type.{u2}) (E : Type.{u1}) [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2] [_inst_4 : TopologicalSpace.{u1} E], Iff (LocallyConvexSpace.{u2, u1} π•œ E _inst_1 _inst_2 _inst_3 _inst_4) (forall (x : E) (U : Set.{u1} E), (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) U (nhds.{u1} E _inst_4 x)) -> (Exists.{succ u1} (Set.{u1} E) (fun (S : Set.{u1} E) => And (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) S (nhds.{u1} E _inst_4 x)) (And (Convex.{u2, u1} π•œ E _inst_1 _inst_2 (SMulZeroClass.toSMul.{u2, u1} π•œ E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (MonoidWithZero.toZero.{u2} π•œ (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)) (Module.toMulActionWithZero.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2 _inst_3)))) S) (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) S U)))))
+Case conversion may be inaccurate. Consider using '#align locally_convex_space_iff_exists_convex_subset locallyConvexSpace_iff_exists_convex_subsetβ‚“'. -/
 theorem locallyConvexSpace_iff_exists_convex_subset :
     LocallyConvexSpace π•œ E ↔ βˆ€ x : E, βˆ€ U ∈ 𝓝 x, βˆƒ S ∈ 𝓝 x, Convex π•œ S ∧ S βŠ† U :=
   (locallyConvexSpace_iff π•œ E).trans (forall_congr' fun x => hasBasis_self)
@@ -81,6 +103,12 @@ section Module
 variable (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
   [TopologicalAddGroup E]
 
+/- warning: locally_convex_space.of_basis_zero -> LocallyConvexSpace.ofBasisZero is a dubious translation:
+lean 3 declaration is
+  forall (π•œ : Type.{u1}) (E : Type.{u2}) [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] {ΞΉ : Type.{u3}} (b : ΞΉ -> (Set.{u2} E)) (p : ΞΉ -> Prop), (Filter.HasBasis.{u2, succ u3} E ΞΉ (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) p b) -> (forall (i : ΞΉ), (p i) -> (Convex.{u1, u2} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (b i))) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_4)
+but is expected to have type
+  forall (π•œ : Type.{u1}) (E : Type.{u2}) [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] {ΞΉ : Type.{u3}} (b : ΞΉ -> (Set.{u2} E)) (p : ΞΉ -> Prop), (Filter.HasBasis.{u2, succ u3} E ΞΉ (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (Zero.toOfNat0.{u2} E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2)))))))) p b) -> (forall (i : ΞΉ), (p i) -> (Convex.{u1, u2} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} π•œ E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π•œ E (MonoidWithZero.toZero.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1)) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (b i))) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_4)
+Case conversion may be inaccurate. Consider using '#align locally_convex_space.of_basis_zero LocallyConvexSpace.ofBasisZeroβ‚“'. -/
 theorem LocallyConvexSpace.ofBasisZero {ΞΉ : Type _} (b : ΞΉ β†’ Set E) (p : ΞΉ β†’ Prop)
     (hbasis : (𝓝 0).HasBasis p b) (hconvex : βˆ€ i, p i β†’ Convex π•œ (b i)) : LocallyConvexSpace π•œ E :=
   by
@@ -91,6 +119,12 @@ theorem LocallyConvexSpace.ofBasisZero {ΞΉ : Type _} (b : ΞΉ β†’ Set E) (p : ΞΉ
   exact hbasis.map _
 #align locally_convex_space.of_basis_zero LocallyConvexSpace.ofBasisZero
 
+/- warning: locally_convex_space_iff_zero -> locallyConvexSpace_iff_zero is a dubious translation:
+lean 3 declaration is
+  forall (π•œ : Type.{u1}) (E : Type.{u2}) [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)], Iff (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_4) (Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) (fun (s : Set.{u2} E) => And (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) s (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))))) (Convex.{u1, u2} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) (id.{succ u2} (Set.{u2} E)))
+but is expected to have type
+  forall (π•œ : Type.{u2}) (E : Type.{u1}) [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : TopologicalSpace.{u1} E] [_inst_5 : TopologicalAddGroup.{u1} E _inst_4 (AddCommGroup.toAddGroup.{u1} E _inst_2)], Iff (LocallyConvexSpace.{u2, u1} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_4) (Filter.HasBasis.{u1, succ u1} E (Set.{u1} E) (nhds.{u1} E _inst_4 (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)))))))) (fun (s : Set.{u1} E) => And (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) s (nhds.{u1} E _inst_4 (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))))))))) (Convex.{u2, u1} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (MonoidWithZero.toZero.{u2} π•œ (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1)) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s)) (id.{succ u1} (Set.{u1} E)))
+Case conversion may be inaccurate. Consider using '#align locally_convex_space_iff_zero locallyConvexSpace_iff_zeroβ‚“'. -/
 theorem locallyConvexSpace_iff_zero :
     LocallyConvexSpace π•œ E ↔
       (𝓝 0 : Filter E).HasBasis (fun s : Set E => s ∈ (𝓝 0 : Filter E) ∧ Convex π•œ s) id :=
@@ -98,17 +132,25 @@ theorem locallyConvexSpace_iff_zero :
     LocallyConvexSpace.ofBasisZero π•œ E _ _ h fun s => And.right⟩
 #align locally_convex_space_iff_zero locallyConvexSpace_iff_zero
 
+/- warning: locally_convex_space_iff_exists_convex_subset_zero -> locallyConvexSpace_iff_exists_convex_subset_zero is a dubious translation:
+lean 3 declaration is
+  forall (π•œ : Type.{u1}) (E : Type.{u2}) [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)], Iff (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_4) (forall (U : Set.{u2} E), (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) U (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))))) -> (Exists.{succ u2} (Set.{u2} E) (fun (S : Set.{u2} E) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) S (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))))) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) S (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))))) => And (Convex.{u1, u2} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) S) (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) S U)))))
+but is expected to have type
+  forall (π•œ : Type.{u2}) (E : Type.{u1}) [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : TopologicalSpace.{u1} E] [_inst_5 : TopologicalAddGroup.{u1} E _inst_4 (AddCommGroup.toAddGroup.{u1} E _inst_2)], Iff (LocallyConvexSpace.{u2, u1} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_4) (forall (U : Set.{u1} E), (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) U (nhds.{u1} E _inst_4 (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))))))))) -> (Exists.{succ u1} (Set.{u1} E) (fun (S : Set.{u1} E) => And (Membership.mem.{u1, u1} (Set.{u1} E) (Filter.{u1} E) (instMembershipSetFilter.{u1} E) S (nhds.{u1} E _inst_4 (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))))))))) (And (Convex.{u2, u1} π•œ E _inst_1 (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (MonoidWithZero.toZero.{u2} π•œ (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1)) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) S) (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) S U)))))
+Case conversion may be inaccurate. Consider using '#align locally_convex_space_iff_exists_convex_subset_zero locallyConvexSpace_iff_exists_convex_subset_zeroβ‚“'. -/
 theorem locallyConvexSpace_iff_exists_convex_subset_zero :
     LocallyConvexSpace π•œ E ↔ βˆ€ U ∈ (𝓝 0 : Filter E), βˆƒ S ∈ (𝓝 0 : Filter E), Convex π•œ S ∧ S βŠ† U :=
   (locallyConvexSpace_iff_zero π•œ E).trans hasBasis_self
 #align locally_convex_space_iff_exists_convex_subset_zero locallyConvexSpace_iff_exists_convex_subset_zero
 
+#print LocallyConvexSpace.toLocallyConnectedSpace /-
 -- see Note [lower instance priority]
-instance (priority := 100) LocallyConvexSpace.to_locallyConnectedSpace [Module ℝ E]
+instance (priority := 100) LocallyConvexSpace.toLocallyConnectedSpace [Module ℝ E]
     [ContinuousSMul ℝ E] [LocallyConvexSpace ℝ E] : LocallyConnectedSpace E :=
   locallyConnectedSpace_of_connected_bases _ _
     (fun x => @LocallyConvexSpace.convex_basis ℝ _ _ _ _ _ _ x) fun x s hs => hs.2.IsPreconnected
-#align locally_convex_space.to_locally_connected_space LocallyConvexSpace.to_locallyConnectedSpace
+#align locally_convex_space.to_locally_connected_space LocallyConvexSpace.toLocallyConnectedSpace
+-/
 
 end Module
 
@@ -117,6 +159,12 @@ section LinearOrderedField
 variable (π•œ E : Type _) [LinearOrderedField π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
   [TopologicalAddGroup E] [ContinuousConstSMul π•œ E]
 
+/- warning: locally_convex_space.convex_open_basis_zero -> LocallyConvexSpace.convex_open_basis_zero is a dubious translation:
+lean 3 declaration is
+  forall (π•œ : Type.{u1}) (E : Type.{u2}) [_inst_1 : LinearOrderedField.{u1} π•œ] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_6 : ContinuousConstSMul.{u1, u2} π•œ E _inst_4 (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] [_inst_7 : LocallyConvexSpace.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_4], Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))))))) (fun (s : Set.{u2} E) => And (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))))) s) (And (IsOpen.{u2} E _inst_4 s) (Convex.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))) (id.{succ u2} (Set.{u2} E))
+but is expected to have type
+  forall (π•œ : Type.{u2}) (E : Type.{u1}) [_inst_1 : LinearOrderedField.{u2} π•œ] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : TopologicalSpace.{u1} E] [_inst_5 : TopologicalAddGroup.{u1} E _inst_4 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_6 : ContinuousConstSMul.{u2, u1} π•œ E _inst_4 (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] [_inst_7 : LocallyConvexSpace.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_4], Filter.HasBasis.{u1, succ u1} E (Set.{u1} E) (nhds.{u1} E _inst_4 (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)))))))) (fun (s : Set.{u1} E) => And (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) (And (IsOpen.{u1} E _inst_4 s) (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s))) (id.{succ u1} (Set.{u1} E))
+Case conversion may be inaccurate. Consider using '#align locally_convex_space.convex_open_basis_zero LocallyConvexSpace.convex_open_basis_zeroβ‚“'. -/
 theorem LocallyConvexSpace.convex_open_basis_zero [LocallyConvexSpace π•œ E] :
     (𝓝 0 : Filter E).HasBasis (fun s => (0 : E) ∈ s ∧ IsOpen s ∧ Convex π•œ s) id :=
   (LocallyConvexSpace.convex_basis_zero π•œ E).to_hasBasis
@@ -128,6 +176,12 @@ theorem LocallyConvexSpace.convex_open_basis_zero [LocallyConvexSpace π•œ E] :
 
 variable {π•œ E}
 
+/- warning: disjoint.exists_open_convexes -> Disjoint.exists_open_convexes is a dubious translation:
+lean 3 declaration is
+  forall {π•œ : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} π•œ] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : TopologicalAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_6 : ContinuousConstSMul.{u1, u2} π•œ E _inst_4 (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))] [_inst_7 : LocallyConvexSpace.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 _inst_4] {s : Set.{u2} E} {t : Set.{u2} E}, (Disjoint.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E))) s t) -> (Convex.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s) -> (IsCompact.{u2} E _inst_4 s) -> (Convex.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) t) -> (IsClosed.{u2} E _inst_4 t) -> (Exists.{succ u2} (Set.{u2} E) (fun (u : Set.{u2} E) => Exists.{succ u2} (Set.{u2} E) (fun (v : Set.{u2} E) => And (IsOpen.{u2} E _inst_4 u) (And (IsOpen.{u2} E _inst_4 v) (And (Convex.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) u) (And (Convex.{u1, u2} π•œ E (StrictOrderedSemiring.toOrderedSemiring.{u1} π•œ (StrictOrderedRing.toStrictOrderedSemiring.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} π•œ E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} π•œ E (MulZeroClass.toHasZero.{u1} π•œ (MulZeroOneClass.toMulZeroClass.{u1} π•œ (MonoidWithZero.toMulZeroOneClass.{u1} π•œ (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} π•œ E (Semiring.toMonoidWithZero.{u1} π•œ (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} π•œ E (Ring.toSemiring.{u1} π•œ (StrictOrderedRing.toRing.{u1} π•œ (LinearOrderedRing.toStrictOrderedRing.{u1} π•œ (LinearOrderedCommRing.toLinearOrderedRing.{u1} π•œ (LinearOrderedField.toLinearOrderedCommRing.{u1} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) v) (And (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s u) (And (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) t v) (Disjoint.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} E) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} E) (Set.booleanAlgebra.{u2} E))) u v)))))))))
+but is expected to have type
+  forall {π•œ : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} π•œ] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : TopologicalSpace.{u1} E] [_inst_5 : TopologicalAddGroup.{u1} E _inst_4 (AddCommGroup.toAddGroup.{u1} E _inst_2)] [_inst_6 : ContinuousConstSMul.{u2, u1} π•œ E _inst_4 (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))] [_inst_7 : LocallyConvexSpace.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 _inst_4] {s : Set.{u1} E} {t : Set.{u1} E}, (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) -> (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s) -> (IsCompact.{u1} E _inst_4 s) -> (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) t) -> (IsClosed.{u1} E _inst_4 t) -> (Exists.{succ u1} (Set.{u1} E) (fun (u : Set.{u1} E) => Exists.{succ u1} (Set.{u1} E) (fun (v : Set.{u1} E) => And (IsOpen.{u1} E _inst_4 u) (And (IsOpen.{u1} E _inst_4 v) (And (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) u) (And (Convex.{u2, u1} π•œ E (OrderedCommSemiring.toOrderedSemiring.{u2} π•œ (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} π•œ (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} π•œ E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} π•œ E (CommMonoidWithZero.toZero.{u2} π•œ (CommGroupWithZero.toCommMonoidWithZero.{u2} π•œ (Semifield.toCommGroupWithZero.{u2} π•œ (LinearOrderedSemifield.toSemifield.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} π•œ E (Semiring.toMonoidWithZero.{u2} π•œ (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} π•œ E (StrictOrderedSemiring.toSemiring.{u2} π•œ (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} π•œ (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} π•œ (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} π•œ (LinearOrderedField.toLinearOrderedSemifield.{u2} π•œ _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) v) (And (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s u) (And (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) t v) (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)))))) u v)))))))))
+Case conversion may be inaccurate. Consider using '#align disjoint.exists_open_convexes Disjoint.exists_open_convexesβ‚“'. -/
 /-- In a locally convex space, if `s`, `t` are disjoint convex sets, `s` is compact and `t` is
 closed, then we can find open disjoint convex sets containing them. -/
 theorem Disjoint.exists_open_convexes [LocallyConvexSpace π•œ E] {s t : Set E} (disj : Disjoint s t)
@@ -154,7 +208,13 @@ section LatticeOps
 variable {ΞΉ : Sort _} {π•œ E F : Type _} [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E]
   [AddCommMonoid F] [Module π•œ F]
 
-theorem locallyConvexSpaceInf {ts : Set (TopologicalSpace E)}
+/- warning: locally_convex_space_Inf -> locallyConvexSpace_sInf is a dubious translation:
+lean 3 declaration is
+  forall {π•œ : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] {ts : Set.{u2} (TopologicalSpace.{u2} E)}, (forall (t : TopologicalSpace.{u2} E), (Membership.Mem.{u2, u2} (TopologicalSpace.{u2} E) (Set.{u2} (TopologicalSpace.{u2} E)) (Set.hasMem.{u2} (TopologicalSpace.{u2} E)) t ts) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 t)) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 (InfSet.sInf.{u2} (TopologicalSpace.{u2} E) (ConditionallyCompleteLattice.toHasInf.{u2} (TopologicalSpace.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.completeLattice.{u2} E))) ts))
+but is expected to have type
+  forall {π•œ : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] {ts : Set.{u2} (TopologicalSpace.{u2} E)}, (forall (t : TopologicalSpace.{u2} E), (Membership.mem.{u2, u2} (TopologicalSpace.{u2} E) (Set.{u2} (TopologicalSpace.{u2} E)) (Set.instMembershipSet.{u2} (TopologicalSpace.{u2} E)) t ts) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 t)) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 (InfSet.sInf.{u2} (TopologicalSpace.{u2} E) (ConditionallyCompleteLattice.toInfSet.{u2} (TopologicalSpace.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.instCompleteLatticeTopologicalSpace.{u2} E))) ts))
+Case conversion may be inaccurate. Consider using '#align locally_convex_space_Inf locallyConvexSpace_sInfβ‚“'. -/
+theorem locallyConvexSpace_sInf {ts : Set (TopologicalSpace E)}
     (h : βˆ€ t ∈ ts, @LocallyConvexSpace π•œ E _ _ _ t) : @LocallyConvexSpace π•œ E _ _ _ (sInf ts) :=
   by
   letI : TopologicalSpace E := Inf ts
@@ -165,29 +225,43 @@ theorem locallyConvexSpaceInf {ts : Set (TopologicalSpace E)}
       (fun x => _) fun x If hif => convex_iInter fun i => convex_iInter fun hi => (hif.2 i hi).2
   rw [nhds_sInf, ← iInf_subtype'']
   exact has_basis_infi' fun i : ts => (@locallyConvexSpace_iff π•œ E _ _ _ ↑i).mp (h (↑i) i.2) x
-#align locally_convex_space_Inf locallyConvexSpaceInf
-
-theorem locallyConvexSpaceInfi {ts' : ΞΉ β†’ TopologicalSpace E}
+#align locally_convex_space_Inf locallyConvexSpace_sInf
+
+/- warning: locally_convex_space_infi -> locallyConvexSpace_iInf is a dubious translation:
+lean 3 declaration is
+  forall {ΞΉ : Sort.{u1}} {π•œ : Type.{u2}} {E : Type.{u3}} [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : Module.{u2, u3} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2] {ts' : ΞΉ -> (TopologicalSpace.{u3} E)}, (forall (i : ΞΉ), LocallyConvexSpace.{u2, u3} π•œ E _inst_1 _inst_2 _inst_3 (ts' i)) -> (LocallyConvexSpace.{u2, u3} π•œ E _inst_1 _inst_2 _inst_3 (iInf.{u3, u1} (TopologicalSpace.{u3} E) (ConditionallyCompleteLattice.toHasInf.{u3} (TopologicalSpace.{u3} E) (CompleteLattice.toConditionallyCompleteLattice.{u3} (TopologicalSpace.{u3} E) (TopologicalSpace.completeLattice.{u3} E))) ΞΉ (fun (i : ΞΉ) => ts' i)))
+but is expected to have type
+  forall {ΞΉ : Sort.{u1}} {π•œ : Type.{u2}} {E : Type.{u3}} [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : Module.{u2, u3} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2] {ts' : ΞΉ -> (TopologicalSpace.{u3} E)}, (forall (i : ΞΉ), LocallyConvexSpace.{u2, u3} π•œ E _inst_1 _inst_2 _inst_3 (ts' i)) -> (LocallyConvexSpace.{u2, u3} π•œ E _inst_1 _inst_2 _inst_3 (iInf.{u3, u1} (TopologicalSpace.{u3} E) (ConditionallyCompleteLattice.toInfSet.{u3} (TopologicalSpace.{u3} E) (CompleteLattice.toConditionallyCompleteLattice.{u3} (TopologicalSpace.{u3} E) (TopologicalSpace.instCompleteLatticeTopologicalSpace.{u3} E))) ΞΉ (fun (i : ΞΉ) => ts' i)))
+Case conversion may be inaccurate. Consider using '#align locally_convex_space_infi locallyConvexSpace_iInfβ‚“'. -/
+theorem locallyConvexSpace_iInf {ts' : ΞΉ β†’ TopologicalSpace E}
     (h' : βˆ€ i, @LocallyConvexSpace π•œ E _ _ _ (ts' i)) :
     @LocallyConvexSpace π•œ E _ _ _ (β¨… i, ts' i) :=
   by
-  refine' locallyConvexSpaceInf _
+  refine' locallyConvexSpace_sInf _
   rwa [forall_range_iff]
-#align locally_convex_space_infi locallyConvexSpaceInfi
-
-/- warning: locally_convex_space_inf clashes with locally_convex_space_Inf -> locallyConvexSpaceInf
-Case conversion may be inaccurate. Consider using '#align locally_convex_space_inf locallyConvexSpaceInfβ‚“'. -/
-#print locallyConvexSpaceInf /-
-theorem locallyConvexSpaceInf {t₁ tβ‚‚ : TopologicalSpace E} (h₁ : @LocallyConvexSpace π•œ E _ _ _ t₁)
+#align locally_convex_space_infi locallyConvexSpace_iInf
+
+/- warning: locally_convex_space_inf -> locallyConvexSpace_inf is a dubious translation:
+lean 3 declaration is
+  forall {π•œ : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] {t₁ : TopologicalSpace.{u2} E} {tβ‚‚ : TopologicalSpace.{u2} E}, (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 t₁) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 tβ‚‚) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 (Inf.inf.{u2} (TopologicalSpace.{u2} E) (SemilatticeInf.toHasInf.{u2} (TopologicalSpace.{u2} E) (Lattice.toSemilatticeInf.{u2} (TopologicalSpace.{u2} E) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.completeLattice.{u2} E))))) t₁ tβ‚‚))
+but is expected to have type
+  forall {π•œ : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] {t₁ : TopologicalSpace.{u2} E} {tβ‚‚ : TopologicalSpace.{u2} E}, (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 t₁) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 tβ‚‚) -> (LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 (Inf.inf.{u2} (TopologicalSpace.{u2} E) (Lattice.toInf.{u2} (TopologicalSpace.{u2} E) (ConditionallyCompleteLattice.toLattice.{u2} (TopologicalSpace.{u2} E) (CompleteLattice.toConditionallyCompleteLattice.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.instCompleteLatticeTopologicalSpace.{u2} E)))) t₁ tβ‚‚))
+Case conversion may be inaccurate. Consider using '#align locally_convex_space_inf locallyConvexSpace_infβ‚“'. -/
+theorem locallyConvexSpace_inf {t₁ tβ‚‚ : TopologicalSpace E} (h₁ : @LocallyConvexSpace π•œ E _ _ _ t₁)
     (hβ‚‚ : @LocallyConvexSpace π•œ E _ _ _ tβ‚‚) : @LocallyConvexSpace π•œ E _ _ _ (t₁ βŠ“ tβ‚‚) :=
   by
   rw [inf_eq_iInf]
-  refine' locallyConvexSpaceInfi fun b => _
+  refine' locallyConvexSpace_iInf fun b => _
   cases b <;> assumption
-#align locally_convex_space_inf locallyConvexSpaceInf
--/
-
-theorem locallyConvexSpaceInduced {t : TopologicalSpace F} [LocallyConvexSpace π•œ F]
+#align locally_convex_space_inf locallyConvexSpace_inf
+
+/- warning: locally_convex_space_induced -> locallyConvexSpace_induced is a dubious translation:
+lean 3 declaration is
+  forall {π•œ : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u1} π•œ] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} π•œ E (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} F] [_inst_5 : Module.{u1, u3} π•œ F (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_4] {t : TopologicalSpace.{u3} F} [_inst_6 : LocallyConvexSpace.{u1, u3} π•œ F _inst_1 _inst_4 _inst_5 t] (f : LinearMap.{u1, u1, u2, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (RingHom.id.{u1} π•œ (Semiring.toNonAssocSemiring.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5), LocallyConvexSpace.{u1, u2} π•œ E _inst_1 _inst_2 _inst_3 (TopologicalSpace.induced.{u2, u3} E F (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (RingHom.id.{u1} π•œ (Semiring.toNonAssocSemiring.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (RingHom.id.{u1} π•œ (Semiring.toNonAssocSemiring.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5) => E -> F) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} π•œ π•œ E F (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) (OrderedSemiring.toSemiring.{u1} π•œ _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u1} π•œ (Semiring.toNonAssocSemiring.{u1} π•œ (OrderedSemiring.toSemiring.{u1} π•œ _inst_1)))) f) t)
+but is expected to have type
+  forall {π•œ : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u2} π•œ] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} π•œ E (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2] [_inst_4 : AddCommMonoid.{u3} F] [_inst_5 : Module.{u2, u3} π•œ F (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_4] {t : TopologicalSpace.{u3} F} [_inst_6 : LocallyConvexSpace.{u2, u3} π•œ F _inst_1 _inst_4 _inst_5 t] (f : LinearMap.{u2, u2, u1, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (RingHom.id.{u2} π•œ (Semiring.toNonAssocSemiring.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5), LocallyConvexSpace.{u2, u1} π•œ E _inst_1 _inst_2 _inst_3 (TopologicalSpace.induced.{u1, u3} E F (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (LinearMap.{u2, u2, u1, u3} π•œ π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (RingHom.id.{u2} π•œ (Semiring.toNonAssocSemiring.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1))) E F _inst_2 _inst_4 _inst_3 _inst_5) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => F) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u3} π•œ π•œ E F (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) (OrderedSemiring.toSemiring.{u2} π•œ _inst_1) _inst_2 _inst_4 _inst_3 _inst_5 (RingHom.id.{u2} π•œ (Semiring.toNonAssocSemiring.{u2} π•œ (OrderedSemiring.toSemiring.{u2} π•œ _inst_1)))) f) t)
+Case conversion may be inaccurate. Consider using '#align locally_convex_space_induced locallyConvexSpace_inducedβ‚“'. -/
+theorem locallyConvexSpace_induced {t : TopologicalSpace F} [LocallyConvexSpace π•œ F]
     (f : E β†’β‚—[π•œ] F) : @LocallyConvexSpace π•œ E _ _ _ (t.induced f) :=
   by
   letI : TopologicalSpace E := t.induced f
@@ -197,16 +271,16 @@ theorem locallyConvexSpaceInduced {t : TopologicalSpace F} [LocallyConvexSpace 
       hs.linear_preimage f
   rw [nhds_induced]
   exact (LocallyConvexSpace.convex_basis <| f x).comap f
-#align locally_convex_space_induced locallyConvexSpaceInduced
+#align locally_convex_space_induced locallyConvexSpace_induced
 
 instance {ΞΉ : Type _} {X : ΞΉ β†’ Type _} [βˆ€ i, AddCommMonoid (X i)] [βˆ€ i, TopologicalSpace (X i)]
     [βˆ€ i, Module π•œ (X i)] [βˆ€ i, LocallyConvexSpace π•œ (X i)] : LocallyConvexSpace π•œ (βˆ€ i, X i) :=
-  locallyConvexSpaceInfi fun i => locallyConvexSpaceInduced (LinearMap.proj i)
+  locallyConvexSpace_iInf fun i => locallyConvexSpace_induced (LinearMap.proj i)
 
 instance [TopologicalSpace E] [TopologicalSpace F] [LocallyConvexSpace π•œ E]
     [LocallyConvexSpace π•œ F] : LocallyConvexSpace π•œ (E Γ— F) :=
-  locallyConvexSpaceInf (locallyConvexSpaceInduced (LinearMap.fst _ _ _))
-    (locallyConvexSpaceInduced (LinearMap.snd _ _ _))
+  locallyConvexSpace_inf (locallyConvexSpace_induced (LinearMap.fst _ _ _))
+    (locallyConvexSpace_induced (LinearMap.snd _ _ _))
 
 end LatticeOps
 
Diff
@@ -155,15 +155,15 @@ variable {ΞΉ : Sort _} {π•œ E F : Type _} [OrderedSemiring π•œ] [AddCommMonoid
   [AddCommMonoid F] [Module π•œ F]
 
 theorem locallyConvexSpaceInf {ts : Set (TopologicalSpace E)}
-    (h : βˆ€ t ∈ ts, @LocallyConvexSpace π•œ E _ _ _ t) : @LocallyConvexSpace π•œ E _ _ _ (infβ‚› ts) :=
+    (h : βˆ€ t ∈ ts, @LocallyConvexSpace π•œ E _ _ _ t) : @LocallyConvexSpace π•œ E _ _ _ (sInf ts) :=
   by
   letI : TopologicalSpace E := Inf ts
   refine'
     LocallyConvexSpace.ofBases π•œ E (fun x => fun If : Set ts Γ— (ts β†’ Set E) => β‹‚ i ∈ If.1, If.2 i)
       (fun x => fun If : Set ts Γ— (ts β†’ Set E) =>
         If.1.Finite ∧ βˆ€ i ∈ If.1, If.2 i ∈ @nhds _ (↑i) x ∧ Convex π•œ (If.2 i))
-      (fun x => _) fun x If hif => convex_interα΅’ fun i => convex_interα΅’ fun hi => (hif.2 i hi).2
-  rw [nhds_infβ‚›, ← infα΅’_subtype'']
+      (fun x => _) fun x If hif => convex_iInter fun i => convex_iInter fun hi => (hif.2 i hi).2
+  rw [nhds_sInf, ← iInf_subtype'']
   exact has_basis_infi' fun i : ts => (@locallyConvexSpace_iff π•œ E _ _ _ ↑i).mp (h (↑i) i.2) x
 #align locally_convex_space_Inf locallyConvexSpaceInf
 
@@ -181,7 +181,7 @@ Case conversion may be inaccurate. Consider using '#align locally_convex_space_i
 theorem locallyConvexSpaceInf {t₁ tβ‚‚ : TopologicalSpace E} (h₁ : @LocallyConvexSpace π•œ E _ _ _ t₁)
     (hβ‚‚ : @LocallyConvexSpace π•œ E _ _ _ tβ‚‚) : @LocallyConvexSpace π•œ E _ _ _ (t₁ βŠ“ tβ‚‚) :=
   by
-  rw [inf_eq_infα΅’]
+  rw [inf_eq_iInf]
   refine' locallyConvexSpaceInfi fun b => _
   cases b <;> assumption
 #align locally_convex_space_inf locallyConvexSpaceInf
Diff
@@ -135,7 +135,7 @@ theorem Disjoint.exists_open_convexes [LocallyConvexSpace π•œ E] {s t : Set E}
     βˆƒ u v, IsOpen u ∧ IsOpen v ∧ Convex π•œ u ∧ Convex π•œ v ∧ s βŠ† u ∧ t βŠ† v ∧ Disjoint u v :=
   by
   letI : UniformSpace E := TopologicalAddGroup.toUniformSpace E
-  haveI : UniformAddGroup E := topological_add_commGroup_is_uniform
+  haveI : UniformAddGroup E := comm_topologicalAddGroup_is_uniform
   have := (LocallyConvexSpace.convex_open_basis_zero π•œ E).comap fun x : E Γ— E => x.2 - x.1
   rw [← uniformity_eq_comap_nhds_zero] at this
   rcases disj.exists_uniform_thickening_of_basis this hsβ‚‚ htβ‚‚ with ⟨V, ⟨hV0, hVopen, hVconvex⟩, hV⟩

Changes in mathlib4

mathlib3
mathlib4
chore: Remove ball and bex from lemma names (#10816)

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.

Diff
@@ -165,7 +165,7 @@ theorem locallyConvexSpace_iInf {ts' : ΞΉ β†’ TopologicalSpace E}
     (h' : βˆ€ i, @LocallyConvexSpace π•œ E _ _ _ (ts' i)) :
     @LocallyConvexSpace π•œ E _ _ _ (β¨… i, ts' i) := by
   refine' locallyConvexSpace_sInf _
-  rwa [forall_range_iff]
+  rwa [forall_mem_range]
 #align locally_convex_space_infi locallyConvexSpace_iInf
 
 theorem locallyConvexSpace_inf {t₁ tβ‚‚ : TopologicalSpace E} (h₁ : @LocallyConvexSpace π•œ E _ _ _ t₁)
style: reduce spacing variation in "porting note" comments (#10886)

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

Diff
@@ -193,7 +193,7 @@ instance Pi.locallyConvexSpace {ΞΉ : Type*} {X : ΞΉ β†’ Type*} [βˆ€ i, AddCommMo
 
 instance Prod.locallyConvexSpace [TopologicalSpace E] [TopologicalSpace F] [LocallyConvexSpace π•œ E]
     [LocallyConvexSpace π•œ F] : LocallyConvexSpace π•œ (E Γ— F) :=
--- Porting note : had to specify `t₁` and `tβ‚‚`
+-- Porting note: had to specify `t₁` and `tβ‚‚`
   locallyConvexSpace_inf (t₁ := induced Prod.fst _) (tβ‚‚ := induced Prod.snd _)
     (locallyConvexSpace_induced (LinearMap.fst _ _ _))
     (locallyConvexSpace_induced (LinearMap.snd _ _ _))
chore: Replace (Β· op Β·) a by (a op Β·) (#8843)

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

Diff
@@ -83,7 +83,7 @@ variable (π•œ E : Type*) [OrderedSemiring π•œ] [AddCommGroup E] [Module π•œ E
 theorem LocallyConvexSpace.ofBasisZero {ΞΉ : Type*} (b : ΞΉ β†’ Set E) (p : ΞΉ β†’ Prop)
     (hbasis : (𝓝 0).HasBasis p b) (hconvex : βˆ€ i, p i β†’ Convex π•œ (b i)) :
     LocallyConvexSpace π•œ E := by
-  refine' LocallyConvexSpace.ofBases π•œ E (fun (x : E) (i : ΞΉ) => (Β· + Β·) x '' b i) (fun _ => p)
+  refine' LocallyConvexSpace.ofBases π•œ E (fun (x : E) (i : ΞΉ) => (x + Β·) '' b i) (fun _ => p)
     (fun x => _) fun x i hi => (hconvex i hi).translate x
   rw [← map_add_left_nhds_zero]
   exact hbasis.map _
chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

Diff
@@ -41,19 +41,19 @@ section Semimodule
 
 /-- A `LocallyConvexSpace` is a topological semimodule over an ordered semiring in which convex
 neighborhoods of a point form a neighborhood basis at that point. -/
-class LocallyConvexSpace (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E]
+class LocallyConvexSpace (π•œ E : Type*) [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E]
     [TopologicalSpace E] : Prop where
   convex_basis : βˆ€ x : E, (𝓝 x).HasBasis (fun s : Set E => s ∈ 𝓝 x ∧ Convex π•œ s) id
 #align locally_convex_space LocallyConvexSpace
 
-variable (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E] [TopologicalSpace E]
+variable (π•œ E : Type*) [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E] [TopologicalSpace E]
 
 theorem locallyConvexSpace_iff :
     LocallyConvexSpace π•œ E ↔ βˆ€ x : E, (𝓝 x).HasBasis (fun s : Set E => s ∈ 𝓝 x ∧ Convex π•œ s) id :=
   ⟨@LocallyConvexSpace.convex_basis _ _ _ _ _ _, LocallyConvexSpace.mk⟩
 #align locally_convex_space_iff locallyConvexSpace_iff
 
-theorem LocallyConvexSpace.ofBases {ΞΉ : Type _} (b : E β†’ ΞΉ β†’ Set E) (p : E β†’ ΞΉ β†’ Prop)
+theorem LocallyConvexSpace.ofBases {ΞΉ : Type*} (b : E β†’ ΞΉ β†’ Set E) (p : E β†’ ΞΉ β†’ Prop)
     (hbasis : βˆ€ x : E, (𝓝 x).HasBasis (p x) (b x)) (hconvex : βˆ€ x i, p x i β†’ Convex π•œ (b x i)) :
     LocallyConvexSpace π•œ E :=
   ⟨fun x =>
@@ -77,10 +77,10 @@ end Semimodule
 
 section Module
 
-variable (π•œ E : Type _) [OrderedSemiring π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
+variable (π•œ E : Type*) [OrderedSemiring π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
   [TopologicalAddGroup E]
 
-theorem LocallyConvexSpace.ofBasisZero {ΞΉ : Type _} (b : ΞΉ β†’ Set E) (p : ΞΉ β†’ Prop)
+theorem LocallyConvexSpace.ofBasisZero {ΞΉ : Type*} (b : ΞΉ β†’ Set E) (p : ΞΉ β†’ Prop)
     (hbasis : (𝓝 0).HasBasis p b) (hconvex : βˆ€ i, p i β†’ Convex π•œ (b i)) :
     LocallyConvexSpace π•œ E := by
   refine' LocallyConvexSpace.ofBases π•œ E (fun (x : E) (i : ΞΉ) => (Β· + Β·) x '' b i) (fun _ => p)
@@ -111,7 +111,7 @@ end Module
 
 section LinearOrderedField
 
-variable (π•œ E : Type _) [LinearOrderedField π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
+variable (π•œ E : Type*) [LinearOrderedField π•œ] [AddCommGroup E] [Module π•œ E] [TopologicalSpace E]
   [TopologicalAddGroup E] [ContinuousConstSMul π•œ E]
 
 theorem LocallyConvexSpace.convex_open_basis_zero [LocallyConvexSpace π•œ E] :
@@ -146,7 +146,7 @@ end LinearOrderedField
 
 section LatticeOps
 
-variable {ΞΉ : Sort _} {π•œ E F : Type _} [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E]
+variable {ΞΉ : Sort*} {π•œ E F : Type*} [OrderedSemiring π•œ] [AddCommMonoid E] [Module π•œ E]
   [AddCommMonoid F] [Module π•œ F]
 
 theorem locallyConvexSpace_sInf {ts : Set (TopologicalSpace E)}
@@ -185,7 +185,7 @@ theorem locallyConvexSpace_induced {t : TopologicalSpace F} [LocallyConvexSpace
   exact (LocallyConvexSpace.convex_basis <| f x).comap f
 #align locally_convex_space_induced locallyConvexSpace_induced
 
-instance Pi.locallyConvexSpace {ΞΉ : Type _} {X : ΞΉ β†’ Type _} [βˆ€ i, AddCommMonoid (X i)]
+instance Pi.locallyConvexSpace {ΞΉ : Type*} {X : ΞΉ β†’ Type*} [βˆ€ i, AddCommMonoid (X i)]
     [βˆ€ i, TopologicalSpace (X i)] [βˆ€ i, Module π•œ (X i)] [βˆ€ i, LocallyConvexSpace π•œ (X i)] :
     LocallyConvexSpace π•œ (βˆ€ i, X i) :=
   locallyConvexSpace_iInf fun i => locallyConvexSpace_induced (LinearMap.proj i)
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

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

Diff
@@ -2,14 +2,11 @@
 Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module topology.algebra.module.locally_convex
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Convex.Topology
 
+#align_import topology.algebra.module.locally_convex from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Locally convex topological modules
 
feat: port Topology.Algebra.Module.LocallyConvex (#3637)

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

Dependencies 10 + 574

575 files ported (98.3%)
252821 lines ported (97.9%)
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The unported dependencies are

The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file