analysis.locally_convex.balanced_core_hull

Changes since the initial port

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

Changes in mathlib3

f2ce6086

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

4f4a1c87

bump to nightly-2024-04-25-08

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

ad7a2212

Diff

@@ -95,7 +95,7 @@ theorem balancedCore_empty : balancedCore 𝕜 (∅ : Set E) = ∅ :=
 
 #print mem_balancedCore_iff /-
 theorem mem_balancedCore_iff : x ∈ balancedCore 𝕜 s ↔ ∃ t, Balanced 𝕜 t ∧ t ⊆ s ∧ x ∈ t := by
-  simp_rw [balancedCore, mem_sUnion, mem_set_of_eq, exists_prop, and_assoc']
+  simp_rw [balancedCore, mem_sUnion, mem_set_of_eq, exists_prop, and_assoc]
 #align mem_balanced_core_iff mem_balancedCore_iff
 -/

4f4a1c87

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
-import Analysis.LocallyConvex.Basic
+import Topology.Bornology.Absorbs
 
 #align_import analysis.locally_convex.balanced_core_hull from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"

4f4a1c87

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -104,7 +104,7 @@ theorem smul_balancedCore_subset (s : Set E) {a : 𝕜} (ha : ‖a‖ ≤ 1) :
     a • balancedCore 𝕜 s ⊆ balancedCore 𝕜 s :=
   by
   rintro x ⟨y, hy, rfl⟩
-  rw [mem_balancedCore_iff] at hy 
+  rw [mem_balancedCore_iff] at hy
   rcases hy with ⟨t, ht1, ht2, hy⟩
   exact ⟨t, ⟨ht1, ht2⟩, ht1 a ha (smul_mem_smul_set hy)⟩
 #align smul_balanced_core_subset smul_balancedCore_subset
@@ -185,7 +185,7 @@ theorem balancedHull.balanced (s : Set E) : Balanced 𝕜 (balancedHull 𝕜 s)
   intro a ha
   simp_rw [balancedHull, smul_set_Union₂, subset_def, mem_Union₂]
   rintro x ⟨r, hr, hx⟩
-  rw [← smul_assoc] at hx 
+  rw [← smul_assoc] at hx
   exact ⟨a • r, (SeminormedRing.norm_hMul _ _).trans (mul_le_one ha (norm_nonneg r) hr), hx⟩
 #align balanced_hull.balanced balancedHull.balanced
 -/
@@ -226,7 +226,7 @@ theorem balancedCoreAux_balanced (h0 : (0 : E) ∈ balancedCoreAux 𝕜 s) :
     rw [norm_smul, norm_inv]
     exact one_le_mul_of_one_le_of_one_le (one_le_inv (norm_pos_iff.mpr h) ha) hr
   have h' := hy (a⁻¹ • r) h''
-  rwa [smul_assoc, mem_inv_smul_set_iff₀ h] at h' 
+  rwa [smul_assoc, mem_inv_smul_set_iff₀ h] at h'
 #align balanced_core_aux_balanced balancedCoreAux_balanced
 -/
 
@@ -289,7 +289,7 @@ protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCo
     refine' isClosed_iInter fun a => _
     refine' isClosed_iInter fun ha => _
     have ha' := lt_of_lt_of_le zero_lt_one ha
-    rw [norm_pos_iff] at ha' 
+    rw [norm_pos_iff] at ha'
     refine' isClosedMap_smul_of_ne_zero ha' U hU
   convert isClosed_empty
   contrapose! h
@@ -309,7 +309,7 @@ theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜
     simpa only [← Prod.exists', ← Prod.forall', ← and_imp, ← and_assoc, exists_prop] using
       h.basis_left (normed_add_comm_group.nhds_zero_basis_norm_lt.prod_nhds (𝓝 _).basis_sets) U hU
   rcases NormedField.exists_norm_lt 𝕜 hr with ⟨y, hy₀, hyr⟩
-  rw [norm_pos_iff] at hy₀ 
+  rw [norm_pos_iff] at hy₀
   have : y • V ∈ 𝓝 (0 : E) := (set_smul_mem_nhds_zero_iff hy₀).mpr hV
   -- It remains to show that `y • V ⊆ balanced_core 𝕜 U`
   refine' Filter.mem_of_superset this (subset_balancedCore (mem_of_mem_nhds hU) fun a ha => _)

4f4a1c87

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
-import Mathbin.Analysis.LocallyConvex.Basic
+import Analysis.LocallyConvex.Basic
 
 #align_import analysis.locally_convex.balanced_core_hull from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"

4f4a1c87

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -186,7 +186,7 @@ theorem balancedHull.balanced (s : Set E) : Balanced 𝕜 (balancedHull 𝕜 s)
   simp_rw [balancedHull, smul_set_Union₂, subset_def, mem_Union₂]
   rintro x ⟨r, hr, hx⟩
   rw [← smul_assoc] at hx 
-  exact ⟨a • r, (SeminormedRing.norm_mul _ _).trans (mul_le_one ha (norm_nonneg r) hr), hx⟩
+  exact ⟨a • r, (SeminormedRing.norm_hMul _ _).trans (mul_le_one ha (norm_nonneg r) hr), hx⟩
 #align balanced_hull.balanced balancedHull.balanced
 -/

4f4a1c87

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module analysis.locally_convex.balanced_core_hull
-! leanprover-community/mathlib commit 4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.LocallyConvex.Basic
 
+#align_import analysis.locally_convex.balanced_core_hull from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"
+
 /-!
 # Balanced Core and Balanced Hull

4f4a1c87

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -102,6 +102,7 @@ theorem mem_balancedCore_iff : x ∈ balancedCore 𝕜 s ↔ ∃ t, Balanced 
 #align mem_balanced_core_iff mem_balancedCore_iff
 -/
 
+#print smul_balancedCore_subset /-
 theorem smul_balancedCore_subset (s : Set E) {a : 𝕜} (ha : ‖a‖ ≤ 1) :
     a • balancedCore 𝕜 s ⊆ balancedCore 𝕜 s :=
   by
@@ -110,6 +111,7 @@ theorem smul_balancedCore_subset (s : Set E) {a : 𝕜} (ha : ‖a‖ ≤ 1) :
   rcases hy with ⟨t, ht1, ht2, hy⟩
   exact ⟨t, ⟨ht1, ht2⟩, ht1 a ha (smul_mem_smul_set hy)⟩
 #align smul_balanced_core_subset smul_balancedCore_subset
+-/
 
 #print balancedCore_balanced /-
 theorem balancedCore_balanced (s : Set E) : Balanced 𝕜 (balancedCore 𝕜 s) := fun _ =>
@@ -117,27 +119,35 @@ theorem balancedCore_balanced (s : Set E) : Balanced 𝕜 (balancedCore 𝕜 s)
 #align balanced_core_balanced balancedCore_balanced
 -/
 
+#print Balanced.subset_balancedCore_of_subset /-
 /-- The balanced core of `t` is maximal in the sense that it contains any balanced subset
 `s` of `t`.-/
 theorem Balanced.subset_balancedCore_of_subset (hs : Balanced 𝕜 s) (h : s ⊆ t) :
     s ⊆ balancedCore 𝕜 t :=
   subset_sUnion_of_mem ⟨hs, h⟩
 #align balanced.subset_core_of_subset Balanced.subset_balancedCore_of_subset
+-/
 
+#print mem_balancedCoreAux_iff /-
 theorem mem_balancedCoreAux_iff : x ∈ balancedCoreAux 𝕜 s ↔ ∀ r : 𝕜, 1 ≤ ‖r‖ → x ∈ r • s :=
   mem_iInter₂
 #align mem_balanced_core_aux_iff mem_balancedCoreAux_iff
+-/
 
+#print mem_balancedHull_iff /-
 theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜) (hr : ‖r‖ ≤ 1), x ∈ r • s :=
   mem_iUnion₂
 #align mem_balanced_hull_iff mem_balancedHull_iff
+-/
 
+#print Balanced.balancedHull_subset_of_subset /-
 /-- The balanced hull of `s` is minimal in the sense that it is contained in any balanced superset
 `t` of `s`. -/
 theorem Balanced.balancedHull_subset_of_subset (ht : Balanced 𝕜 t) (h : s ⊆ t) :
     balancedHull 𝕜 s ⊆ t := fun x hx => by obtain ⟨r, hr, y, hy, rfl⟩ := mem_balancedHull_iff.1 hx;
   exact ht.smul_mem hr (h hy)
 #align balanced.hull_subset_of_subset Balanced.balancedHull_subset_of_subset
+-/
 
 end SMul
 
@@ -145,10 +155,13 @@ section Module
 
 variable [AddCommGroup E] [Module 𝕜 E] {s : Set E}
 
+#print balancedCore_zero_mem /-
 theorem balancedCore_zero_mem (hs : (0 : E) ∈ s) : (0 : E) ∈ balancedCore 𝕜 s :=
   mem_balancedCore_iff.2 ⟨0, balanced_zero, zero_subset.2 hs, zero_mem_zero⟩
 #align balanced_core_zero_mem balancedCore_zero_mem
+-/
 
+#print balancedCore_nonempty_iff /-
 theorem balancedCore_nonempty_iff : (balancedCore 𝕜 s).Nonempty ↔ (0 : E) ∈ s :=
   ⟨fun h =>
     zero_subset.1 <|
@@ -157,12 +170,15 @@ theorem balancedCore_nonempty_iff : (balancedCore 𝕜 s).Nonempty ↔ (0 : E) 
           balancedCore_subset _,
     fun h => ⟨0, balancedCore_zero_mem h⟩⟩
 #align balanced_core_nonempty_iff balancedCore_nonempty_iff
+-/
 
 variable (𝕜)
 
+#print subset_balancedHull /-
 theorem subset_balancedHull [NormOneClass 𝕜] {s : Set E} : s ⊆ balancedHull 𝕜 s := fun _ hx =>
   mem_balancedHull_iff.2 ⟨1, norm_one.le, _, hx, one_smul _ _⟩
 #align subset_balanced_hull subset_balancedHull
+-/
 
 variable {𝕜}
 
@@ -200,6 +216,7 @@ theorem balancedCoreAux_subset (s : Set E) : balancedCoreAux 𝕜 s ⊆ s := fun
 #align balanced_core_aux_subset balancedCoreAux_subset
 -/
 
+#print balancedCoreAux_balanced /-
 theorem balancedCoreAux_balanced (h0 : (0 : E) ∈ balancedCoreAux 𝕜 s) :
     Balanced 𝕜 (balancedCoreAux 𝕜 s) :=
   by
@@ -214,6 +231,7 @@ theorem balancedCoreAux_balanced (h0 : (0 : E) ∈ balancedCoreAux 𝕜 s) :
   have h' := hy (a⁻¹ • r) h''
   rwa [smul_assoc, mem_inv_smul_set_iff₀ h] at h' 
 #align balanced_core_aux_balanced balancedCoreAux_balanced
+-/
 
 #print balancedCoreAux_maximal /-
 theorem balancedCoreAux_maximal (h : t ⊆ s) (ht : Balanced 𝕜 t) : t ⊆ balancedCoreAux 𝕜 s :=
@@ -232,6 +250,7 @@ theorem balancedCore_subset_balancedCoreAux : balancedCore 𝕜 s ⊆ balancedCo
 #align balanced_core_subset_balanced_core_aux balancedCore_subset_balancedCoreAux
 -/
 
+#print balancedCore_eq_iInter /-
 theorem balancedCore_eq_iInter (hs : (0 : E) ∈ s) :
     balancedCore 𝕜 s = ⋂ (r : 𝕜) (hr : 1 ≤ ‖r‖), r • s :=
   by
@@ -239,7 +258,9 @@ theorem balancedCore_eq_iInter (hs : (0 : E) ∈ s) :
   refine' (balancedCoreAux_balanced _).subset_balancedCore_of_subset (balancedCoreAux_subset s)
   exact balancedCore_subset_balancedCoreAux (balancedCore_zero_mem hs)
 #align balanced_core_eq_Inter balancedCore_eq_iInter
+-/
 
+#print subset_balancedCore /-
 theorem subset_balancedCore (ht : (0 : E) ∈ t) (hst : ∀ (a : 𝕜) (ha : ‖a‖ ≤ 1), a • s ⊆ t) :
     s ⊆ balancedCore 𝕜 t := by
   rw [balancedCore_eq_iInter ht]
@@ -249,6 +270,7 @@ theorem subset_balancedCore (ht : (0 : E) ∈ t) (hst : ∀ (a : 𝕜) (ha : ‖
   rw [norm_inv]
   exact inv_le_one ha
 #align subset_balanced_core subset_balancedCore
+-/
 
 end NormedField
 
@@ -278,6 +300,7 @@ protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCo
 #align is_closed.balanced_core IsClosed.balancedCore
 -/
 
+#print balancedCore_mem_nhds_zero /-
 theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜 U ∈ 𝓝 (0 : E) :=
   by
   -- Getting neighborhoods of the origin for `0 : 𝕜` and `0 : E`
@@ -299,16 +322,20 @@ theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜
   rw [norm_mul, ← one_mul r]
   exact mul_lt_mul' ha hyr (norm_nonneg y) one_pos
 #align balanced_core_mem_nhds_zero balancedCore_mem_nhds_zero
+-/
 
 variable (𝕜 E)
 
+#print nhds_basis_balanced /-
 theorem nhds_basis_balanced :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ 𝓝 (0 : E) ∧ Balanced 𝕜 s) id :=
   Filter.hasBasis_self.mpr fun s hs =>
     ⟨balancedCore 𝕜 s, balancedCore_mem_nhds_zero hs, balancedCore_balanced s,
       balancedCore_subset s⟩
 #align nhds_basis_balanced nhds_basis_balanced
+-/
 
+#print nhds_basis_closed_balanced /-
 theorem nhds_basis_closed_balanced [RegularSpace E] :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ 𝓝 (0 : E) ∧ IsClosed s ∧ Balanced 𝕜 s) id :=
   by
@@ -317,6 +344,7 @@ theorem nhds_basis_closed_balanced [RegularSpace E] :
   refine' ⟨balancedCore 𝕜 s, ⟨balancedCore_mem_nhds_zero hs.1, _⟩, balancedCore_subset s⟩
   exact ⟨hs.2.balancedCore, balancedCore_balanced s⟩
 #align nhds_basis_closed_balanced nhds_basis_closed_balanced
+-/
 
 end Topology

4f4a1c87

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -64,7 +64,7 @@ variable (𝕜) [SMul 𝕜 E] {s t : Set E} {x : E}
 #print balancedCore /-
 /-- The largest balanced subset of `s`.-/
 def balancedCore (s : Set E) :=
-  ⋃₀ { t : Set E | Balanced 𝕜 t ∧ t ⊆ s }
+  ⋃₀ {t : Set E | Balanced 𝕜 t ∧ t ⊆ s}
 #align balanced_core balancedCore
 -/

4f4a1c87

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -106,7 +106,7 @@ theorem smul_balancedCore_subset (s : Set E) {a : 𝕜} (ha : ‖a‖ ≤ 1) :
     a • balancedCore 𝕜 s ⊆ balancedCore 𝕜 s :=
   by
   rintro x ⟨y, hy, rfl⟩
-  rw [mem_balancedCore_iff] at hy
+  rw [mem_balancedCore_iff] at hy 
   rcases hy with ⟨t, ht1, ht2, hy⟩
   exact ⟨t, ⟨ht1, ht2⟩, ht1 a ha (smul_mem_smul_set hy)⟩
 #align smul_balanced_core_subset smul_balancedCore_subset
@@ -128,7 +128,7 @@ theorem mem_balancedCoreAux_iff : x ∈ balancedCoreAux 𝕜 s ↔ ∀ r : 𝕜,
   mem_iInter₂
 #align mem_balanced_core_aux_iff mem_balancedCoreAux_iff
 
-theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜)(hr : ‖r‖ ≤ 1), x ∈ r • s :=
+theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜) (hr : ‖r‖ ≤ 1), x ∈ r • s :=
   mem_iUnion₂
 #align mem_balanced_hull_iff mem_balancedHull_iff
 
@@ -172,7 +172,7 @@ theorem balancedHull.balanced (s : Set E) : Balanced 𝕜 (balancedHull 𝕜 s)
   intro a ha
   simp_rw [balancedHull, smul_set_Union₂, subset_def, mem_Union₂]
   rintro x ⟨r, hr, hx⟩
-  rw [← smul_assoc] at hx
+  rw [← smul_assoc] at hx 
   exact ⟨a • r, (SeminormedRing.norm_mul _ _).trans (mul_le_one ha (norm_nonneg r) hr), hx⟩
 #align balanced_hull.balanced balancedHull.balanced
 -/
@@ -206,13 +206,13 @@ theorem balancedCoreAux_balanced (h0 : (0 : E) ∈ balancedCoreAux 𝕜 s) :
   rintro a ha x ⟨y, hy, rfl⟩
   obtain rfl | h := eq_or_ne a 0
   · rwa [zero_smul]
-  rw [mem_balancedCoreAux_iff] at hy⊢
+  rw [mem_balancedCoreAux_iff] at hy ⊢
   intro r hr
   have h'' : 1 ≤ ‖a⁻¹ • r‖ := by
     rw [norm_smul, norm_inv]
     exact one_le_mul_of_one_le_of_one_le (one_le_inv (norm_pos_iff.mpr h) ha) hr
   have h' := hy (a⁻¹ • r) h''
-  rwa [smul_assoc, mem_inv_smul_set_iff₀ h] at h'
+  rwa [smul_assoc, mem_inv_smul_set_iff₀ h] at h' 
 #align balanced_core_aux_balanced balancedCoreAux_balanced
 
 #print balancedCoreAux_maximal /-
@@ -270,7 +270,7 @@ protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCo
     refine' isClosed_iInter fun a => _
     refine' isClosed_iInter fun ha => _
     have ha' := lt_of_lt_of_le zero_lt_one ha
-    rw [norm_pos_iff] at ha'
+    rw [norm_pos_iff] at ha' 
     refine' isClosedMap_smul_of_ne_zero ha' U hU
   convert isClosed_empty
   contrapose! h
@@ -282,14 +282,14 @@ theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜
   by
   -- Getting neighborhoods of the origin for `0 : 𝕜` and `0 : E`
   obtain ⟨r, V, hr, hV, hrVU⟩ :
-    ∃ (r : ℝ)(V : Set E), 0 < r ∧ V ∈ 𝓝 (0 : E) ∧ ∀ (c : 𝕜) (y : E), ‖c‖ < r → y ∈ V → c • y ∈ U :=
+    ∃ (r : ℝ) (V : Set E), 0 < r ∧ V ∈ 𝓝 (0 : E) ∧ ∀ (c : 𝕜) (y : E), ‖c‖ < r → y ∈ V → c • y ∈ U :=
     by
     have h : Filter.Tendsto (fun x : 𝕜 × E => x.fst • x.snd) (𝓝 (0, 0)) (𝓝 0) :=
       continuous_smul.tendsto' (0, 0) _ (smul_zero _)
     simpa only [← Prod.exists', ← Prod.forall', ← and_imp, ← and_assoc, exists_prop] using
       h.basis_left (normed_add_comm_group.nhds_zero_basis_norm_lt.prod_nhds (𝓝 _).basis_sets) U hU
   rcases NormedField.exists_norm_lt 𝕜 hr with ⟨y, hy₀, hyr⟩
-  rw [norm_pos_iff] at hy₀
+  rw [norm_pos_iff] at hy₀ 
   have : y • V ∈ 𝓝 (0 : E) := (set_smul_mem_nhds_zero_iff hy₀).mpr hV
   -- It remains to show that `y • V ⊆ balanced_core 𝕜 U`
   refine' Filter.mem_of_superset this (subset_balancedCore (mem_of_mem_nhds hU) fun a ha => _)

4f4a1c87

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -47,7 +47,7 @@ balanced
 
 open Set
 
-open Pointwise Topology Filter
+open scoped Pointwise Topology Filter
 
 variable {𝕜 E ι : Type _}

4f4a1c87

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -102,12 +102,6 @@ theorem mem_balancedCore_iff : x ∈ balancedCore 𝕜 s ↔ ∃ t, Balanced 
 #align mem_balanced_core_iff mem_balancedCore_iff
 -/
 
-/- warning: smul_balanced_core_subset -> smul_balancedCore_subset is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] (s : Set.{u2} E) {a : 𝕜}, (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (SeminormedRing.toHasNorm.{u1} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E _inst_2) a (balancedCore.{u1, u2} 𝕜 E _inst_1 _inst_2 s)) (balancedCore.{u1, u2} 𝕜 E _inst_1 _inst_2 s))
-but is expected to have type
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 theorem smul_balancedCore_subset (s : Set E) {a : 𝕜} (ha : ‖a‖ ≤ 1) :
     a • balancedCore 𝕜 s ⊆ balancedCore 𝕜 s :=
   by
@@ -123,12 +117,6 @@ theorem balancedCore_balanced (s : Set E) : Balanced 𝕜 (balancedCore 𝕜 s)
 #align balanced_core_balanced balancedCore_balanced
 -/
 
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 /-- The balanced core of `t` is maximal in the sense that it contains any balanced subset
 `s` of `t`.-/
 theorem Balanced.subset_balancedCore_of_subset (hs : Balanced 𝕜 s) (h : s ⊆ t) :
@@ -136,32 +124,14 @@ theorem Balanced.subset_balancedCore_of_subset (hs : Balanced 𝕜 s) (h : s ⊆
   subset_sUnion_of_mem ⟨hs, h⟩
 #align balanced.subset_core_of_subset Balanced.subset_balancedCore_of_subset
 
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 theorem mem_balancedCoreAux_iff : x ∈ balancedCoreAux 𝕜 s ↔ ∀ r : 𝕜, 1 ≤ ‖r‖ → x ∈ r • s :=
   mem_iInter₂
 #align mem_balanced_core_aux_iff mem_balancedCoreAux_iff
 
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 theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜)(hr : ‖r‖ ≤ 1), x ∈ r • s :=
   mem_iUnion₂
 #align mem_balanced_hull_iff mem_balancedHull_iff
 
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 /-- The balanced hull of `s` is minimal in the sense that it is contained in any balanced superset
 `t` of `s`. -/
 theorem Balanced.balancedHull_subset_of_subset (ht : Balanced 𝕜 t) (h : s ⊆ t) :
@@ -175,22 +145,10 @@ section Module
 
 variable [AddCommGroup E] [Module 𝕜 E] {s : Set E}
 
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 theorem balancedCore_zero_mem (hs : (0 : E) ∈ s) : (0 : E) ∈ balancedCore 𝕜 s :=
   mem_balancedCore_iff.2 ⟨0, balanced_zero, zero_subset.2 hs, zero_mem_zero⟩
 #align balanced_core_zero_mem balancedCore_zero_mem
 
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-Case conversion may be inaccurate. Consider using '#align balanced_core_nonempty_iff balancedCore_nonempty_iffₓ'. -/
 theorem balancedCore_nonempty_iff : (balancedCore 𝕜 s).Nonempty ↔ (0 : E) ∈ s :=
   ⟨fun h =>
     zero_subset.1 <|
@@ -202,12 +160,6 @@ theorem balancedCore_nonempty_iff : (balancedCore 𝕜 s).Nonempty ↔ (0 : E) 
 
 variable (𝕜)
 
-/- warning: subset_balanced_hull -> subset_balancedHull is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align subset_balanced_hull subset_balancedHullₓ'. -/
 theorem subset_balancedHull [NormOneClass 𝕜] {s : Set E} : s ⊆ balancedHull 𝕜 s := fun _ hx =>
   mem_balancedHull_iff.2 ⟨1, norm_one.le, _, hx, one_smul _ _⟩
 #align subset_balanced_hull subset_balancedHull
@@ -248,9 +200,6 @@ theorem balancedCoreAux_subset (s : Set E) : balancedCoreAux 𝕜 s ⊆ s := fun
 #align balanced_core_aux_subset balancedCoreAux_subset
 -/
 
-/- warning: balanced_core_aux_balanced -> balancedCoreAux_balanced is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align balanced_core_aux_balanced balancedCoreAux_balancedₓ'. -/
 theorem balancedCoreAux_balanced (h0 : (0 : E) ∈ balancedCoreAux 𝕜 s) :
     Balanced 𝕜 (balancedCoreAux 𝕜 s) :=
   by
@@ -283,12 +232,6 @@ theorem balancedCore_subset_balancedCoreAux : balancedCore 𝕜 s ⊆ balancedCo
 #align balanced_core_subset_balanced_core_aux balancedCore_subset_balancedCoreAux
 -/
 
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) s) -> (Eq.{succ u2} (Set.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s) (Set.iInter.{u2, succ u1} E 𝕜 (fun (r : 𝕜) => Set.iInter.{u2, 0} E (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r)) (fun (hr : LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r)) => HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))) r s))))
-Case conversion may be inaccurate. Consider using '#align balanced_core_eq_Inter balancedCore_eq_iInterₓ'. -/
 theorem balancedCore_eq_iInter (hs : (0 : E) ∈ s) :
     balancedCore 𝕜 s = ⋂ (r : 𝕜) (hr : 1 ≤ ‖r‖), r • s :=
   by
@@ -297,12 +240,6 @@ theorem balancedCore_eq_iInter (hs : (0 : E) ∈ s) :
   exact balancedCore_subset_balancedCoreAux (balancedCore_zero_mem hs)
 #align balanced_core_eq_Inter balancedCore_eq_iInter
 
-/- warning: subset_balanced_core -> subset_balancedCore is a dubious translation:
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {t : Set.{u2} E}, (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)))))))) t) -> (forall (a : 𝕜), (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) a s) t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) t))
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) t) -> (forall (a : 𝕜), (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))) a s) t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) s (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) t))
-Case conversion may be inaccurate. Consider using '#align subset_balanced_core subset_balancedCoreₓ'. -/
 theorem subset_balancedCore (ht : (0 : E) ∈ t) (hst : ∀ (a : 𝕜) (ha : ‖a‖ ≤ 1), a • s ⊆ t) :
     s ⊆ balancedCore 𝕜 t := by
   rw [balancedCore_eq_iInter ht]
@@ -341,12 +278,6 @@ protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCo
 #align is_closed.balanced_core IsClosed.balancedCore
 -/
 
-/- warning: balanced_core_mem_nhds_zero -> balancedCore_mem_nhds_zero is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4] {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)))))))))) -> (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) 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))))))))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4] {U : Set.{u2} E}, (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) U (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))))))))) -> (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) U) (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)))))))))
-Case conversion may be inaccurate. Consider using '#align balanced_core_mem_nhds_zero balancedCore_mem_nhds_zeroₓ'. -/
 theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜 U ∈ 𝓝 (0 : E) :=
   by
   -- Getting neighborhoods of the origin for `0 : 𝕜` and `0 : E`
@@ -371,12 +302,6 @@ theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜
 
 variable (𝕜 E)
 
-/- warning: nhds_basis_balanced -> nhds_basis_balanced is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _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)))))))))) (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) (id.{succ u2} (Set.{u2} E))
-but is expected to have type
-  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4], Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (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)))))))) (fun (s : Set.{u2} E) => And (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) s (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))))))))) (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) (id.{succ u2} (Set.{u2} E))
-Case conversion may be inaccurate. Consider using '#align nhds_basis_balanced nhds_basis_balancedₓ'. -/
 theorem nhds_basis_balanced :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ 𝓝 (0 : E) ∧ Balanced 𝕜 s) id :=
   Filter.hasBasis_self.mpr fun s hs =>
@@ -384,12 +309,6 @@ theorem nhds_basis_balanced :
       balancedCore_subset s⟩
 #align nhds_basis_balanced nhds_basis_balanced
 
-/- warning: nhds_basis_closed_balanced -> nhds_basis_closed_balanced is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4] [_inst_6 : RegularSpace.{u2} E _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)))))))))) (And (IsClosed.{u2} E _inst_4 s) (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))) (id.{succ u2} (Set.{u2} E))
-but is expected to have type
-  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4] [_inst_6 : RegularSpace.{u2} E _inst_4], Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (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)))))))) (fun (s : Set.{u2} E) => And (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) s (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))))))))) (And (IsClosed.{u2} E _inst_4 s) (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))) (id.{succ u2} (Set.{u2} E))
-Case conversion may be inaccurate. Consider using '#align nhds_basis_closed_balanced nhds_basis_closed_balancedₓ'. -/
 theorem nhds_basis_closed_balanced [RegularSpace E] :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ 𝓝 (0 : E) ∧ IsClosed s ∧ Balanced 𝕜 s) id :=
   by

4f4a1c87

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -165,9 +165,7 @@ Case conversion may be inaccurate. Consider using '#align balanced.hull_subset_o
 /-- The balanced hull of `s` is minimal in the sense that it is contained in any balanced superset
 `t` of `s`. -/
 theorem Balanced.balancedHull_subset_of_subset (ht : Balanced 𝕜 t) (h : s ⊆ t) :
-    balancedHull 𝕜 s ⊆ t := fun x hx =>
-  by
-  obtain ⟨r, hr, y, hy, rfl⟩ := mem_balancedHull_iff.1 hx
+    balancedHull 𝕜 s ⊆ t := fun x hx => by obtain ⟨r, hr, y, hy, rfl⟩ := mem_balancedHull_iff.1 hx;
   exact ht.smul_mem hr (h hy)
 #align balanced.hull_subset_of_subset Balanced.balancedHull_subset_of_subset

4f4a1c87

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -251,10 +251,7 @@ theorem balancedCoreAux_subset (s : Set E) : balancedCoreAux 𝕜 s ⊆ s := fun
 -/
 
 /- warning: balanced_core_aux_balanced -> balancedCoreAux_balanced is a dubious translation:
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (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)))))))) (balancedCoreAux.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) -> (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (balancedCoreAux.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) (balancedCoreAux.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) -> (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (balancedCoreAux.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align balanced_core_aux_balanced balancedCoreAux_balancedₓ'. -/
 theorem balancedCoreAux_balanced (h0 : (0 : E) ∈ balancedCoreAux 𝕜 s) :
     Balanced 𝕜 (balancedCoreAux 𝕜 s) :=

4f4a1c87

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -86,7 +86,7 @@ variable {𝕜}
 
 #print balancedCore_subset /-
 theorem balancedCore_subset (s : Set E) : balancedCore 𝕜 s ⊆ s :=
-  unionₛ_subset fun t ht => ht.2
+  sUnion_subset fun t ht => ht.2
 #align balanced_core_subset balancedCore_subset
 -/
 
@@ -133,7 +133,7 @@ Case conversion may be inaccurate. Consider using '#align balanced.subset_core_o
 `s` of `t`.-/
 theorem Balanced.subset_balancedCore_of_subset (hs : Balanced 𝕜 s) (h : s ⊆ t) :
     s ⊆ balancedCore 𝕜 t :=
-  subset_unionₛ_of_mem ⟨hs, h⟩
+  subset_sUnion_of_mem ⟨hs, h⟩
 #align balanced.subset_core_of_subset Balanced.subset_balancedCore_of_subset
 
 /- warning: mem_balanced_core_aux_iff -> mem_balancedCoreAux_iff is a dubious translation:
@@ -143,7 +143,7 @@ but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (balancedCoreAux.{u1, u2} 𝕜 E _inst_1 _inst_2 s)) (forall (r : 𝕜), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (SeminormedRing.toNorm.{u1} 𝕜 _inst_1) r)) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E _inst_2)) r s)))
 Case conversion may be inaccurate. Consider using '#align mem_balanced_core_aux_iff mem_balancedCoreAux_iffₓ'. -/
 theorem mem_balancedCoreAux_iff : x ∈ balancedCoreAux 𝕜 s ↔ ∀ r : 𝕜, 1 ≤ ‖r‖ → x ∈ r • s :=
-  mem_interᵢ₂
+  mem_iInter₂
 #align mem_balanced_core_aux_iff mem_balancedCoreAux_iff
 
 /- warning: mem_balanced_hull_iff -> mem_balancedHull_iff is a dubious translation:
@@ -153,7 +153,7 @@ but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (balancedHull.{u1, u2} 𝕜 E _inst_1 _inst_2 s)) (Exists.{succ u1} 𝕜 (fun (r : 𝕜) => Exists.{0} (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} 𝕜 (SeminormedRing.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (fun (hr : LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} 𝕜 (SeminormedRing.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E _inst_2)) r s))))
 Case conversion may be inaccurate. Consider using '#align mem_balanced_hull_iff mem_balancedHull_iffₓ'. -/
 theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜)(hr : ‖r‖ ≤ 1), x ∈ r • s :=
-  mem_unionᵢ₂
+  mem_iUnion₂
 #align mem_balanced_hull_iff mem_balancedHull_iff
 
 /- warning: balanced.hull_subset_of_subset -> Balanced.balancedHull_subset_of_subset is a dubious translation:
@@ -288,19 +288,19 @@ theorem balancedCore_subset_balancedCoreAux : balancedCore 𝕜 s ⊆ balancedCo
 #align balanced_core_subset_balanced_core_aux balancedCore_subset_balancedCoreAux
 -/
 
-/- warning: balanced_core_eq_Inter -> balancedCore_eq_interᵢ is a dubious translation:
+/- warning: balanced_core_eq_Inter -> balancedCore_eq_iInter is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (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) -> (Eq.{succ u2} (Set.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s) (Set.interᵢ.{u2, succ u1} E 𝕜 (fun (r : 𝕜) => Set.interᵢ.{u2, 0} E (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r)) (fun (hr : LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r)) => SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) r s))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (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) -> (Eq.{succ u2} (Set.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s) (Set.iInter.{u2, succ u1} E 𝕜 (fun (r : 𝕜) => Set.iInter.{u2, 0} E (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r)) (fun (hr : LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r)) => SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) r s))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) s) -> (Eq.{succ u2} (Set.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s) (Set.interᵢ.{u2, succ u1} E 𝕜 (fun (r : 𝕜) => Set.interᵢ.{u2, 0} E (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r)) (fun (hr : LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r)) => HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))) r s))))
-Case conversion may be inaccurate. Consider using '#align balanced_core_eq_Inter balancedCore_eq_interᵢₓ'. -/
-theorem balancedCore_eq_interᵢ (hs : (0 : E) ∈ s) :
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) s) -> (Eq.{succ u2} (Set.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s) (Set.iInter.{u2, succ u1} E 𝕜 (fun (r : 𝕜) => Set.iInter.{u2, 0} E (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r)) (fun (hr : LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r)) => HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))) r s))))
+Case conversion may be inaccurate. Consider using '#align balanced_core_eq_Inter balancedCore_eq_iInterₓ'. -/
+theorem balancedCore_eq_iInter (hs : (0 : E) ∈ s) :
     balancedCore 𝕜 s = ⋂ (r : 𝕜) (hr : 1 ≤ ‖r‖), r • s :=
   by
   refine' balanced_core_subset_balanced_core_aux.antisymm _
   refine' (balancedCoreAux_balanced _).subset_balancedCore_of_subset (balancedCoreAux_subset s)
   exact balancedCore_subset_balancedCoreAux (balancedCore_zero_mem hs)
-#align balanced_core_eq_Inter balancedCore_eq_interᵢ
+#align balanced_core_eq_Inter balancedCore_eq_iInter
 
 /- warning: subset_balanced_core -> subset_balancedCore is a dubious translation:
 lean 3 declaration is
@@ -310,7 +310,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align subset_balanced_core subset_balancedCoreₓ'. -/
 theorem subset_balancedCore (ht : (0 : E) ∈ t) (hst : ∀ (a : 𝕜) (ha : ‖a‖ ≤ 1), a • s ⊆ t) :
     s ⊆ balancedCore 𝕜 t := by
-  rw [balancedCore_eq_interᵢ ht]
+  rw [balancedCore_eq_iInter ht]
   refine' subset_Inter₂ fun a ha => _
   rw [← smul_inv_smul₀ (norm_pos_iff.mp <| zero_lt_one.trans_le ha) s]
   refine' smul_set_mono (hst _ _)
@@ -334,9 +334,9 @@ variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Topolo
 protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCore 𝕜 U) :=
   by
   by_cases h : (0 : E) ∈ U
-  · rw [balancedCore_eq_interᵢ h]
-    refine' isClosed_interᵢ fun a => _
-    refine' isClosed_interᵢ fun ha => _
+  · rw [balancedCore_eq_iInter h]
+    refine' isClosed_iInter fun a => _
+    refine' isClosed_iInter fun ha => _
     have ha' := lt_of_lt_of_le zero_lt_one ha
     rw [norm_pos_iff] at ha'
     refine' isClosedMap_smul_of_ne_zero ha' U hU

4f4a1c87

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -208,7 +208,7 @@ variable (𝕜)
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : NormOneClass.{u1} 𝕜 (SeminormedRing.toHasNorm.{u1} 𝕜 _inst_1) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))))] {s : Set.{u2} E}, HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (balancedHull.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)
 but is expected to have type
-  forall (𝕜 : Type.{u2}) {E : Type.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : NormOneClass.{u2} 𝕜 (SeminormedRing.toNorm.{u2} 𝕜 _inst_1) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)))] {s : Set.{u1} E}, HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s (balancedHull.{u2, u1} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s)
+  forall (𝕜 : Type.{u2}) {E : Type.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : NormOneClass.{u2} 𝕜 (SeminormedRing.toNorm.{u2} 𝕜 _inst_1) (Semiring.toOne.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)))] {s : Set.{u1} E}, HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s (balancedHull.{u2, u1} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s)
 Case conversion may be inaccurate. Consider using '#align subset_balanced_hull subset_balancedHullₓ'. -/
 theorem subset_balancedHull [NormOneClass 𝕜] {s : Set E} : s ⊆ balancedHull 𝕜 s := fun _ hx =>
   mem_balancedHull_iff.2 ⟨1, norm_one.le, _, hx, one_smul _ _⟩

4f4a1c87

bump to nightly-2023-04-16-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b

63127953

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.locally_convex.balanced_core_hull
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b
 ! 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.LocallyConvex.Basic
 /-!
 # Balanced Core and Balanced Hull
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `balanced_core`: The largest balanced subset of a set `s`.

f2ce6086

bump to nightly-2023-04-13-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

7a1b67c7

Diff

@@ -58,35 +58,53 @@ section SMul
 
 variable (𝕜) [SMul 𝕜 E] {s t : Set E} {x : E}
 
+#print balancedCore /-
 /-- The largest balanced subset of `s`.-/
 def balancedCore (s : Set E) :=
   ⋃₀ { t : Set E | Balanced 𝕜 t ∧ t ⊆ s }
 #align balanced_core balancedCore
+-/
 
+#print balancedCoreAux /-
 /-- Helper definition to prove `balanced_core_eq_Inter`-/
 def balancedCoreAux (s : Set E) :=
   ⋂ (r : 𝕜) (hr : 1 ≤ ‖r‖), r • s
 #align balanced_core_aux balancedCoreAux
+-/
 
+#print balancedHull /-
 /-- The smallest balanced superset of `s`.-/
 def balancedHull (s : Set E) :=
   ⋃ (r : 𝕜) (hr : ‖r‖ ≤ 1), r • s
 #align balanced_hull balancedHull
+-/
 
 variable {𝕜}
 
+#print balancedCore_subset /-
 theorem balancedCore_subset (s : Set E) : balancedCore 𝕜 s ⊆ s :=
   unionₛ_subset fun t ht => ht.2
 #align balanced_core_subset balancedCore_subset
+-/
 
+#print balancedCore_empty /-
 theorem balancedCore_empty : balancedCore 𝕜 (∅ : Set E) = ∅ :=
   eq_empty_of_subset_empty (balancedCore_subset _)
 #align balanced_core_empty balancedCore_empty
+-/
 
+#print mem_balancedCore_iff /-
 theorem mem_balancedCore_iff : x ∈ balancedCore 𝕜 s ↔ ∃ t, Balanced 𝕜 t ∧ t ⊆ s ∧ x ∈ t := by
   simp_rw [balancedCore, mem_sUnion, mem_set_of_eq, exists_prop, and_assoc']
 #align mem_balanced_core_iff mem_balancedCore_iff
+-/
 
+/- warning: smul_balanced_core_subset -> smul_balancedCore_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] (s : Set.{u2} E) {a : 𝕜}, (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (SeminormedRing.toHasNorm.{u1} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E _inst_2) a (balancedCore.{u1, u2} 𝕜 E _inst_1 _inst_2 s)) (balancedCore.{u1, u2} 𝕜 E _inst_1 _inst_2 s))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] (s : Set.{u2} E) {a : 𝕜}, (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} 𝕜 (SeminormedRing.toNorm.{u1} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E _inst_2)) a (balancedCore.{u1, u2} 𝕜 E _inst_1 _inst_2 s)) (balancedCore.{u1, u2} 𝕜 E _inst_1 _inst_2 s))
+Case conversion may be inaccurate. Consider using '#align smul_balanced_core_subset smul_balancedCore_subsetₓ'. -/
 theorem smul_balancedCore_subset (s : Set E) {a : 𝕜} (ha : ‖a‖ ≤ 1) :
     a • balancedCore 𝕜 s ⊆ balancedCore 𝕜 s :=
   by
@@ -96,31 +114,59 @@ theorem smul_balancedCore_subset (s : Set E) {a : 𝕜} (ha : ‖a‖ ≤ 1) :
   exact ⟨t, ⟨ht1, ht2⟩, ht1 a ha (smul_mem_smul_set hy)⟩
 #align smul_balanced_core_subset smul_balancedCore_subset
 
+#print balancedCore_balanced /-
 theorem balancedCore_balanced (s : Set E) : Balanced 𝕜 (balancedCore 𝕜 s) := fun _ =>
   smul_balancedCore_subset s
 #align balanced_core_balanced balancedCore_balanced
+-/
 
+/- warning: balanced.subset_core_of_subset -> Balanced.subset_balancedCore_of_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {t : Set.{u2} E}, (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 s) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s t) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (balancedCore.{u1, u2} 𝕜 E _inst_1 _inst_2 t))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u1} 𝕜 E] {s : Set.{u1} E} {t : Set.{u1} E}, (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 s) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s t) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s (balancedCore.{u2, u1} 𝕜 E _inst_1 _inst_2 t))
+Case conversion may be inaccurate. Consider using '#align balanced.subset_core_of_subset Balanced.subset_balancedCore_of_subsetₓ'. -/
 /-- The balanced core of `t` is maximal in the sense that it contains any balanced subset
 `s` of `t`.-/
-theorem Balanced.subset_core_of_subset (hs : Balanced 𝕜 s) (h : s ⊆ t) : s ⊆ balancedCore 𝕜 t :=
+theorem Balanced.subset_balancedCore_of_subset (hs : Balanced 𝕜 s) (h : s ⊆ t) :
+    s ⊆ balancedCore 𝕜 t :=
   subset_unionₛ_of_mem ⟨hs, h⟩
-#align balanced.subset_core_of_subset Balanced.subset_core_of_subset
-
+#align balanced.subset_core_of_subset Balanced.subset_balancedCore_of_subset
+
+/- warning: mem_balanced_core_aux_iff -> mem_balancedCoreAux_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (balancedCoreAux.{u1, u2} 𝕜 E _inst_1 _inst_2 s)) (forall (r : 𝕜), (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Norm.norm.{u1} 𝕜 (SeminormedRing.toHasNorm.{u1} 𝕜 _inst_1) r)) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E _inst_2) r s)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (balancedCoreAux.{u1, u2} 𝕜 E _inst_1 _inst_2 s)) (forall (r : 𝕜), (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (SeminormedRing.toNorm.{u1} 𝕜 _inst_1) r)) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E _inst_2)) r s)))
+Case conversion may be inaccurate. Consider using '#align mem_balanced_core_aux_iff mem_balancedCoreAux_iffₓ'. -/
 theorem mem_balancedCoreAux_iff : x ∈ balancedCoreAux 𝕜 s ↔ ∀ r : 𝕜, 1 ≤ ‖r‖ → x ∈ r • s :=
   mem_interᵢ₂
 #align mem_balanced_core_aux_iff mem_balancedCoreAux_iff
 
+/- warning: mem_balanced_hull_iff -> mem_balancedHull_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (balancedHull.{u1, u2} 𝕜 E _inst_1 _inst_2 s)) (Exists.{succ u1} 𝕜 (fun (r : 𝕜) => Exists.{0} (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (SeminormedRing.toHasNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (fun (hr : LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (SeminormedRing.toHasNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E _inst_2) r s))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (balancedHull.{u1, u2} 𝕜 E _inst_1 _inst_2 s)) (Exists.{succ u1} 𝕜 (fun (r : 𝕜) => Exists.{0} (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} 𝕜 (SeminormedRing.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (fun (hr : LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} 𝕜 (SeminormedRing.toNorm.{u1} 𝕜 _inst_1) r) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) => Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E _inst_2)) r s))))
+Case conversion may be inaccurate. Consider using '#align mem_balanced_hull_iff mem_balancedHull_iffₓ'. -/
 theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜)(hr : ‖r‖ ≤ 1), x ∈ r • s :=
   mem_unionᵢ₂
 #align mem_balanced_hull_iff mem_balancedHull_iff
 
+/- warning: balanced.hull_subset_of_subset -> Balanced.balancedHull_subset_of_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {t : Set.{u2} E}, (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 t) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s t) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (balancedHull.{u1, u2} 𝕜 E _inst_1 _inst_2 s) t)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u1} 𝕜 E] {s : Set.{u1} E} {t : Set.{u1} E}, (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 t) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s t) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) (balancedHull.{u2, u1} 𝕜 E _inst_1 _inst_2 s) t)
+Case conversion may be inaccurate. Consider using '#align balanced.hull_subset_of_subset Balanced.balancedHull_subset_of_subsetₓ'. -/
 /-- The balanced hull of `s` is minimal in the sense that it is contained in any balanced superset
 `t` of `s`. -/
-theorem Balanced.hull_subset_of_subset (ht : Balanced 𝕜 t) (h : s ⊆ t) : balancedHull 𝕜 s ⊆ t :=
-  fun x hx => by
+theorem Balanced.balancedHull_subset_of_subset (ht : Balanced 𝕜 t) (h : s ⊆ t) :
+    balancedHull 𝕜 s ⊆ t := fun x hx =>
+  by
   obtain ⟨r, hr, y, hy, rfl⟩ := mem_balancedHull_iff.1 hx
   exact ht.smul_mem hr (h hy)
-#align balanced.hull_subset_of_subset Balanced.hull_subset_of_subset
+#align balanced.hull_subset_of_subset Balanced.balancedHull_subset_of_subset
 
 end SMul
 
@@ -128,10 +174,22 @@ section Module
 
 variable [AddCommGroup E] [Module 𝕜 E] {s : Set E}
 
+/- warning: balanced_core_zero_mem -> balancedCore_zero_mem is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (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) -> (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)))))))) (balancedCore.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) s) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) (balancedCore.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))
+Case conversion may be inaccurate. Consider using '#align balanced_core_zero_mem balancedCore_zero_memₓ'. -/
 theorem balancedCore_zero_mem (hs : (0 : E) ∈ s) : (0 : E) ∈ balancedCore 𝕜 s :=
   mem_balancedCore_iff.2 ⟨0, balanced_zero, zero_subset.2 hs, zero_mem_zero⟩
 #align balanced_core_zero_mem balancedCore_zero_mem
 
+/- warning: balanced_core_nonempty_iff -> balancedCore_nonempty_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, Iff (Set.Nonempty.{u2} E (balancedCore.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) (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)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, Iff (Set.Nonempty.{u2} E (balancedCore.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) s)
+Case conversion may be inaccurate. Consider using '#align balanced_core_nonempty_iff balancedCore_nonempty_iffₓ'. -/
 theorem balancedCore_nonempty_iff : (balancedCore 𝕜 s).Nonempty ↔ (0 : E) ∈ s :=
   ⟨fun h =>
     zero_subset.1 <|
@@ -143,12 +201,19 @@ theorem balancedCore_nonempty_iff : (balancedCore 𝕜 s).Nonempty ↔ (0 : E) 
 
 variable (𝕜)
 
+/- warning: subset_balanced_hull -> subset_balancedHull is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : NormOneClass.{u1} 𝕜 (SeminormedRing.toHasNorm.{u1} 𝕜 _inst_1) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))))] {s : Set.{u2} E}, HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (balancedHull.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)
+but is expected to have type
+  forall (𝕜 : Type.{u2}) {E : Type.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : NormOneClass.{u2} 𝕜 (SeminormedRing.toNorm.{u2} 𝕜 _inst_1) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)))] {s : Set.{u1} E}, HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s (balancedHull.{u2, u1} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (SeminormedRing.toRing.{u2} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s)
+Case conversion may be inaccurate. Consider using '#align subset_balanced_hull subset_balancedHullₓ'. -/
 theorem subset_balancedHull [NormOneClass 𝕜] {s : Set E} : s ⊆ balancedHull 𝕜 s := fun _ hx =>
   mem_balancedHull_iff.2 ⟨1, norm_one.le, _, hx, one_smul _ _⟩
 #align subset_balanced_hull subset_balancedHull
 
 variable {𝕜}
 
+#print balancedHull.balanced /-
 theorem balancedHull.balanced (s : Set E) : Balanced 𝕜 (balancedHull 𝕜 s) :=
   by
   intro a ha
@@ -157,6 +222,7 @@ theorem balancedHull.balanced (s : Set E) : Balanced 𝕜 (balancedHull 𝕜 s)
   rw [← smul_assoc] at hx
   exact ⟨a • r, (SeminormedRing.norm_mul _ _).trans (mul_le_one ha (norm_nonneg r) hr), hx⟩
 #align balanced_hull.balanced balancedHull.balanced
+-/
 
 end Module
 
@@ -166,17 +232,27 @@ section NormedField
 
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {s t : Set E}
 
+#print balancedCoreAux_empty /-
 @[simp]
 theorem balancedCoreAux_empty : balancedCoreAux 𝕜 (∅ : Set E) = ∅ :=
   by
   simp_rw [balancedCoreAux, Inter₂_eq_empty_iff, smul_set_empty]
   exact fun _ => ⟨1, norm_one.ge, not_mem_empty _⟩
 #align balanced_core_aux_empty balancedCoreAux_empty
+-/
 
+#print balancedCoreAux_subset /-
 theorem balancedCoreAux_subset (s : Set E) : balancedCoreAux 𝕜 s ⊆ s := fun x hx => by
   simpa only [one_smul] using mem_balancedCoreAux_iff.1 hx 1 norm_one.ge
 #align balanced_core_aux_subset balancedCoreAux_subset
+-/
 
+/- warning: balanced_core_aux_balanced -> balancedCoreAux_balanced is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (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)))))))) (balancedCoreAux.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) -> (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (balancedCoreAux.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) (balancedCoreAux.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) -> (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (balancedCoreAux.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))
+Case conversion may be inaccurate. Consider using '#align balanced_core_aux_balanced balancedCoreAux_balancedₓ'. -/
 theorem balancedCoreAux_balanced (h0 : (0 : E) ∈ balancedCoreAux 𝕜 s) :
     Balanced 𝕜 (balancedCoreAux 𝕜 s) :=
   by
@@ -192,6 +268,7 @@ theorem balancedCoreAux_balanced (h0 : (0 : E) ∈ balancedCoreAux 𝕜 s) :
   rwa [smul_assoc, mem_inv_smul_set_iff₀ h] at h'
 #align balanced_core_aux_balanced balancedCoreAux_balanced
 
+#print balancedCoreAux_maximal /-
 theorem balancedCoreAux_maximal (h : t ⊆ s) (ht : Balanced 𝕜 t) : t ⊆ balancedCoreAux 𝕜 s :=
   by
   refine' fun x hx => mem_balancedCoreAux_iff.2 fun r hr => _
@@ -200,19 +277,34 @@ theorem balancedCoreAux_maximal (h : t ⊆ s) (ht : Balanced 𝕜 t) : t ⊆ bal
   rw [norm_inv]
   exact inv_le_one hr
 #align balanced_core_aux_maximal balancedCoreAux_maximal
+-/
 
+#print balancedCore_subset_balancedCoreAux /-
 theorem balancedCore_subset_balancedCoreAux : balancedCore 𝕜 s ⊆ balancedCoreAux 𝕜 s :=
   balancedCoreAux_maximal (balancedCore_subset s) (balancedCore_balanced s)
 #align balanced_core_subset_balanced_core_aux balancedCore_subset_balancedCoreAux
+-/
 
+/- warning: balanced_core_eq_Inter -> balancedCore_eq_interᵢ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (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) -> (Eq.{succ u2} (Set.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s) (Set.interᵢ.{u2, succ u1} E 𝕜 (fun (r : 𝕜) => Set.interᵢ.{u2, 0} E (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r)) (fun (hr : LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) r)) => SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) r s))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) s) -> (Eq.{succ u2} (Set.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s) (Set.interᵢ.{u2, succ u1} E 𝕜 (fun (r : 𝕜) => Set.interᵢ.{u2, 0} E (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r)) (fun (hr : LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) r)) => HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))) r s))))
+Case conversion may be inaccurate. Consider using '#align balanced_core_eq_Inter balancedCore_eq_interᵢₓ'. -/
 theorem balancedCore_eq_interᵢ (hs : (0 : E) ∈ s) :
     balancedCore 𝕜 s = ⋂ (r : 𝕜) (hr : 1 ≤ ‖r‖), r • s :=
   by
   refine' balanced_core_subset_balanced_core_aux.antisymm _
-  refine' (balancedCoreAux_balanced _).subset_core_of_subset (balancedCoreAux_subset s)
+  refine' (balancedCoreAux_balanced _).subset_balancedCore_of_subset (balancedCoreAux_subset s)
   exact balancedCore_subset_balancedCoreAux (balancedCore_zero_mem hs)
 #align balanced_core_eq_Inter balancedCore_eq_interᵢ
 
+/- warning: subset_balanced_core -> subset_balancedCore is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {t : Set.{u2} E}, (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)))))))) t) -> (forall (a : 𝕜), (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (SMul.smul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) a s) t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) t))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {s : Set.{u2} E} {t : Set.{u2} E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (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))))))) t) -> (forall (a : 𝕜), (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (HSMul.hSMul.{u1, u2, u2} 𝕜 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕜 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))))) a s) t)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) s (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) t))
+Case conversion may be inaccurate. Consider using '#align subset_balanced_core subset_balancedCoreₓ'. -/
 theorem subset_balancedCore (ht : (0 : E) ∈ t) (hst : ∀ (a : 𝕜) (ha : ‖a‖ ≤ 1), a • s ⊆ t) :
     s ⊆ balancedCore 𝕜 t := by
   rw [balancedCore_eq_interᵢ ht]
@@ -235,6 +327,7 @@ section Topology
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [TopologicalSpace E]
   [ContinuousSMul 𝕜 E] {U : Set E}
 
+#print IsClosed.balancedCore /-
 protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCore 𝕜 U) :=
   by
   by_cases h : (0 : E) ∈ U
@@ -248,7 +341,14 @@ protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCo
   contrapose! h
   exact balanced_core_nonempty_iff.mp (Set.nonempty_iff_ne_empty.2 h)
 #align is_closed.balanced_core IsClosed.balancedCore
+-/
 
+/- warning: balanced_core_mem_nhds_zero -> balancedCore_mem_nhds_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4] {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)))))))))) -> (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) 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))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4] {U : Set.{u2} E}, (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) U (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))))))))) -> (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) (balancedCore.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) U) (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)))))))))
+Case conversion may be inaccurate. Consider using '#align balanced_core_mem_nhds_zero balancedCore_mem_nhds_zeroₓ'. -/
 theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜 U ∈ 𝓝 (0 : E) :=
   by
   -- Getting neighborhoods of the origin for `0 : 𝕜` and `0 : E`
@@ -273,6 +373,12 @@ theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜
 
 variable (𝕜 E)
 
+/- warning: nhds_basis_balanced -> nhds_basis_balanced is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _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)))))))))) (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) (id.{succ u2} (Set.{u2} E))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4], Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (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)))))))) (fun (s : Set.{u2} E) => And (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) s (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))))))))) (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s)) (id.{succ u2} (Set.{u2} E))
+Case conversion may be inaccurate. Consider using '#align nhds_basis_balanced nhds_basis_balancedₓ'. -/
 theorem nhds_basis_balanced :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ 𝓝 (0 : E) ∧ Balanced 𝕜 s) id :=
   Filter.hasBasis_self.mpr fun s hs =>
@@ -280,6 +386,12 @@ theorem nhds_basis_balanced :
       balancedCore_subset s⟩
 #align nhds_basis_balanced nhds_basis_balanced
 
+/- warning: nhds_basis_closed_balanced -> nhds_basis_closed_balanced is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4] [_inst_6 : RegularSpace.{u2} E _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)))))))))) (And (IsClosed.{u2} E _inst_4 s) (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))) (id.{succ u2} (Set.{u2} E))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_4] [_inst_6 : RegularSpace.{u2} E _inst_4], Filter.HasBasis.{u2, succ u2} E (Set.{u2} E) (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)))))))) (fun (s : Set.{u2} E) => And (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) s (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))))))))) (And (IsClosed.{u2} E _inst_4 s) (Balanced.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) s))) (id.{succ u2} (Set.{u2} E))
+Case conversion may be inaccurate. Consider using '#align nhds_basis_closed_balanced nhds_basis_closed_balancedₓ'. -/
 theorem nhds_basis_closed_balanced [RegularSpace E] :
     (𝓝 (0 : E)).HasBasis (fun s : Set E => s ∈ 𝓝 (0 : E) ∧ IsClosed s ∧ Balanced 𝕜 s) id :=
   by

f2ce6086

bump to nightly-2023-03-13-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

66e1e587

Diff

@@ -50,9 +50,9 @@ variable {𝕜 E ι : Type _}
 
 section balancedHull
 
-section SemiNormedRing
+section SeminormedRing
 
-variable [SemiNormedRing 𝕜]
+variable [SeminormedRing 𝕜]
 
 section SMul
 
@@ -155,12 +155,12 @@ theorem balancedHull.balanced (s : Set E) : Balanced 𝕜 (balancedHull 𝕜 s)
   simp_rw [balancedHull, smul_set_Union₂, subset_def, mem_Union₂]
   rintro x ⟨r, hr, hx⟩
   rw [← smul_assoc] at hx
-  exact ⟨a • r, (SemiNormedRing.norm_mul _ _).trans (mul_le_one ha (norm_nonneg r) hr), hx⟩
+  exact ⟨a • r, (SeminormedRing.norm_mul _ _).trans (mul_le_one ha (norm_nonneg r) hr), hx⟩
 #align balanced_hull.balanced balancedHull.balanced
 
 end Module
 
-end SemiNormedRing
+end SeminormedRing
 
 section NormedField

f2ce6086

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f2ce6086

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -53,7 +53,7 @@ section SMul
 
 variable (𝕜) [SMul 𝕜 E] {s t : Set E} {x : E}
 
-/-- The largest balanced subset of `s`.-/
+/-- The largest balanced subset of `s`. -/
 def balancedCore (s : Set E) :=
   ⋃₀ { t : Set E | Balanced 𝕜 t ∧ t ⊆ s }
 #align balanced_core balancedCore
@@ -63,7 +63,7 @@ def balancedCoreAux (s : Set E) :=
   ⋂ (r : 𝕜) (_ : 1 ≤ ‖r‖), r • s
 #align balanced_core_aux balancedCoreAux
 
-/-- The smallest balanced superset of `s`.-/
+/-- The smallest balanced superset of `s`. -/
 def balancedHull (s : Set E) :=
   ⋃ (r : 𝕜) (_ : ‖r‖ ≤ 1), r • s
 #align balanced_hull balancedHull
@@ -95,7 +95,7 @@ theorem balancedCore_balanced (s : Set E) : Balanced 𝕜 (balancedCore 𝕜 s)
 #align balanced_core_balanced balancedCore_balanced
 
 /-- The balanced core of `t` is maximal in the sense that it contains any balanced subset
-`s` of `t`.-/
+`s` of `t`. -/
 theorem Balanced.subset_balancedCore_of_subset (hs : Balanced 𝕜 s) (h : s ⊆ t) :
     s ⊆ balancedCore 𝕜 t :=
   subset_sUnion_of_mem ⟨hs, h⟩

f2ce6086

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

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

In some rare cases, golf proofs that needed fixing.

14c72960

Diff

@@ -105,8 +105,8 @@ theorem mem_balancedCoreAux_iff : x ∈ balancedCoreAux 𝕜 s ↔ ∀ r : 𝕜,
   mem_iInter₂
 #align mem_balanced_core_aux_iff mem_balancedCoreAux_iff
 
-theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜) (_ : ‖r‖ ≤ 1), x ∈ r • s :=
-  mem_iUnion₂
+theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ r : 𝕜, ‖r‖ ≤ 1 ∧ x ∈ r • s := by
+  simp [balancedHull]
 #align mem_balanced_hull_iff mem_balancedHull_iff
 
 /-- The balanced hull of `s` is minimal in the sense that it is contained in any balanced superset
@@ -202,7 +202,7 @@ theorem balancedCore_eq_iInter (hs : (0 : E) ∈ s) :
   exact balancedCore_subset_balancedCoreAux (balancedCore_zero_mem hs)
 #align balanced_core_eq_Inter balancedCore_eq_iInter
 
-theorem subset_balancedCore (ht : (0 : E) ∈ t) (hst : ∀ (a : 𝕜) (_ : ‖a‖ ≤ 1), a • s ⊆ t) :
+theorem subset_balancedCore (ht : (0 : E) ∈ t) (hst : ∀ a : 𝕜, ‖a‖ ≤ 1 → a • s ⊆ t) :
     s ⊆ balancedCore 𝕜 t := by
   rw [balancedCore_eq_iInter ht]
   refine' subset_iInter₂ fun a ha => _

f2ce6086

feat: let push_neg replace not (Set.Nonempty s) with s = emptyset (#8000)

Co-authored-by: Kyle Miller <kmill31415@gmail.com>

43030491

Diff

@@ -234,7 +234,7 @@ protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCo
     exact isClosedMap_smul_of_ne_zero ha' U hU
   · have : balancedCore 𝕜 U = ∅ := by
       contrapose! h
-      exact balancedCore_nonempty_iff.mp (Set.nonempty_iff_ne_empty.2 h)
+      exact balancedCore_nonempty_iff.mp h
     rw [this]
     exact isClosed_empty
 #align is_closed.balanced_core IsClosed.balancedCore

f2ce6086

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -41,7 +41,7 @@ balanced
 
 open Set Pointwise Topology Filter
 
-variable {𝕜 E ι : Type _}
+variable {𝕜 E ι : Type*}
 
 section balancedHull

f2ce6086

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module analysis.locally_convex.balanced_core_hull
-! 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.LocallyConvex.Basic
 
+#align_import analysis.locally_convex.balanced_core_hull from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Balanced Core and Balanced Hull

f2ce6086

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

Changes are of the form

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

2a870323

Diff

@@ -177,7 +177,7 @@ theorem balancedCoreAux_balanced (h0 : (0 : E) ∈ balancedCoreAux 𝕜 s) :
   rintro a ha x ⟨y, hy, rfl⟩
   obtain rfl | h := eq_or_ne a 0
   · simp_rw [zero_smul, h0]
-  rw [mem_balancedCoreAux_iff] at hy⊢
+  rw [mem_balancedCoreAux_iff] at hy ⊢
   intro r hr
   have h'' : 1 ≤ ‖a⁻¹ • r‖ := by
     rw [norm_smul, norm_inv]

f2ce6086

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -108,7 +108,7 @@ theorem mem_balancedCoreAux_iff : x ∈ balancedCoreAux 𝕜 s ↔ ∀ r : 𝕜,
   mem_iInter₂
 #align mem_balanced_core_aux_iff mem_balancedCoreAux_iff
 
-theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜)(_ : ‖r‖ ≤ 1), x ∈ r • s :=
+theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜) (_ : ‖r‖ ≤ 1), x ∈ r • s :=
   mem_iUnion₂
 #align mem_balanced_hull_iff mem_balancedHull_iff
 
@@ -244,7 +244,7 @@ protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCo
 
 theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜 U ∈ 𝓝 (0 : E) := by
   -- Getting neighborhoods of the origin for `0 : 𝕜` and `0 : E`
-  obtain ⟨r, V, hr, hV, hrVU⟩ : ∃ (r : ℝ)(V : Set E),
+  obtain ⟨r, V, hr, hV, hrVU⟩ : ∃ (r : ℝ) (V : Set E),
       0 < r ∧ V ∈ 𝓝 (0 : E) ∧ ∀ (c : 𝕜) (y : E), ‖c‖ < r → y ∈ V → c • y ∈ U := by
     have h : Filter.Tendsto (fun x : 𝕜 × E => x.fst • x.snd) (𝓝 (0, 0)) (𝓝 0) :=
       continuous_smul.tendsto' (0, 0) _ (smul_zero _)

f2ce6086

style: allow _ for an argument in notation3 & replace _foo with _ in notation3 (#4652)

e2b5ca37

Diff

@@ -63,12 +63,12 @@ def balancedCore (s : Set E) :=
 
 /-- Helper definition to prove `balanced_core_eq_iInter`-/
 def balancedCoreAux (s : Set E) :=
-  ⋂ (r : 𝕜) (_hr : 1 ≤ ‖r‖), r • s
+  ⋂ (r : 𝕜) (_ : 1 ≤ ‖r‖), r • s
 #align balanced_core_aux balancedCoreAux
 
 /-- The smallest balanced superset of `s`.-/
 def balancedHull (s : Set E) :=
-  ⋃ (r : 𝕜) (_hr : ‖r‖ ≤ 1), r • s
+  ⋃ (r : 𝕜) (_ : ‖r‖ ≤ 1), r • s
 #align balanced_hull balancedHull
 
 variable {𝕜}
@@ -199,7 +199,7 @@ theorem balancedCore_subset_balancedCoreAux : balancedCore 𝕜 s ⊆ balancedCo
 #align balanced_core_subset_balanced_core_aux balancedCore_subset_balancedCoreAux
 
 theorem balancedCore_eq_iInter (hs : (0 : E) ∈ s) :
-    balancedCore 𝕜 s = ⋂ (r : 𝕜) (_hr : 1 ≤ ‖r‖), r • s := by
+    balancedCore 𝕜 s = ⋂ (r : 𝕜) (_ : 1 ≤ ‖r‖), r • s := by
   refine' balancedCore_subset_balancedCoreAux.antisymm _
   refine' (balancedCoreAux_balanced _).subset_balancedCore_of_subset (balancedCoreAux_subset s)
   exact balancedCore_subset_balancedCoreAux (balancedCore_zero_mem hs)

f2ce6086

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -253,7 +253,7 @@ theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜
   rcases NormedField.exists_norm_lt 𝕜 hr with ⟨y, hy₀, hyr⟩
   rw [norm_pos_iff] at hy₀
   have : y • V ∈ 𝓝 (0 : E) := (set_smul_mem_nhds_zero_iff hy₀).mpr hV
-  -- It remains to show that `y • V ⊆ balanced_core 𝕜 U`
+  -- It remains to show that `y • V ⊆ balancedCore 𝕜 U`
   refine' Filter.mem_of_superset this (subset_balancedCore (mem_of_mem_nhds hU) fun a ha => _)
   rw [smul_smul]
   rintro _ ⟨z, hz, rfl⟩

f2ce6086

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

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

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

d1eb6264

Diff

@@ -20,7 +20,7 @@ import Mathlib.Analysis.LocallyConvex.Basic
 
 ## Main statements
 
-* `balancedCore_eq_interᵢ`: Characterization of the balanced core as an intersection over subsets.
+* `balancedCore_eq_iInter`: Characterization of the balanced core as an intersection over subsets.
 * `nhds_basis_closed_balanced`: The closed balanced sets form a basis of the neighborhood filter.
 
 ## Implementation details
@@ -30,7 +30,7 @@ of the union over all balanced sets that are contained in `s`, whereas for the h
 union over `r • s`, for `r` the scalars with `‖r‖ ≤ 1`. We show that `balancedHull` has the
 defining properties of a hull in `Balanced.balancedHull_subset_of_subset` and `subset_balancedHull`.
 For the core we need slightly stronger assumptions to obtain a characterization as an intersection,
-this is `balancedCore_eq_interᵢ`.
+this is `balancedCore_eq_iInter`.
 
 ## References
 
@@ -61,7 +61,7 @@ def balancedCore (s : Set E) :=
   ⋃₀ { t : Set E | Balanced 𝕜 t ∧ t ⊆ s }
 #align balanced_core balancedCore
 
-/-- Helper definition to prove `balanced_core_eq_interᵢ`-/
+/-- Helper definition to prove `balanced_core_eq_iInter`-/
 def balancedCoreAux (s : Set E) :=
   ⋂ (r : 𝕜) (_hr : 1 ≤ ‖r‖), r • s
 #align balanced_core_aux balancedCoreAux
@@ -74,7 +74,7 @@ def balancedHull (s : Set E) :=
 variable {𝕜}
 
 theorem balancedCore_subset (s : Set E) : balancedCore 𝕜 s ⊆ s :=
-  unionₛ_subset fun _ ht => ht.2
+  sUnion_subset fun _ ht => ht.2
 #align balanced_core_subset balancedCore_subset
 
 theorem balancedCore_empty : balancedCore 𝕜 (∅ : Set E) = ∅ :=
@@ -82,7 +82,7 @@ theorem balancedCore_empty : balancedCore 𝕜 (∅ : Set E) = ∅ :=
 #align balanced_core_empty balancedCore_empty
 
 theorem mem_balancedCore_iff : x ∈ balancedCore 𝕜 s ↔ ∃ t, Balanced 𝕜 t ∧ t ⊆ s ∧ x ∈ t := by
-  simp_rw [balancedCore, mem_unionₛ, mem_setOf_eq, and_assoc]
+  simp_rw [balancedCore, mem_sUnion, mem_setOf_eq, and_assoc]
 #align mem_balanced_core_iff mem_balancedCore_iff
 
 theorem smul_balancedCore_subset (s : Set E) {a : 𝕜} (ha : ‖a‖ ≤ 1) :
@@ -101,15 +101,15 @@ theorem balancedCore_balanced (s : Set E) : Balanced 𝕜 (balancedCore 𝕜 s)
 `s` of `t`.-/
 theorem Balanced.subset_balancedCore_of_subset (hs : Balanced 𝕜 s) (h : s ⊆ t) :
     s ⊆ balancedCore 𝕜 t :=
-  subset_unionₛ_of_mem ⟨hs, h⟩
+  subset_sUnion_of_mem ⟨hs, h⟩
 #align balanced.subset_core_of_subset Balanced.subset_balancedCore_of_subset
 
 theorem mem_balancedCoreAux_iff : x ∈ balancedCoreAux 𝕜 s ↔ ∀ r : 𝕜, 1 ≤ ‖r‖ → x ∈ r • s :=
-  mem_interᵢ₂
+  mem_iInter₂
 #align mem_balanced_core_aux_iff mem_balancedCoreAux_iff
 
 theorem mem_balancedHull_iff : x ∈ balancedHull 𝕜 s ↔ ∃ (r : 𝕜)(_ : ‖r‖ ≤ 1), x ∈ r • s :=
-  mem_unionᵢ₂
+  mem_iUnion₂
 #align mem_balanced_hull_iff mem_balancedHull_iff
 
 /-- The balanced hull of `s` is minimal in the sense that it is contained in any balanced superset
@@ -148,7 +148,7 @@ variable {𝕜}
 
 theorem balancedHull.balanced (s : Set E) : Balanced 𝕜 (balancedHull 𝕜 s) := by
   intro a ha
-  simp_rw [balancedHull, smul_set_unionᵢ₂, subset_def, mem_unionᵢ₂]
+  simp_rw [balancedHull, smul_set_iUnion₂, subset_def, mem_iUnion₂]
   rintro x ⟨r, hr, hx⟩
   rw [← smul_assoc] at hx
   exact ⟨a • r, (SeminormedRing.norm_mul _ _).trans (mul_le_one ha (norm_nonneg r) hr), hx⟩
@@ -164,7 +164,7 @@ variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {s t : Set E}
 
 @[simp]
 theorem balancedCoreAux_empty : balancedCoreAux 𝕜 (∅ : Set E) = ∅ := by
-  simp_rw [balancedCoreAux, interᵢ₂_eq_empty_iff, smul_set_empty]
+  simp_rw [balancedCoreAux, iInter₂_eq_empty_iff, smul_set_empty]
   exact fun _ => ⟨1, norm_one.ge, not_mem_empty _⟩
 #align balanced_core_aux_empty balancedCoreAux_empty
 
@@ -198,17 +198,17 @@ theorem balancedCore_subset_balancedCoreAux : balancedCore 𝕜 s ⊆ balancedCo
   balancedCoreAux_maximal (balancedCore_subset s) (balancedCore_balanced s)
 #align balanced_core_subset_balanced_core_aux balancedCore_subset_balancedCoreAux
 
-theorem balancedCore_eq_interᵢ (hs : (0 : E) ∈ s) :
+theorem balancedCore_eq_iInter (hs : (0 : E) ∈ s) :
     balancedCore 𝕜 s = ⋂ (r : 𝕜) (_hr : 1 ≤ ‖r‖), r • s := by
   refine' balancedCore_subset_balancedCoreAux.antisymm _
   refine' (balancedCoreAux_balanced _).subset_balancedCore_of_subset (balancedCoreAux_subset s)
   exact balancedCore_subset_balancedCoreAux (balancedCore_zero_mem hs)
-#align balanced_core_eq_Inter balancedCore_eq_interᵢ
+#align balanced_core_eq_Inter balancedCore_eq_iInter
 
 theorem subset_balancedCore (ht : (0 : E) ∈ t) (hst : ∀ (a : 𝕜) (_ : ‖a‖ ≤ 1), a • s ⊆ t) :
     s ⊆ balancedCore 𝕜 t := by
-  rw [balancedCore_eq_interᵢ ht]
-  refine' subset_interᵢ₂ fun a ha => _
+  rw [balancedCore_eq_iInter ht]
+  refine' subset_iInter₂ fun a ha => _
   rw [← smul_inv_smul₀ (norm_pos_iff.mp <| zero_lt_one.trans_le ha) s]
   refine' smul_set_mono (hst _ _)
   rw [norm_inv]
@@ -229,9 +229,9 @@ variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [Topolo
 
 protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCore 𝕜 U) := by
   by_cases h : (0 : E) ∈ U
-  · rw [balancedCore_eq_interᵢ h]
-    refine' isClosed_interᵢ fun a => _
-    refine' isClosed_interᵢ fun ha => _
+  · rw [balancedCore_eq_iInter h]
+    refine' isClosed_iInter fun a => _
+    refine' isClosed_iInter fun ha => _
     have ha' := lt_of_lt_of_le zero_lt_one ha
     rw [norm_pos_iff] at ha'
     exact isClosedMap_smul_of_ne_zero ha' U hU

f2ce6086

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -244,9 +244,8 @@ protected theorem IsClosed.balancedCore (hU : IsClosed U) : IsClosed (balancedCo
 
 theorem balancedCore_mem_nhds_zero (hU : U ∈ 𝓝 (0 : E)) : balancedCore 𝕜 U ∈ 𝓝 (0 : E) := by
   -- Getting neighborhoods of the origin for `0 : 𝕜` and `0 : E`
-  obtain ⟨r, V, hr, hV, hrVU⟩ :
-    ∃ (r : ℝ)(V : Set E), 0 < r ∧ V ∈ 𝓝 (0 : E) ∧ ∀ (c : 𝕜) (y : E), ‖c‖ < r → y ∈ V → c • y ∈ U :=
-    by
+  obtain ⟨r, V, hr, hV, hrVU⟩ : ∃ (r : ℝ)(V : Set E),
+      0 < r ∧ V ∈ 𝓝 (0 : E) ∧ ∀ (c : 𝕜) (y : E), ‖c‖ < r → y ∈ V → c • y ∈ U := by
     have h : Filter.Tendsto (fun x : 𝕜 × E => x.fst • x.snd) (𝓝 (0, 0)) (𝓝 0) :=
       continuous_smul.tendsto' (0, 0) _ (smul_zero _)
     simpa only [← Prod.exists', ← Prod.forall', ← and_imp, ← and_assoc, exists_prop] using

f2ce6086

feat: implement intermediate state for simp_rw (#3738)

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

ff334843

Diff

@@ -82,7 +82,7 @@ theorem balancedCore_empty : balancedCore 𝕜 (∅ : Set E) = ∅ :=
 #align balanced_core_empty balancedCore_empty
 
 theorem mem_balancedCore_iff : x ∈ balancedCore 𝕜 s ↔ ∃ t, Balanced 𝕜 t ∧ t ⊆ s ∧ x ∈ t := by
-  simp_rw [balancedCore, mem_unionₛ, mem_setOf_eq, exists_prop, and_assoc]
+  simp_rw [balancedCore, mem_unionₛ, mem_setOf_eq, and_assoc]
 #align mem_balanced_core_iff mem_balancedCore_iff
 
 theorem smul_balancedCore_subset (s : Set E) {a : 𝕜} (ha : ‖a‖ ≤ 1) :

f2ce6086

feat: port Analysis.LocallyConvex.BalancedCoreHull (#3415)

Slightly rewrote the one proof to avoid convert and renamed two lemmas, so that their names fit better with the naming convention.

1f7abb82

`analysis.locally_convex.balanced_core_hull` ⟷ `Mathlib.Analysis.LocallyConvex.BalancedCoreHull`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 10 + 623

analysis.locally_convex.balanced_core_hull ⟷ Mathlib.Analysis.LocallyConvex.BalancedCoreHull

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 10 + 623

`analysis.locally_convex.balanced_core_hull` ⟷ `Mathlib.Analysis.LocallyConvex.BalancedCoreHull`