analysis.locally_convex.basic ⟷ Mathlib.Topology.Bornology.Absorbs

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

@@ -329,7 +329,7 @@ variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGr
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s :=
   by
   obtain rfl | hb := eq_or_ne b 0
-  · rw [norm_zero] at h 
+  · rw [norm_zero] at h
     rw [norm_eq_zero.1 (h.antisymm <| norm_nonneg _)]
     obtain rfl | h := s.eq_empty_or_nonempty
     · simp_rw [smul_set_empty]
@@ -360,7 +360,7 @@ theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆
   by
   refine' (subset_set_smul_iff₀ _).2 (hA a⁻¹ _)
   · rintro rfl
-    rw [norm_zero] at ha 
+    rw [norm_zero] at ha
     exact zero_lt_one.not_le ha
   · rw [norm_inv]
     exact inv_le_one ha
@@ -377,7 +377,7 @@ theorem Balanced.smul_eq (hA : Balanced 𝕜 A) (ha : ‖a‖ = 1) : a • A = A
 theorem Balanced.smul_mem_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s :=
   by
   obtain rfl | hb := eq_or_ne b 0
-  · rw [norm_zero, norm_eq_zero] at h 
+  · rw [norm_zero, norm_eq_zero] at h
     rw [h]
   have ha : a ≠ 0 := norm_ne_zero_iff.1 (ne_of_eq_of_ne h <| norm_ne_zero_iff.2 hb)
   constructor <;> intro h' <;> [rw [← inv_mul_cancel_right₀ ha b];
@@ -494,7 +494,7 @@ theorem absorbs_zero_iff : Absorbs 𝕜 s 0 ↔ (0 : E) ∈ s :=
   rintro ⟨r, hr, h⟩
   obtain ⟨a, ha⟩ := NormedSpace.exists_lt_norm 𝕜 𝕜 r
   have := h _ ha.le
-  rwa [zero_subset, zero_mem_smul_set_iff] at this 
+  rwa [zero_subset, zero_mem_smul_set_iff] at this
   exact norm_ne_zero_iff.1 (hr.trans ha).ne'
 #align absorbs_zero_iff absorbs_zero_iff
 -/
@@ -531,7 +531,7 @@ variable [AddCommGroup E] [Module ℝ E] {s : Set E}
 theorem balanced_iff_neg_mem (hs : Convex ℝ s) : Balanced ℝ s ↔ ∀ ⦃x⦄, x ∈ s → -x ∈ s :=
   by
   refine' ⟨fun h x => h.neg_mem_iff.2, fun h a ha => smul_set_subset_iff.2 fun x hx => _⟩
-  rw [Real.norm_eq_abs, abs_le] at ha 
+  rw [Real.norm_eq_abs, abs_le] at ha
   rw [show a = -((1 - a) / 2) + (a - -1) / 2 by ring, add_smul, neg_smul, ← smul_neg]
   exact
     hs (h hx) hx (div_nonneg (sub_nonneg_of_le ha.2) zero_le_two)

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

@@ -373,8 +373,8 @@ theorem Balanced.smul_eq (hA : Balanced 𝕜 A) (ha : ‖a‖ = 1) : a • A = A
 #align balanced.smul_eq Balanced.smul_eq
 -/
 
-#print Balanced.mem_smul_iff /-
-theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s :=
+#print Balanced.smul_mem_iff /-
+theorem Balanced.smul_mem_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s :=
   by
   obtain rfl | hb := eq_or_ne b 0
   · rw [norm_zero, norm_eq_zero] at h 
@@ -385,7 +385,7 @@ theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a
     · rw [← smul_eq_mul, smul_assoc]
       refine' hs.smul_mem _ h'
       simp [← h, ha]
-#align balanced.mem_smul_iff Balanced.mem_smul_iff
+#align balanced.mem_smul_iff Balanced.smul_mem_iff
 -/
 
 #print Balanced.neg_mem_iff /-
@@ -445,9 +445,9 @@ theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
 #align absorbent_nhds_zero absorbent_nhds_zero
 -/
 
-#print balanced_zero_union_interior /-
+#print Balanced.zero_insert_interior /-
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
-theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0 : Set E) ∪ interior A) :=
+theorem Balanced.zero_insert_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0 : Set E) ∪ interior A) :=
   by
   intro a ha
   obtain rfl | h := eq_or_ne a 0
@@ -461,7 +461,7 @@ theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0
       calc
         a • interior A ⊆ interior (a • A) := (isOpenMap_smul₀ h).image_interior_subset A
         _ ⊆ interior A := interior_mono (hA _ ha)
-#align balanced_zero_union_interior balanced_zero_union_interior
+#align balanced_zero_union_interior Balanced.zero_insert_interior
 -/
 
 #print Balanced.interior /-
@@ -470,7 +470,7 @@ theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
     Balanced 𝕜 (interior A) :=
   by
   rw [← union_eq_self_of_subset_left (singleton_subset_iff.2 h)]
-  exact balanced_zero_union_interior hA
+  exact Balanced.zero_insert_interior hA
 #align balanced.interior Balanced.interior
 -/
 
@@ -507,8 +507,8 @@ theorem Absorbent.zero_mem (hs : Absorbent 𝕜 s) : (0 : E) ∈ s :=
 
 variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
 
-#print balanced_convexHull_of_balanced /-
-theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) :=
+#print Balanced.convexHull /-
+theorem Balanced.convexHull (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) :=
   by
   suffices Convex ℝ {x | ∀ a : 𝕜, ‖a‖ ≤ 1 → a • x ∈ convexHull ℝ s}
     by
@@ -518,7 +518,7 @@ theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (
   intro x hx y hy u v hu hv huv a ha
   simp only [smul_add, ← smul_comm]
   exact convex_convexHull ℝ s (hx a ha) (hy a ha) hu hv huv
-#align balanced_convex_hull_of_balanced balanced_convexHull_of_balanced
+#align balanced_convex_hull_of_balanced Balanced.convexHull
 -/
 
 end NontriviallyNormedField

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

@@ -113,7 +113,17 @@ theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorb
 
 #print absorbs_biUnion_finset /-
 theorem absorbs_biUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
-    Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by classical
+    Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
+  classical
+  induction' t using Finset.induction_on with i t ht hi
+  ·
+    simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, Absorbs.empty,
+      IsEmpty.forall_iff, imp_true_iff]
+  rw [Finset.set_biUnion_insert, absorbs_union, hi]
+  constructor <;> intro h
+  · refine' fun _ hi' => (finset.mem_insert.mp hi').elim _ (h.2 _)
+    exact fun hi'' => by rw [hi'']; exact h.1
+  exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
 #align absorbs_Union_finset absorbs_biUnion_finset
 -/
 

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

@@ -113,17 +113,7 @@ theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorb
 
 #print absorbs_biUnion_finset /-
 theorem absorbs_biUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
-    Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
-  classical
-  induction' t using Finset.induction_on with i t ht hi
-  ·
-    simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, Absorbs.empty,
-      IsEmpty.forall_iff, imp_true_iff]
-  rw [Finset.set_biUnion_insert, absorbs_union, hi]
-  constructor <;> intro h
-  · refine' fun _ hi' => (finset.mem_insert.mp hi').elim _ (h.2 _)
-    exact fun hi'' => by rw [hi'']; exact h.1
-  exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
+    Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by classical
 #align absorbs_Union_finset absorbs_biUnion_finset
 -/
 

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

@@ -66,11 +66,11 @@ def Absorbs (A B : Set E) :=
 
 variable {𝕜} {s t u v A B : Set E}
 
-#print absorbs_empty /-
+#print Absorbs.empty /-
 @[simp]
-theorem absorbs_empty {s : Set E} : Absorbs 𝕜 s (∅ : Set E) :=
+theorem Absorbs.empty {s : Set E} : Absorbs 𝕜 s (∅ : Set E) :=
   ⟨1, one_pos, fun a ha => Set.empty_subset _⟩
-#align absorbs_empty absorbs_empty
+#align absorbs_empty Absorbs.empty
 -/
 
 #print Absorbs.mono /-
@@ -111,30 +111,30 @@ theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorb
 #align absorbs_union absorbs_union
 -/
 
-#print absorbs_iUnion_finset /-
-theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
+#print absorbs_biUnion_finset /-
+theorem absorbs_biUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
     Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   classical
   induction' t using Finset.induction_on with i t ht hi
   ·
-    simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
+    simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, Absorbs.empty,
       IsEmpty.forall_iff, imp_true_iff]
   rw [Finset.set_biUnion_insert, absorbs_union, hi]
   constructor <;> intro h
   · refine' fun _ hi' => (finset.mem_insert.mp hi').elim _ (h.2 _)
     exact fun hi'' => by rw [hi'']; exact h.1
   exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
-#align absorbs_Union_finset absorbs_iUnion_finset
+#align absorbs_Union_finset absorbs_biUnion_finset
 -/
 
-#print Set.Finite.absorbs_iUnion /-
-theorem Set.Finite.absorbs_iUnion {ι : Type _} {s : Set E} {t : Set ι} {f : ι → Set E}
+#print Set.Finite.absorbs_biUnion /-
+theorem Set.Finite.absorbs_biUnion {ι : Type _} {s : Set E} {t : Set ι} {f : ι → Set E}
     (hi : t.Finite) : Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) :=
   by
   lift t to Finset ι using hi
   simp only [Finset.mem_coe]
-  exact absorbs_iUnion_finset
-#align set.finite.absorbs_Union Set.Finite.absorbs_iUnion
+  exact absorbs_biUnion_finset
+#align set.finite.absorbs_Union Set.Finite.absorbs_biUnion
 -/
 
 variable (𝕜)
@@ -148,12 +148,12 @@ def Absorbent (A : Set E) :=
 
 variable {𝕜}
 
-#print Absorbent.subset /-
-theorem Absorbent.subset (hA : Absorbent 𝕜 A) (hAB : A ⊆ B) : Absorbent 𝕜 B :=
+#print Absorbent.mono /-
+theorem Absorbent.mono (hA : Absorbent 𝕜 A) (hAB : A ⊆ B) : Absorbent 𝕜 B :=
   by
   refine' forall_imp (fun x => _) hA
   exact Exists.imp fun r => And.imp_right <| forall₂_imp fun a ha hx => Set.smul_set_mono hAB hx
-#align absorbent.subset Absorbent.subset
+#align absorbent.subset Absorbent.mono
 -/
 
 #print absorbent_iff_forall_absorbs_singleton /-
@@ -168,7 +168,6 @@ theorem Absorbent.absorbs (hs : Absorbent 𝕜 s) {x : E} : Absorbs 𝕜 s {x} :
 #align absorbent.absorbs Absorbent.absorbs
 -/
 
-#print absorbent_iff_nonneg_lt /-
 theorem absorbent_iff_nonneg_lt :
     Absorbent 𝕜 A ↔ ∀ x, ∃ r, 0 ≤ r ∧ ∀ ⦃a : 𝕜⦄, r < ‖a‖ → x ∈ a • A :=
   forall_congr' fun x =>
@@ -176,7 +175,6 @@ theorem absorbent_iff_nonneg_lt :
       ⟨r + 1, add_pos_of_nonneg_of_pos hr zero_lt_one, fun a ha =>
         hx ((lt_add_of_pos_right r zero_lt_one).trans_le ha)⟩⟩
 #align absorbent_iff_nonneg_lt absorbent_iff_nonneg_lt
--/
 
 #print Absorbent.absorbs_finite /-
 theorem Absorbent.absorbs_finite {s : Set E} (hs : Absorbent 𝕜 s) {v : Set E} (hv : v.Finite) :
@@ -272,11 +270,11 @@ section Module
 
 variable [AddCommGroup E] [Module 𝕜 E] {s s₁ s₂ t t₁ t₂ : Set E}
 
-#print Absorbs.neg /-
-theorem Absorbs.neg : Absorbs 𝕜 s t → Absorbs 𝕜 (-s) (-t) :=
+#print Absorbs.neg_neg /-
+theorem Absorbs.neg_neg : Absorbs 𝕜 s t → Absorbs 𝕜 (-s) (-t) :=
   Exists.imp fun r =>
     And.imp_right <| forall₂_imp fun _ _ h => (neg_subset_neg.2 h).trans (smul_set_neg _ _).Superset
-#align absorbs.neg Absorbs.neg
+#align absorbs.neg Absorbs.neg_neg
 -/
 
 #print Balanced.neg /-

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

@@ -232,7 +232,7 @@ theorem Balanced.inter (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced
 
 #print balanced_iUnion /-
 theorem balanced_iUnion {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋃ i, f i) :=
-  fun a ha => (smul_set_Union _ _).Subset.trans <| iUnion_mono fun _ => h _ _ ha
+  fun a ha => (smul_set_iUnion _ _).Subset.trans <| iUnion_mono fun _ => h _ _ ha
 #align balanced_Union balanced_iUnion
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2019 Jean Lo. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo, Bhavik Mehta, Yaël Dillies
 -/
-import Mathbin.Analysis.Convex.Basic
-import Mathbin.Analysis.Convex.Hull
-import Mathbin.Analysis.NormedSpace.Basic
+import Analysis.Convex.Basic
+import Analysis.Convex.Hull
+import Analysis.NormedSpace.Basic
 
 #align_import analysis.locally_convex.basic from "leanprover-community/mathlib"@"9a48a083b390d9b84a71efbdc4e8dfa26a687104"
 

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

@@ -203,7 +203,7 @@ theorem balanced_iff_smul_mem : Balanced 𝕜 s ↔ ∀ ⦃a : 𝕜⦄, ‖a‖
 #align balanced_iff_smul_mem balanced_iff_smul_mem
 -/
 
-alias balanced_iff_smul_mem ↔ Balanced.smul_mem _
+alias ⟨Balanced.smul_mem, _⟩ := balanced_iff_smul_mem
 #align balanced.smul_mem Balanced.smul_mem
 
 #print balanced_empty /-

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Jean Lo. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo, Bhavik Mehta, Yaël Dillies
-
-! This file was ported from Lean 3 source module analysis.locally_convex.basic
-! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Convex.Basic
 import Mathbin.Analysis.Convex.Hull
 import Mathbin.Analysis.NormedSpace.Basic
 
+#align_import analysis.locally_convex.basic from "leanprover-community/mathlib"@"9a48a083b390d9b84a71efbdc4e8dfa26a687104"
+
 /-!
 # Local convexity
 

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

@@ -76,19 +76,26 @@ theorem absorbs_empty {s : Set E} : Absorbs 𝕜 s (∅ : Set E) :=
 #align absorbs_empty absorbs_empty
 -/
 
+#print Absorbs.mono /-
 theorem Absorbs.mono (hs : Absorbs 𝕜 s u) (hst : s ⊆ t) (hvu : v ⊆ u) : Absorbs 𝕜 t v :=
   let ⟨r, hr, h⟩ := hs
   ⟨r, hr, fun a ha => hvu.trans <| (h _ ha).trans <| smul_set_mono hst⟩
 #align absorbs.mono Absorbs.mono
+-/
 
+#print Absorbs.mono_left /-
 theorem Absorbs.mono_left (hs : Absorbs 𝕜 s u) (h : s ⊆ t) : Absorbs 𝕜 t u :=
   hs.mono h Subset.rfl
 #align absorbs.mono_left Absorbs.mono_left
+-/
 
+#print Absorbs.mono_right /-
 theorem Absorbs.mono_right (hs : Absorbs 𝕜 s u) (h : v ⊆ u) : Absorbs 𝕜 s v :=
   hs.mono Subset.rfl h
 #align absorbs.mono_right Absorbs.mono_right
+-/
 
+#print Absorbs.union /-
 theorem Absorbs.union (hu : Absorbs 𝕜 s u) (hv : Absorbs 𝕜 s v) : Absorbs 𝕜 s (u ∪ v) :=
   by
   obtain ⟨a, ha, hu⟩ := hu
@@ -97,12 +104,15 @@ theorem Absorbs.union (hu : Absorbs 𝕜 s u) (hv : Absorbs 𝕜 s v) : Absorbs
     ⟨max a b, lt_max_of_lt_left ha, fun c hc =>
       union_subset (hu _ <| le_of_max_le_left hc) (hv _ <| le_of_max_le_right hc)⟩
 #align absorbs.union Absorbs.union
+-/
 
+#print absorbs_union /-
 @[simp]
 theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorbs 𝕜 s v :=
   ⟨fun h => ⟨h.mono_right <| subset_union_left _ _, h.mono_right <| subset_union_right _ _⟩,
     fun h => h.1.union h.2⟩
 #align absorbs_union absorbs_union
+-/
 
 #print absorbs_iUnion_finset /-
 theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
@@ -141,20 +151,27 @@ def Absorbent (A : Set E) :=
 
 variable {𝕜}
 
+#print Absorbent.subset /-
 theorem Absorbent.subset (hA : Absorbent 𝕜 A) (hAB : A ⊆ B) : Absorbent 𝕜 B :=
   by
   refine' forall_imp (fun x => _) hA
   exact Exists.imp fun r => And.imp_right <| forall₂_imp fun a ha hx => Set.smul_set_mono hAB hx
 #align absorbent.subset Absorbent.subset
+-/
 
+#print absorbent_iff_forall_absorbs_singleton /-
 theorem absorbent_iff_forall_absorbs_singleton : Absorbent 𝕜 A ↔ ∀ x, Absorbs 𝕜 A {x} := by
   simp_rw [Absorbs, Absorbent, singleton_subset_iff]
 #align absorbent_iff_forall_absorbs_singleton absorbent_iff_forall_absorbs_singleton
+-/
 
+#print Absorbent.absorbs /-
 theorem Absorbent.absorbs (hs : Absorbent 𝕜 s) {x : E} : Absorbs 𝕜 s {x} :=
   absorbent_iff_forall_absorbs_singleton.1 hs _
 #align absorbent.absorbs Absorbent.absorbs
+-/
 
+#print absorbent_iff_nonneg_lt /-
 theorem absorbent_iff_nonneg_lt :
     Absorbent 𝕜 A ↔ ∀ x, ∃ r, 0 ≤ r ∧ ∀ ⦃a : 𝕜⦄, r < ‖a‖ → x ∈ a • A :=
   forall_congr' fun x =>
@@ -162,6 +179,7 @@ theorem absorbent_iff_nonneg_lt :
       ⟨r + 1, add_pos_of_nonneg_of_pos hr zero_lt_one, fun a ha =>
         hx ((lt_add_of_pos_right r zero_lt_one).trans_le ha)⟩⟩
 #align absorbent_iff_nonneg_lt absorbent_iff_nonneg_lt
+-/
 
 #print Absorbent.absorbs_finite /-
 theorem Absorbent.absorbs_finite {s : Set E} (hs : Absorbent 𝕜 s) {v : Set E} (hv : v.Finite) :
@@ -182,54 +200,74 @@ def Balanced (A : Set E) :=
 
 variable {𝕜}
 
+#print balanced_iff_smul_mem /-
 theorem balanced_iff_smul_mem : Balanced 𝕜 s ↔ ∀ ⦃a : 𝕜⦄, ‖a‖ ≤ 1 → ∀ ⦃x : E⦄, x ∈ s → a • x ∈ s :=
   forall₂_congr fun a ha => smul_set_subset_iff
 #align balanced_iff_smul_mem balanced_iff_smul_mem
+-/
 
 alias balanced_iff_smul_mem ↔ Balanced.smul_mem _
 #align balanced.smul_mem Balanced.smul_mem
 
+#print balanced_empty /-
 @[simp]
 theorem balanced_empty : Balanced 𝕜 (∅ : Set E) := fun _ _ => by rw [smul_set_empty]
 #align balanced_empty balanced_empty
+-/
 
+#print balanced_univ /-
 @[simp]
 theorem balanced_univ : Balanced 𝕜 (univ : Set E) := fun a ha => subset_univ _
 #align balanced_univ balanced_univ
+-/
 
+#print Balanced.union /-
 theorem Balanced.union (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced 𝕜 (A ∪ B) := fun a ha =>
   smul_set_union.Subset.trans <| union_subset_union (hA _ ha) <| hB _ ha
 #align balanced.union Balanced.union
+-/
 
+#print Balanced.inter /-
 theorem Balanced.inter (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced 𝕜 (A ∩ B) := fun a ha =>
   smul_set_inter_subset.trans <| inter_subset_inter (hA _ ha) <| hB _ ha
 #align balanced.inter Balanced.inter
+-/
 
+#print balanced_iUnion /-
 theorem balanced_iUnion {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋃ i, f i) :=
   fun a ha => (smul_set_Union _ _).Subset.trans <| iUnion_mono fun _ => h _ _ ha
 #align balanced_Union balanced_iUnion
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print balanced_iUnion₂ /-
 theorem balanced_iUnion₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋃ (i) (j), f i j) :=
   balanced_iUnion fun _ => balanced_iUnion <| h _
 #align balanced_Union₂ balanced_iUnion₂
+-/
 
+#print balanced_iInter /-
 theorem balanced_iInter {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋂ i, f i) :=
   fun a ha => (smul_set_iInter_subset _ _).trans <| iInter_mono fun _ => h _ _ ha
 #align balanced_Inter balanced_iInter
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print balanced_iInter₂ /-
 theorem balanced_iInter₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋂ (i) (j), f i j) :=
   balanced_iInter fun _ => balanced_iInter <| h _
 #align balanced_Inter₂ balanced_iInter₂
+-/
 
 variable [SMul 𝕝 E] [SMulCommClass 𝕜 𝕝 E]
 
+#print Balanced.smul /-
 theorem Balanced.smul (a : 𝕝) (hs : Balanced 𝕜 s) : Balanced 𝕜 (a • s) := fun b hb =>
   (smul_comm _ _ _).Subset.trans <| smul_set_mono <| hs _ hb
 #align balanced.smul Balanced.smul
+-/
 
 end SMul
 
@@ -237,36 +275,50 @@ section Module
 
 variable [AddCommGroup E] [Module 𝕜 E] {s s₁ s₂ t t₁ t₂ : Set E}
 
+#print Absorbs.neg /-
 theorem Absorbs.neg : Absorbs 𝕜 s t → Absorbs 𝕜 (-s) (-t) :=
   Exists.imp fun r =>
     And.imp_right <| forall₂_imp fun _ _ h => (neg_subset_neg.2 h).trans (smul_set_neg _ _).Superset
 #align absorbs.neg Absorbs.neg
+-/
 
+#print Balanced.neg /-
 theorem Balanced.neg : Balanced 𝕜 s → Balanced 𝕜 (-s) :=
   forall₂_imp fun _ _ h => (smul_set_neg _ _).Subset.trans <| neg_subset_neg.2 h
 #align balanced.neg Balanced.neg
+-/
 
+#print Absorbs.add /-
 theorem Absorbs.add : Absorbs 𝕜 s₁ t₁ → Absorbs 𝕜 s₂ t₂ → Absorbs 𝕜 (s₁ + s₂) (t₁ + t₂) :=
   fun ⟨r₁, hr₁, h₁⟩ ⟨r₂, hr₂, h₂⟩ =>
   ⟨max r₁ r₂, lt_max_of_lt_left hr₁, fun a ha =>
     (add_subset_add (h₁ _ <| le_of_max_le_left ha) <| h₂ _ <| le_of_max_le_right ha).trans
       (smul_add _ _ _).Superset⟩
 #align absorbs.add Absorbs.add
+-/
 
+#print Balanced.add /-
 theorem Balanced.add (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s + t) := fun a ha =>
   (smul_add _ _ _).Subset.trans <| add_subset_add (hs _ ha) <| ht _ ha
 #align balanced.add Balanced.add
+-/
 
+#print Absorbs.sub /-
 theorem Absorbs.sub (h₁ : Absorbs 𝕜 s₁ t₁) (h₂ : Absorbs 𝕜 s₂ t₂) : Absorbs 𝕜 (s₁ - s₂) (t₁ - t₂) :=
   by simp_rw [sub_eq_add_neg]; exact h₁.add h₂.neg
 #align absorbs.sub Absorbs.sub
+-/
 
+#print Balanced.sub /-
 theorem Balanced.sub (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s - t) := by
   simp_rw [sub_eq_add_neg]; exact hs.add ht.neg
 #align balanced.sub Balanced.sub
+-/
 
+#print balanced_zero /-
 theorem balanced_zero : Balanced 𝕜 (0 : Set E) := fun a ha => (smul_zero _).Subset
 #align balanced_zero balanced_zero
+-/
 
 end Module
 
@@ -277,6 +329,7 @@ section NormedField
 variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGroup E] [Module 𝕜 E]
   [SMulWithZero 𝕝 E] [IsScalarTower 𝕜 𝕝 E] {s t u v A B : Set E} {x : E} {a b : 𝕜}
 
+#print Balanced.smul_mono /-
 /-- Scalar multiplication (by possibly different types) of a balanced set is monotone. -/
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s :=
   by
@@ -293,7 +346,9 @@ theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖
   rw [norm_smul, norm_inv, ← div_eq_inv_mul]
   exact div_le_one_of_le h (norm_nonneg _)
 #align balanced.smul_mono Balanced.smul_mono
+-/
 
+#print Balanced.absorbs_self /-
 /-- A balanced set absorbs itself. -/
 theorem Balanced.absorbs_self (hA : Balanced 𝕜 A) : Absorbs 𝕜 A A :=
   by
@@ -303,7 +358,9 @@ theorem Balanced.absorbs_self (hA : Balanced 𝕜 A) : Absorbs 𝕜 A A :=
   rw [norm_inv]
   exact inv_le_one ha
 #align balanced.absorbs_self Balanced.absorbs_self
+-/
 
+#print Balanced.subset_smul /-
 theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆ a • A :=
   by
   refine' (subset_set_smul_iff₀ _).2 (hA a⁻¹ _)
@@ -313,11 +370,15 @@ theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆
   · rw [norm_inv]
     exact inv_le_one ha
 #align balanced.subset_smul Balanced.subset_smul
+-/
 
+#print Balanced.smul_eq /-
 theorem Balanced.smul_eq (hA : Balanced 𝕜 A) (ha : ‖a‖ = 1) : a • A = A :=
   (hA _ ha.le).antisymm <| hA.subset_smul ha.ge
 #align balanced.smul_eq Balanced.smul_eq
+-/
 
+#print Balanced.mem_smul_iff /-
 theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s :=
   by
   obtain rfl | hb := eq_or_ne b 0
@@ -330,11 +391,15 @@ theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a
       refine' hs.smul_mem _ h'
       simp [← h, ha]
 #align balanced.mem_smul_iff Balanced.mem_smul_iff
+-/
 
+#print Balanced.neg_mem_iff /-
 theorem Balanced.neg_mem_iff (hs : Balanced 𝕜 s) : -x ∈ s ↔ x ∈ s := by
   convert hs.mem_smul_iff (norm_neg 1) <;> simp only [neg_smul, one_smul]
 #align balanced.neg_mem_iff Balanced.neg_mem_iff
+-/
 
+#print Absorbs.inter /-
 theorem Absorbs.inter (hs : Absorbs 𝕜 s u) (ht : Absorbs 𝕜 t u) : Absorbs 𝕜 (s ∩ t) u :=
   by
   obtain ⟨a, ha, hs⟩ := hs
@@ -344,22 +409,28 @@ theorem Absorbs.inter (hs : Absorbs 𝕜 s u) (ht : Absorbs 𝕜 t u) : Absorbs
   rw [smul_set_inter₀ (norm_pos_iff.1 <| h.trans_le hc)]
   exact subset_inter (hs _ <| le_of_max_le_left hc) (ht _ <| le_of_max_le_right hc)
 #align absorbs.inter Absorbs.inter
+-/
 
+#print absorbs_inter /-
 @[simp]
 theorem absorbs_inter : Absorbs 𝕜 (s ∩ t) u ↔ Absorbs 𝕜 s u ∧ Absorbs 𝕜 t u :=
   ⟨fun h => ⟨h.mono_left <| inter_subset_left _ _, h.mono_left <| inter_subset_right _ _⟩, fun h =>
     h.1.inter h.2⟩
 #align absorbs_inter absorbs_inter
+-/
 
+#print absorbent_univ /-
 theorem absorbent_univ : Absorbent 𝕜 (univ : Set E) :=
   by
   refine' fun x => ⟨1, zero_lt_one, fun a ha => _⟩
   rw [smul_set_univ₀ (norm_pos_iff.1 <| zero_lt_one.trans_le ha)]
   exact trivial
 #align absorbent_univ absorbent_univ
+-/
 
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
+#print absorbent_nhds_zero /-
 /-- Every neighbourhood of the origin is absorbent. -/
 theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
   by
@@ -377,7 +448,9 @@ theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
     ‖a‖⁻¹ ≤ r / 2 := (inv_le (half_pos hr₁) ha₂).mp ha₁
     _ < r := half_lt_self hr₁
 #align absorbent_nhds_zero absorbent_nhds_zero
+-/
 
+#print balanced_zero_union_interior /-
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
 theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0 : Set E) ∪ interior A) :=
   by
@@ -394,7 +467,9 @@ theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0
         a • interior A ⊆ interior (a • A) := (isOpenMap_smul₀ h).image_interior_subset A
         _ ⊆ interior A := interior_mono (hA _ ha)
 #align balanced_zero_union_interior balanced_zero_union_interior
+-/
 
+#print Balanced.interior /-
 /-- The interior of a balanced set is balanced if it contains the origin. -/
 theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
     Balanced 𝕜 (interior A) :=
@@ -402,11 +477,14 @@ theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
   rw [← union_eq_self_of_subset_left (singleton_subset_iff.2 h)]
   exact balanced_zero_union_interior hA
 #align balanced.interior Balanced.interior
+-/
 
+#print Balanced.closure /-
 theorem Balanced.closure (hA : Balanced 𝕜 A) : Balanced 𝕜 (closure A) := fun a ha =>
   (image_closure_subset_closure_image <| continuous_id.const_smul _).trans <|
     closure_mono <| hA _ ha
 #align balanced.closure Balanced.closure
+-/
 
 end NormedField
 
@@ -414,6 +492,7 @@ section NontriviallyNormedField
 
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {s : Set E}
 
+#print absorbs_zero_iff /-
 theorem absorbs_zero_iff : Absorbs 𝕜 s 0 ↔ (0 : E) ∈ s :=
   by
   refine' ⟨_, fun h => ⟨1, zero_lt_one, fun a _ => zero_subset.2 <| zero_mem_smul_set h⟩⟩
@@ -423,13 +502,17 @@ theorem absorbs_zero_iff : Absorbs 𝕜 s 0 ↔ (0 : E) ∈ s :=
   rwa [zero_subset, zero_mem_smul_set_iff] at this 
   exact norm_ne_zero_iff.1 (hr.trans ha).ne'
 #align absorbs_zero_iff absorbs_zero_iff
+-/
 
+#print Absorbent.zero_mem /-
 theorem Absorbent.zero_mem (hs : Absorbent 𝕜 s) : (0 : E) ∈ s :=
   absorbs_zero_iff.1 <| absorbent_iff_forall_absorbs_singleton.1 hs _
 #align absorbent.zero_mem Absorbent.zero_mem
+-/
 
 variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
 
+#print balanced_convexHull_of_balanced /-
 theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) :=
   by
   suffices Convex ℝ {x | ∀ a : 𝕜, ‖a‖ ≤ 1 → a • x ∈ convexHull ℝ s}
@@ -441,6 +524,7 @@ theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (
   simp only [smul_add, ← smul_comm]
   exact convex_convexHull ℝ s (hx a ha) (hy a ha) hu hv huv
 #align balanced_convex_hull_of_balanced balanced_convexHull_of_balanced
+-/
 
 end NontriviallyNormedField
 
@@ -448,6 +532,7 @@ section Real
 
 variable [AddCommGroup E] [Module ℝ E] {s : Set E}
 
+#print balanced_iff_neg_mem /-
 theorem balanced_iff_neg_mem (hs : Convex ℝ s) : Balanced ℝ s ↔ ∀ ⦃x⦄, x ∈ s → -x ∈ s :=
   by
   refine' ⟨fun h x => h.neg_mem_iff.2, fun h a ha => smul_set_subset_iff.2 fun x hx => _⟩
@@ -457,6 +542,7 @@ theorem balanced_iff_neg_mem (hs : Convex ℝ s) : Balanced ℝ s ↔ ∀ ⦃x
     hs (h hx) hx (div_nonneg (sub_nonneg_of_le ha.2) zero_le_two)
       (div_nonneg (sub_nonneg_of_le ha.1) zero_le_two) (by ring)
 #align balanced_iff_neg_mem balanced_iff_neg_mem
+-/
 
 end Real
 

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

@@ -376,7 +376,6 @@ theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
   calc
     ‖a‖⁻¹ ≤ r / 2 := (inv_le (half_pos hr₁) ha₂).mp ha₁
     _ < r := half_lt_self hr₁
-    
 #align absorbent_nhds_zero absorbent_nhds_zero
 
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
@@ -394,7 +393,6 @@ theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0
       calc
         a • interior A ⊆ interior (a • A) := (isOpenMap_smul₀ h).image_interior_subset A
         _ ⊆ interior A := interior_mono (hA _ ha)
-        
 #align balanced_zero_union_interior balanced_zero_union_interior
 
 /-- The interior of a balanced set is balanced if it contains the origin. -/

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

@@ -108,15 +108,15 @@ theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorb
 theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
     Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   classical
-    induction' t using Finset.induction_on with i t ht hi
-    ·
-      simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
-        IsEmpty.forall_iff, imp_true_iff]
-    rw [Finset.set_biUnion_insert, absorbs_union, hi]
-    constructor <;> intro h
-    · refine' fun _ hi' => (finset.mem_insert.mp hi').elim _ (h.2 _)
-      exact fun hi'' => by rw [hi'']; exact h.1
-    exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
+  induction' t using Finset.induction_on with i t ht hi
+  ·
+    simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
+      IsEmpty.forall_iff, imp_true_iff]
+  rw [Finset.set_biUnion_insert, absorbs_union, hi]
+  constructor <;> intro h
+  · refine' fun _ hi' => (finset.mem_insert.mp hi').elim _ (h.2 _)
+    exact fun hi'' => by rw [hi'']; exact h.1
+  exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
 #align absorbs_Union_finset absorbs_iUnion_finset
 -/
 
@@ -434,7 +434,7 @@ variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
 
 theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) :=
   by
-  suffices Convex ℝ { x | ∀ a : 𝕜, ‖a‖ ≤ 1 → a • x ∈ convexHull ℝ s }
+  suffices Convex ℝ {x | ∀ a : 𝕜, ‖a‖ ≤ 1 → a • x ∈ convexHull ℝ s}
     by
     rw [balanced_iff_smul_mem] at hs ⊢
     refine' fun a ha x hx => convexHull_min _ this hx a ha

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

@@ -281,7 +281,7 @@ variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGr
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s :=
   by
   obtain rfl | hb := eq_or_ne b 0
-  · rw [norm_zero] at h
+  · rw [norm_zero] at h 
     rw [norm_eq_zero.1 (h.antisymm <| norm_nonneg _)]
     obtain rfl | h := s.eq_empty_or_nonempty
     · simp_rw [smul_set_empty]
@@ -308,7 +308,7 @@ theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆
   by
   refine' (subset_set_smul_iff₀ _).2 (hA a⁻¹ _)
   · rintro rfl
-    rw [norm_zero] at ha
+    rw [norm_zero] at ha 
     exact zero_lt_one.not_le ha
   · rw [norm_inv]
     exact inv_le_one ha
@@ -321,11 +321,11 @@ theorem Balanced.smul_eq (hA : Balanced 𝕜 A) (ha : ‖a‖ = 1) : a • A = A
 theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s :=
   by
   obtain rfl | hb := eq_or_ne b 0
-  · rw [norm_zero, norm_eq_zero] at h
+  · rw [norm_zero, norm_eq_zero] at h 
     rw [h]
   have ha : a ≠ 0 := norm_ne_zero_iff.1 (ne_of_eq_of_ne h <| norm_ne_zero_iff.2 hb)
-  constructor <;> intro h' <;>
-      [rw [← inv_mul_cancel_right₀ ha b];rw [← inv_mul_cancel_right₀ hb a]] <;>
+  constructor <;> intro h' <;> [rw [← inv_mul_cancel_right₀ ha b];
+      rw [← inv_mul_cancel_right₀ hb a]] <;>
     · rw [← smul_eq_mul, smul_assoc]
       refine' hs.smul_mem _ h'
       simp [← h, ha]
@@ -385,7 +385,7 @@ theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0
   intro a ha
   obtain rfl | h := eq_or_ne a 0
   · rw [zero_smul_set]
-    exacts[subset_union_left _ _, ⟨0, Or.inl rfl⟩]
+    exacts [subset_union_left _ _, ⟨0, Or.inl rfl⟩]
   · rw [← image_smul, image_union]
     apply union_subset_union
     · rw [image_zero, smul_zero]
@@ -422,7 +422,7 @@ theorem absorbs_zero_iff : Absorbs 𝕜 s 0 ↔ (0 : E) ∈ s :=
   rintro ⟨r, hr, h⟩
   obtain ⟨a, ha⟩ := NormedSpace.exists_lt_norm 𝕜 𝕜 r
   have := h _ ha.le
-  rwa [zero_subset, zero_mem_smul_set_iff] at this
+  rwa [zero_subset, zero_mem_smul_set_iff] at this 
   exact norm_ne_zero_iff.1 (hr.trans ha).ne'
 #align absorbs_zero_iff absorbs_zero_iff
 
@@ -436,7 +436,7 @@ theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (
   by
   suffices Convex ℝ { x | ∀ a : 𝕜, ‖a‖ ≤ 1 → a • x ∈ convexHull ℝ s }
     by
-    rw [balanced_iff_smul_mem] at hs⊢
+    rw [balanced_iff_smul_mem] at hs ⊢
     refine' fun a ha x hx => convexHull_min _ this hx a ha
     exact fun y hy a ha => subset_convexHull ℝ s (hs ha hy)
   intro x hx y hy u v hu hv huv a ha
@@ -453,7 +453,7 @@ variable [AddCommGroup E] [Module ℝ E] {s : Set E}
 theorem balanced_iff_neg_mem (hs : Convex ℝ s) : Balanced ℝ s ↔ ∀ ⦃x⦄, x ∈ s → -x ∈ s :=
   by
   refine' ⟨fun h x => h.neg_mem_iff.2, fun h a ha => smul_set_subset_iff.2 fun x hx => _⟩
-  rw [Real.norm_eq_abs, abs_le] at ha
+  rw [Real.norm_eq_abs, abs_le] at ha 
   rw [show a = -((1 - a) / 2) + (a - -1) / 2 by ring, add_smul, neg_smul, ← smul_neg]
   exact
     hs (h hx) hx (div_nonneg (sub_nonneg_of_le ha.2) zero_le_two)

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

@@ -47,7 +47,7 @@ absorbent, balanced, locally convex, LCTVS
 
 open Set
 
-open Pointwise Topology
+open scoped Pointwise Topology
 
 variable {𝕜 𝕝 E : Type _} {ι : Sort _} {κ : ι → Sort _}
 

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

@@ -76,43 +76,19 @@ theorem absorbs_empty {s : Set E} : Absorbs 𝕜 s (∅ : Set E) :=
 #align absorbs_empty absorbs_empty
 -/
 
-/- warning: absorbs.mono -> Absorbs.mono is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbs.mono Absorbs.monoₓ'. -/
 theorem Absorbs.mono (hs : Absorbs 𝕜 s u) (hst : s ⊆ t) (hvu : v ⊆ u) : Absorbs 𝕜 t v :=
   let ⟨r, hr, h⟩ := hs
   ⟨r, hr, fun a ha => hvu.trans <| (h _ ha).trans <| smul_set_mono hst⟩
 #align absorbs.mono Absorbs.mono
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbs.mono_left Absorbs.mono_leftₓ'. -/
 theorem Absorbs.mono_left (hs : Absorbs 𝕜 s u) (h : s ⊆ t) : Absorbs 𝕜 t u :=
   hs.mono h Subset.rfl
 #align absorbs.mono_left Absorbs.mono_left
 
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-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbs.mono_right Absorbs.mono_rightₓ'. -/
 theorem Absorbs.mono_right (hs : Absorbs 𝕜 s u) (h : v ⊆ u) : Absorbs 𝕜 s v :=
   hs.mono Subset.rfl h
 #align absorbs.mono_right Absorbs.mono_right
 
-/- warning: absorbs.union -> Absorbs.union is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbs.union Absorbs.unionₓ'. -/
 theorem Absorbs.union (hu : Absorbs 𝕜 s u) (hv : Absorbs 𝕜 s v) : Absorbs 𝕜 s (u ∪ v) :=
   by
   obtain ⟨a, ha, hu⟩ := hu
@@ -122,12 +98,6 @@ theorem Absorbs.union (hu : Absorbs 𝕜 s u) (hv : Absorbs 𝕜 s v) : Absorbs
       union_subset (hu _ <| le_of_max_le_left hc) (hv _ <| le_of_max_le_right hc)⟩
 #align absorbs.union Absorbs.union
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbs_union absorbs_unionₓ'. -/
 @[simp]
 theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorbs 𝕜 s v :=
   ⟨fun h => ⟨h.mono_right <| subset_union_left _ _, h.mono_right <| subset_union_right _ _⟩,
@@ -171,44 +141,20 @@ def Absorbent (A : Set E) :=
 
 variable {𝕜}
 
-/- warning: absorbent.subset -> Absorbent.subset is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbent.subset Absorbent.subsetₓ'. -/
 theorem Absorbent.subset (hA : Absorbent 𝕜 A) (hAB : A ⊆ B) : Absorbent 𝕜 B :=
   by
   refine' forall_imp (fun x => _) hA
   exact Exists.imp fun r => And.imp_right <| forall₂_imp fun a ha hx => Set.smul_set_mono hAB hx
 #align absorbent.subset Absorbent.subset
 
-/- warning: absorbent_iff_forall_absorbs_singleton -> absorbent_iff_forall_absorbs_singleton is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbent_iff_forall_absorbs_singleton absorbent_iff_forall_absorbs_singletonₓ'. -/
 theorem absorbent_iff_forall_absorbs_singleton : Absorbent 𝕜 A ↔ ∀ x, Absorbs 𝕜 A {x} := by
   simp_rw [Absorbs, Absorbent, singleton_subset_iff]
 #align absorbent_iff_forall_absorbs_singleton absorbent_iff_forall_absorbs_singleton
 
-/- warning: absorbent.absorbs -> Absorbent.absorbs is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbent.absorbs Absorbent.absorbsₓ'. -/
 theorem Absorbent.absorbs (hs : Absorbent 𝕜 s) {x : E} : Absorbs 𝕜 s {x} :=
   absorbent_iff_forall_absorbs_singleton.1 hs _
 #align absorbent.absorbs Absorbent.absorbs
 
-/- warning: absorbent_iff_nonneg_lt -> absorbent_iff_nonneg_lt is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbent_iff_nonneg_lt absorbent_iff_nonneg_ltₓ'. -/
 theorem absorbent_iff_nonneg_lt :
     Absorbent 𝕜 A ↔ ∀ x, ∃ r, 0 ≤ r ∧ ∀ ⦃a : 𝕜⦄, r < ‖a‖ → x ∈ a • A :=
   forall_congr' fun x =>
@@ -236,103 +182,43 @@ def Balanced (A : Set E) :=
 
 variable {𝕜}
 
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-Case conversion may be inaccurate. Consider using '#align balanced_iff_smul_mem balanced_iff_smul_memₓ'. -/
 theorem balanced_iff_smul_mem : Balanced 𝕜 s ↔ ∀ ⦃a : 𝕜⦄, ‖a‖ ≤ 1 → ∀ ⦃x : E⦄, x ∈ s → a • x ∈ s :=
   forall₂_congr fun a ha => smul_set_subset_iff
 #align balanced_iff_smul_mem balanced_iff_smul_mem
 
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-Case conversion may be inaccurate. Consider using '#align balanced.smul_mem Balanced.smul_memₓ'. -/
 alias balanced_iff_smul_mem ↔ Balanced.smul_mem _
 #align balanced.smul_mem Balanced.smul_mem
 
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-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align balanced_empty balanced_emptyₓ'. -/
 @[simp]
 theorem balanced_empty : Balanced 𝕜 (∅ : Set E) := fun _ _ => by rw [smul_set_empty]
 #align balanced_empty balanced_empty
 
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-Case conversion may be inaccurate. Consider using '#align balanced_univ balanced_univₓ'. -/
 @[simp]
 theorem balanced_univ : Balanced 𝕜 (univ : Set E) := fun a ha => subset_univ _
 #align balanced_univ balanced_univ
 
-/- warning: balanced.union -> Balanced.union 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] {A : Set.{u2} E} {B : Set.{u2} E}, (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 A) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 B) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) A B))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align balanced.union Balanced.unionₓ'. -/
 theorem Balanced.union (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced 𝕜 (A ∪ B) := fun a ha =>
   smul_set_union.Subset.trans <| union_subset_union (hA _ ha) <| hB _ ha
 #align balanced.union Balanced.union
 
-/- warning: balanced.inter -> Balanced.inter 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] {A : Set.{u2} E} {B : Set.{u2} E}, (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 A) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 B) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) A B))
-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] {A : Set.{u1} E} {B : Set.{u1} E}, (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 A) -> (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 B) -> (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) A B))
-Case conversion may be inaccurate. Consider using '#align balanced.inter Balanced.interₓ'. -/
 theorem Balanced.inter (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced 𝕜 (A ∩ B) := fun a ha =>
   smul_set_inter_subset.trans <| inter_subset_inter (hA _ ha) <| hB _ ha
 #align balanced.inter Balanced.inter
 
-/- warning: balanced_Union -> balanced_iUnion is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : ι -> (Set.{u2} E)}, (forall (i : ι), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.iUnion.{u2, u3} E ι (fun (i : ι) => f i)))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u3} 𝕜 E] {f : ι -> (Set.{u3} E)}, (forall (i : ι), Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (Set.iUnion.{u3, u1} E ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align balanced_Union balanced_iUnionₓ'. -/
 theorem balanced_iUnion {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋃ i, f i) :=
   fun a ha => (smul_set_Union _ _).Subset.trans <| iUnion_mono fun _ => h _ _ ha
 #align balanced_Union balanced_iUnion
 
-/- warning: balanced_Union₂ -> balanced_iUnion₂ is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u4} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u4} E)}, (forall (i : ι) (j : κ i), Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (Set.iUnion.{u4, u2} E ι (fun (i : ι) => Set.iUnion.{u4, u1} E (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align balanced_Union₂ balanced_iUnion₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem balanced_iUnion₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋃ (i) (j), f i j) :=
   balanced_iUnion fun _ => balanced_iUnion <| h _
 #align balanced_Union₂ balanced_iUnion₂
 
-/- warning: balanced_Inter -> balanced_iInter is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : ι -> (Set.{u2} E)}, (forall (i : ι), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.iInter.{u2, u3} E ι (fun (i : ι) => f i)))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u3} 𝕜 E] {f : ι -> (Set.{u3} E)}, (forall (i : ι), Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (Set.iInter.{u3, u1} E ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align balanced_Inter balanced_iInterₓ'. -/
 theorem balanced_iInter {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋂ i, f i) :=
   fun a ha => (smul_set_iInter_subset _ _).trans <| iInter_mono fun _ => h _ _ ha
 #align balanced_Inter balanced_iInter
 
-/- warning: balanced_Inter₂ -> balanced_iInter₂ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u2} E)}, (forall (i : ι) (j : κ i), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.iInter.{u2, u3} E ι (fun (i : ι) => Set.iInter.{u2, u4} E (κ i) (fun (j : κ i) => f i j))))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u4} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u4} E)}, (forall (i : ι) (j : κ i), Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (Set.iInter.{u4, u2} E ι (fun (i : ι) => Set.iInter.{u4, u1} E (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align balanced_Inter₂ balanced_iInter₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem balanced_iInter₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋂ (i) (j), f i j) :=
@@ -341,12 +227,6 @@ theorem balanced_iInter₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 
 
 variable [SMul 𝕝 E] [SMulCommClass 𝕜 𝕝 E]
 
-/- warning: balanced.smul -> Balanced.smul is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {𝕝 : Type.{u2}} {E : Type.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u3} 𝕜 E] {s : Set.{u3} E} [_inst_3 : SMul.{u2, u3} 𝕝 E] [_inst_4 : SMulCommClass.{u1, u2, u3} 𝕜 𝕝 E _inst_2 _inst_3] (a : 𝕝), (Balanced.{u1, u3} 𝕜 E _inst_1 _inst_2 s) -> (Balanced.{u1, u3} 𝕜 E _inst_1 _inst_2 (SMul.smul.{u2, u3} 𝕝 (Set.{u3} E) (Set.smulSet.{u2, u3} 𝕝 E _inst_3) a s))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {𝕝 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u2} 𝕜 E] {s : Set.{u2} E} [_inst_3 : SMul.{u1, u2} 𝕝 E] [_inst_4 : SMulCommClass.{u3, u1, u2} 𝕜 𝕝 E _inst_2 _inst_3] (a : 𝕝), (Balanced.{u3, u2} 𝕜 E _inst_1 _inst_2 s) -> (Balanced.{u3, u2} 𝕜 E _inst_1 _inst_2 (HSMul.hSMul.{u1, u2, u2} 𝕝 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕝 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕝 E _inst_3)) a s))
-Case conversion may be inaccurate. Consider using '#align balanced.smul Balanced.smulₓ'. -/
 theorem Balanced.smul (a : 𝕝) (hs : Balanced 𝕜 s) : Balanced 𝕜 (a • s) := fun b hb =>
   (smul_comm _ _ _).Subset.trans <| smul_set_mono <| hs _ hb
 #align balanced.smul Balanced.smul
@@ -357,33 +237,15 @@ section Module
 
 variable [AddCommGroup E] [Module 𝕜 E] {s s₁ s₂ t t₁ t₂ : Set E}
 
-/- warning: absorbs.neg -> Absorbs.neg is a dubious translation:
-lean 3 declaration is
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-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)] {s : Set.{u1} E} {t : Set.{u1} E}, (Absorbs.{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 t) -> (Absorbs.{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)))) (Neg.neg.{u1} (Set.{u1} E) (Set.neg.{u1} E (NegZeroClass.toNeg.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2)))))) s) (Neg.neg.{u1} (Set.{u1} E) (Set.neg.{u1} E (NegZeroClass.toNeg.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2)))))) t))
-Case conversion may be inaccurate. Consider using '#align absorbs.neg Absorbs.negₓ'. -/
 theorem Absorbs.neg : Absorbs 𝕜 s t → Absorbs 𝕜 (-s) (-t) :=
   Exists.imp fun r =>
     And.imp_right <| forall₂_imp fun _ _ h => (neg_subset_neg.2 h).trans (smul_set_neg _ _).Superset
 #align absorbs.neg Absorbs.neg
 
-/- warning: balanced.neg -> Balanced.neg is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align balanced.neg Balanced.negₓ'. -/
 theorem Balanced.neg : Balanced 𝕜 s → Balanced 𝕜 (-s) :=
   forall₂_imp fun _ _ h => (smul_set_neg _ _).Subset.trans <| neg_subset_neg.2 h
 #align balanced.neg Balanced.neg
 
-/- warning: absorbs.add -> Absorbs.add is a dubious translation:
-lean 3 declaration is
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-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)] {s₁ : Set.{u1} E} {s₂ : Set.{u1} E} {t₁ : Set.{u1} E} {t₂ : Set.{u1} E}, (Absorbs.{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)))) s₁ t₁) -> (Absorbs.{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)))) s₂ t₂) -> (Absorbs.{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)))) (HAdd.hAdd.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHAdd.{u1} (Set.{u1} E) (Set.add.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))))) s₁ s₂) (HAdd.hAdd.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHAdd.{u1} (Set.{u1} E) (Set.add.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))))) t₁ t₂))
-Case conversion may be inaccurate. Consider using '#align absorbs.add Absorbs.addₓ'. -/
 theorem Absorbs.add : Absorbs 𝕜 s₁ t₁ → Absorbs 𝕜 s₂ t₂ → Absorbs 𝕜 (s₁ + s₂) (t₁ + t₂) :=
   fun ⟨r₁, hr₁, h₁⟩ ⟨r₂, hr₂, h₂⟩ =>
   ⟨max r₁ r₂, lt_max_of_lt_left hr₁, fun a ha =>
@@ -391,42 +253,18 @@ theorem Absorbs.add : Absorbs 𝕜 s₁ t₁ → Absorbs 𝕜 s₂ t₂ → Abso
       (smul_add _ _ _).Superset⟩
 #align absorbs.add Absorbs.add
 
-/- warning: balanced.add -> Balanced.add is a dubious translation:
-lean 3 declaration is
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-  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)] {s : Set.{u1} E} {t : Set.{u1} E}, (Balanced.{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) -> (Balanced.{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)))) t) -> (Balanced.{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)))) (HAdd.hAdd.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHAdd.{u1} (Set.{u1} E) (Set.add.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))))) s t))
-Case conversion may be inaccurate. Consider using '#align balanced.add Balanced.addₓ'. -/
 theorem Balanced.add (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s + t) := fun a ha =>
   (smul_add _ _ _).Subset.trans <| add_subset_add (hs _ ha) <| ht _ ha
 #align balanced.add Balanced.add
 
-/- warning: absorbs.sub -> Absorbs.sub is a dubious translation:
-lean 3 declaration is
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-  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)] {s₁ : Set.{u1} E} {s₂ : Set.{u1} E} {t₁ : Set.{u1} E} {t₂ : Set.{u1} E}, (Absorbs.{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)))) s₁ t₁) -> (Absorbs.{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)))) s₂ t₂) -> (Absorbs.{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)))) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))) s₁ s₂) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))) t₁ t₂))
-Case conversion may be inaccurate. Consider using '#align absorbs.sub Absorbs.subₓ'. -/
 theorem Absorbs.sub (h₁ : Absorbs 𝕜 s₁ t₁) (h₂ : Absorbs 𝕜 s₂ t₂) : Absorbs 𝕜 (s₁ - s₂) (t₁ - t₂) :=
   by simp_rw [sub_eq_add_neg]; exact h₁.add h₂.neg
 #align absorbs.sub Absorbs.sub
 
-/- warning: balanced.sub -> Balanced.sub is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align balanced.sub Balanced.subₓ'. -/
 theorem Balanced.sub (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s - t) := by
   simp_rw [sub_eq_add_neg]; exact hs.add ht.neg
 #align balanced.sub Balanced.sub
 
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-Case conversion may be inaccurate. Consider using '#align balanced_zero balanced_zeroₓ'. -/
 theorem balanced_zero : Balanced 𝕜 (0 : Set E) := fun a ha => (smul_zero _).Subset
 #align balanced_zero balanced_zero
 
@@ -439,9 +277,6 @@ section NormedField
 variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGroup E] [Module 𝕜 E]
   [SMulWithZero 𝕝 E] [IsScalarTower 𝕜 𝕝 E] {s t u v A B : Set E} {x : E} {a b : 𝕜}
 
-/- warning: balanced.smul_mono -> Balanced.smul_mono is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align balanced.smul_mono Balanced.smul_monoₓ'. -/
 /-- Scalar multiplication (by possibly different types) of a balanced set is monotone. -/
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s :=
   by
@@ -459,12 +294,6 @@ theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖
   exact div_le_one_of_le h (norm_nonneg _)
 #align balanced.smul_mono Balanced.smul_mono
 
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-Case conversion may be inaccurate. Consider using '#align balanced.absorbs_self Balanced.absorbs_selfₓ'. -/
 /-- A balanced set absorbs itself. -/
 theorem Balanced.absorbs_self (hA : Balanced 𝕜 A) : Absorbs 𝕜 A A :=
   by
@@ -475,12 +304,6 @@ theorem Balanced.absorbs_self (hA : Balanced 𝕜 A) : Absorbs 𝕜 A A :=
   exact inv_le_one ha
 #align balanced.absorbs_self Balanced.absorbs_self
 
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-Case conversion may be inaccurate. Consider using '#align balanced.subset_smul Balanced.subset_smulₓ'. -/
 theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆ a • A :=
   by
   refine' (subset_set_smul_iff₀ _).2 (hA a⁻¹ _)
@@ -491,19 +314,10 @@ theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆
     exact inv_le_one ha
 #align balanced.subset_smul Balanced.subset_smul
 
-/- warning: balanced.smul_eq -> Balanced.smul_eq is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} {a : 𝕜}, (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (Eq.{1} Real (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)))) -> (Eq.{succ u2} (Set.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5))))) a A) A)
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-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {A : Set.{u1} E} {a : 𝕜}, (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (Eq.{1} Real (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} (Set.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))))) a A) A)
-Case conversion may be inaccurate. Consider using '#align balanced.smul_eq Balanced.smul_eqₓ'. -/
 theorem Balanced.smul_eq (hA : Balanced 𝕜 A) (ha : ‖a‖ = 1) : a • A = A :=
   (hA _ ha.le).antisymm <| hA.subset_smul ha.ge
 #align balanced.smul_eq Balanced.smul_eq
 
-/- warning: balanced.mem_smul_iff -> Balanced.mem_smul_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align balanced.mem_smul_iff Balanced.mem_smul_iffₓ'. -/
 theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s :=
   by
   obtain rfl | hb := eq_or_ne b 0
@@ -517,22 +331,10 @@ theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a
       simp [← h, ha]
 #align balanced.mem_smul_iff Balanced.mem_smul_iff
 
-/- warning: balanced.neg_mem_iff -> Balanced.neg_mem_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {s : Set.{u2} E} {x : E}, (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) s) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (Neg.neg.{u2} E (SubNegMonoid.toHasNeg.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_4))) x) s) (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s))
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-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {s : Set.{u1} E} {x : E}, (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) s) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (Neg.neg.{u1} E (NegZeroClass.toNeg.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) x) s) (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s))
-Case conversion may be inaccurate. Consider using '#align balanced.neg_mem_iff Balanced.neg_mem_iffₓ'. -/
 theorem Balanced.neg_mem_iff (hs : Balanced 𝕜 s) : -x ∈ s ↔ x ∈ s := by
   convert hs.mem_smul_iff (norm_neg 1) <;> simp only [neg_smul, one_smul]
 #align balanced.neg_mem_iff Balanced.neg_mem_iff
 
-/- warning: absorbs.inter -> Absorbs.inter is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {s : Set.{u2} E} {t : Set.{u2} E} {u : Set.{u2} E}, (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) s u) -> (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) t u) -> (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) u)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {s : Set.{u1} E} {t : Set.{u1} E} {u : Set.{u1} E}, (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) s u) -> (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) t u) -> (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t) u)
-Case conversion may be inaccurate. Consider using '#align absorbs.inter Absorbs.interₓ'. -/
 theorem Absorbs.inter (hs : Absorbs 𝕜 s u) (ht : Absorbs 𝕜 t u) : Absorbs 𝕜 (s ∩ t) u :=
   by
   obtain ⟨a, ha, hs⟩ := hs
@@ -543,24 +345,12 @@ theorem Absorbs.inter (hs : Absorbs 𝕜 s u) (ht : Absorbs 𝕜 t u) : Absorbs
   exact subset_inter (hs _ <| le_of_max_le_left hc) (ht _ <| le_of_max_le_right hc)
 #align absorbs.inter Absorbs.inter
 
-/- warning: absorbs_inter -> absorbs_inter is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {s : Set.{u2} E} {t : Set.{u2} E} {u : Set.{u2} E}, Iff (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) u) (And (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) s u) (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) t u))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {s : Set.{u1} E} {t : Set.{u1} E} {u : Set.{u1} E}, Iff (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t) u) (And (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) s u) (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) t u))
-Case conversion may be inaccurate. Consider using '#align absorbs_inter absorbs_interₓ'. -/
 @[simp]
 theorem absorbs_inter : Absorbs 𝕜 (s ∩ t) u ↔ Absorbs 𝕜 s u ∧ Absorbs 𝕜 t u :=
   ⟨fun h => ⟨h.mono_left <| inter_subset_left _ _, h.mono_left <| inter_subset_right _ _⟩, fun h =>
     h.1.inter h.2⟩
 #align absorbs_inter absorbs_inter
 
-/- warning: absorbent_univ -> absorbent_univ is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align absorbent_univ absorbent_univₓ'. -/
 theorem absorbent_univ : Absorbent 𝕜 (univ : Set E) :=
   by
   refine' fun x => ⟨1, zero_lt_one, fun a ha => _⟩
@@ -570,12 +360,6 @@ theorem absorbent_univ : Absorbent 𝕜 (univ : Set E) :=
 
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
-/- warning: absorbent_nhds_zero -> absorbent_nhds_zero is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : 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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) A (nhds.{u2} E _inst_8 (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_4)))))))))) -> (Absorbent.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : 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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) A (nhds.{u2} E _inst_8 (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_4))))))))) -> (Absorbent.{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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) A)
-Case conversion may be inaccurate. Consider using '#align absorbent_nhds_zero absorbent_nhds_zeroₓ'. -/
 /-- Every neighbourhood of the origin is absorbent. -/
 theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
   by
@@ -595,9 +379,6 @@ theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
     
 #align absorbent_nhds_zero absorbent_nhds_zero
 
-/- warning: balanced_zero_union_interior -> balanced_zero_union_interior is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align balanced_zero_union_interior balanced_zero_union_interiorₓ'. -/
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
 theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0 : Set E) ∪ interior A) :=
   by
@@ -616,9 +397,6 @@ theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0
         
 #align balanced_zero_union_interior balanced_zero_union_interior
 
-/- warning: balanced.interior -> Balanced.interior is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align balanced.interior Balanced.interiorₓ'. -/
 /-- The interior of a balanced set is balanced if it contains the origin. -/
 theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
     Balanced 𝕜 (interior A) :=
@@ -627,9 +405,6 @@ theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
   exact balanced_zero_union_interior hA
 #align balanced.interior Balanced.interior
 
-/- warning: balanced.closure -> Balanced.closure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align balanced.closure Balanced.closureₓ'. -/
 theorem Balanced.closure (hA : Balanced 𝕜 A) : Balanced 𝕜 (closure A) := fun a ha =>
   (image_closure_subset_closure_image <| continuous_id.const_smul _).trans <|
     closure_mono <| hA _ ha
@@ -641,12 +416,6 @@ section NontriviallyNormedField
 
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {s : Set E}
 
-/- warning: absorbs_zero_iff -> absorbs_zero_iff 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)] {s : Set.{u2} E}, Iff (Absorbs.{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 (OfNat.ofNat.{u2} (Set.{u2} E) 0 (OfNat.mk.{u2} (Set.{u2} E) 0 (Zero.zero.{u2} (Set.{u2} E) (Set.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} 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.{u2}} {E : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E}, Iff (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s (OfNat.ofNat.{u1} (Set.{u1} E) 0 (Zero.toOfNat0.{u1} (Set.{u1} E) (Set.zero.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))))))) (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))))) s)
-Case conversion may be inaccurate. Consider using '#align absorbs_zero_iff absorbs_zero_iffₓ'. -/
 theorem absorbs_zero_iff : Absorbs 𝕜 s 0 ↔ (0 : E) ∈ s :=
   by
   refine' ⟨_, fun h => ⟨1, zero_lt_one, fun a _ => zero_subset.2 <| zero_mem_smul_set h⟩⟩
@@ -657,21 +426,12 @@ theorem absorbs_zero_iff : Absorbs 𝕜 s 0 ↔ (0 : E) ∈ s :=
   exact norm_ne_zero_iff.1 (hr.trans ha).ne'
 #align absorbs_zero_iff absorbs_zero_iff
 
-/- warning: absorbent.zero_mem -> Absorbent.zero_mem 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)] {s : Set.{u2} E}, (Absorbent.{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) -> (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.{u2}} {E : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E}, (Absorbent.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s) -> (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))))) s)
-Case conversion may be inaccurate. Consider using '#align absorbent.zero_mem Absorbent.zero_memₓ'. -/
 theorem Absorbent.zero_mem (hs : Absorbent 𝕜 s) : (0 : E) ∈ s :=
   absorbs_zero_iff.1 <| absorbent_iff_forall_absorbs_singleton.1 hs _
 #align absorbent.zero_mem Absorbent.zero_mem
 
 variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
 
-/- warning: balanced_convex_hull_of_balanced -> balanced_convexHull_of_balanced is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align balanced_convex_hull_of_balanced balanced_convexHull_of_balancedₓ'. -/
 theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) :=
   by
   suffices Convex ℝ { x | ∀ a : 𝕜, ‖a‖ ≤ 1 → a • x ∈ convexHull ℝ s }
@@ -690,12 +450,6 @@ section Real
 
 variable [AddCommGroup E] [Module ℝ E] {s : Set E}
 
-/- warning: balanced_iff_neg_mem -> balanced_iff_neg_mem is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] {s : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) -> (Iff (Balanced.{0, u1} Real E (SeminormedCommRing.toSemiNormedRing.{0} Real (NormedCommRing.toSeminormedCommRing.{0} Real Real.normedCommRing)) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) (forall {{x : E}}, (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s) -> (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) (Neg.neg.{u1} E (SubNegMonoid.toHasNeg.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1))) x) s)))
-but is expected to have type
-  forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] {s : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) -> (Iff (Balanced.{0, u1} Real E (SeminormedCommRing.toSeminormedRing.{0} Real (NormedCommRing.toSeminormedCommRing.{0} Real Real.normedCommRing)) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) (forall {{x : E}}, (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s) -> (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (Neg.neg.{u1} E (NegZeroClass.toNeg.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) x) s)))
-Case conversion may be inaccurate. Consider using '#align balanced_iff_neg_mem balanced_iff_neg_memₓ'. -/
 theorem balanced_iff_neg_mem (hs : Convex ℝ s) : Balanced ℝ s ↔ ∀ ⦃x⦄, x ∈ s → -x ∈ s :=
   by
   refine' ⟨fun h x => h.neg_mem_iff.2, fun h a ha => smul_set_subset_iff.2 fun x hx => _⟩

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

@@ -145,9 +145,7 @@ theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
     rw [Finset.set_biUnion_insert, absorbs_union, hi]
     constructor <;> intro h
     · refine' fun _ hi' => (finset.mem_insert.mp hi').elim _ (h.2 _)
-      exact fun hi'' => by
-        rw [hi'']
-        exact h.1
+      exact fun hi'' => by rw [hi'']; exact h.1
     exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
 #align absorbs_Union_finset absorbs_iUnion_finset
 -/
@@ -410,9 +408,7 @@ 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)] {s₁ : Set.{u1} E} {s₂ : Set.{u1} E} {t₁ : Set.{u1} E} {t₂ : Set.{u1} E}, (Absorbs.{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)))) s₁ t₁) -> (Absorbs.{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)))) s₂ t₂) -> (Absorbs.{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)))) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))) s₁ s₂) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))) t₁ t₂))
 Case conversion may be inaccurate. Consider using '#align absorbs.sub Absorbs.subₓ'. -/
 theorem Absorbs.sub (h₁ : Absorbs 𝕜 s₁ t₁) (h₂ : Absorbs 𝕜 s₂ t₂) : Absorbs 𝕜 (s₁ - s₂) (t₁ - t₂) :=
-  by
-  simp_rw [sub_eq_add_neg]
-  exact h₁.add h₂.neg
+  by simp_rw [sub_eq_add_neg]; exact h₁.add h₂.neg
 #align absorbs.sub Absorbs.sub
 
 /- warning: balanced.sub -> Balanced.sub is a dubious translation:
@@ -421,10 +417,8 @@ lean 3 declaration is
 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)] {s : Set.{u1} E} {t : Set.{u1} E}, (Balanced.{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) -> (Balanced.{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)))) t) -> (Balanced.{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)))) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))) s t))
 Case conversion may be inaccurate. Consider using '#align balanced.sub Balanced.subₓ'. -/
-theorem Balanced.sub (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s - t) :=
-  by
-  simp_rw [sub_eq_add_neg]
-  exact hs.add ht.neg
+theorem Balanced.sub (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s - t) := by
+  simp_rw [sub_eq_add_neg]; exact hs.add ht.neg
 #align balanced.sub Balanced.sub
 
 /- warning: balanced_zero -> balanced_zero is a dubious translation:

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

@@ -446,10 +446,7 @@ variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGr
   [SMulWithZero 𝕝 E] [IsScalarTower 𝕜 𝕝 E] {s t u v A B : Set E} {x : E} {a b : 𝕜}
 
 /- warning: balanced.smul_mono -> Balanced.smul_mono is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {𝕝 : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedRing.{u2} 𝕝] [_inst_3 : NormedSpace.{u1, u2} 𝕜 𝕝 _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2)))] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)] [_inst_6 : SMulWithZero.{u2, u3} 𝕝 E (MulZeroClass.toHasZero.{u2} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕝 (Ring.toNonAssocRing.{u2} 𝕝 (NormedRing.toRing.{u2} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4)))))] [_inst_7 : IsScalarTower.{u1, u2, u3} 𝕜 𝕝 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 𝕝 (AddZeroClass.toHasZero.{u2} 𝕝 (AddMonoid.toAddZeroClass.{u2} 𝕝 (AddCommMonoid.toAddMonoid.{u2} 𝕝 (AddCommGroup.toAddCommMonoid.{u2} 𝕝 (SeminormedAddCommGroup.toAddCommGroup.{u2} 𝕝 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 𝕝 (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} 𝕝 (AddMonoid.toAddZeroClass.{u2} 𝕝 (AddCommMonoid.toAddMonoid.{u2} 𝕝 (AddCommGroup.toAddCommMonoid.{u2} 𝕝 (SeminormedAddCommGroup.toAddCommGroup.{u2} 𝕝 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 𝕝 (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} 𝕝 (AddMonoid.toAddZeroClass.{u2} 𝕝 (AddCommMonoid.toAddMonoid.{u2} 𝕝 (AddCommGroup.toAddCommMonoid.{u2} 𝕝 (SeminormedAddCommGroup.toAddCommGroup.{u2} 𝕝 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 𝕝 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕝 (SeminormedAddCommGroup.toAddCommGroup.{u2} 𝕝 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2))))) (NormedSpace.toModule.{u1, u2} 𝕜 𝕝 _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2))) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕝 E (MulZeroClass.toHasZero.{u2} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕝 (Ring.toNonAssocRing.{u2} 𝕝 (NormedRing.toRing.{u2} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) _inst_6)) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))] {s : Set.{u3} E}, (Balanced.{u2, u3} 𝕝 E (NormedRing.toSeminormedRing.{u2} 𝕝 _inst_2) (SMulZeroClass.toHasSmul.{u2, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕝 E (MulZeroClass.toHasZero.{u2} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕝 (Ring.toNonAssocRing.{u2} 𝕝 (NormedRing.toRing.{u2} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) _inst_6)) s) -> (forall {a : 𝕝} {b : 𝕜}, (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} 𝕝 (NormedRing.toHasNorm.{u2} 𝕝 _inst_2) a) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) b)) -> (HasSubset.Subset.{u3} (Set.{u3} E) (Set.hasSubset.{u3} E) (SMul.smul.{u2, u3} 𝕝 (Set.{u3} E) (Set.smulSet.{u2, u3} 𝕝 E (SMulZeroClass.toHasSmul.{u2, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕝 E (MulZeroClass.toHasZero.{u2} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕝 (Ring.toNonAssocRing.{u2} 𝕝 (NormedRing.toRing.{u2} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) _inst_6))) a s) (SMul.smul.{u1, u3} 𝕜 (Set.{u3} E) (Set.smulSet.{u1, u3} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) b s)))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {𝕝 : Type.{u3}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedRing.{u3} 𝕝] [_inst_3 : NormedSpace.{u1, u3} 𝕜 𝕝 _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u3} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u3} 𝕝 (NormedRing.toNonUnitalNormedRing.{u3} 𝕝 _inst_2)))] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] [_inst_6 : SMulWithZero.{u3, u2} 𝕝 E (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4)))))] [_inst_7 : IsScalarTower.{u1, u3, u2} 𝕜 𝕝 E (SMulZeroClass.toSMul.{u1, u3} 𝕜 𝕝 (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 𝕝 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 𝕝 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2))))) (NormedSpace.toModule.{u1, u3} 𝕜 𝕝 _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u3} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u3} 𝕝 (NormedRing.toNonUnitalNormedRing.{u3} 𝕝 _inst_2))) _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) _inst_6)) (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5))))] {s : Set.{u2} E}, (Balanced.{u3, u2} 𝕝 E (NormedRing.toSeminormedRing.{u3} 𝕝 _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) _inst_6)) s) -> (forall {a : 𝕝} {b : 𝕜}, (LE.le.{0} Real Real.instLEReal (Norm.norm.{u3} 𝕝 (NormedRing.toNorm.{u3} 𝕝 _inst_2) a) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) b)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (HSMul.hSMul.{u3, u2, u2} 𝕝 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u3, u2} 𝕝 (Set.{u2} E) (Set.smulSet.{u3, u2} 𝕝 E (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) _inst_6)))) a s) (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))))) b s)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align balanced.smul_mono Balanced.smul_monoₓ'. -/
 /-- Scalar multiplication (by possibly different types) of a balanced set is monotone. -/
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s :=
@@ -511,10 +508,7 @@ theorem Balanced.smul_eq (hA : Balanced 𝕜 A) (ha : ‖a‖ = 1) : a • A = A
 #align balanced.smul_eq Balanced.smul_eq
 
 /- warning: balanced.mem_smul_iff -> Balanced.mem_smul_iff is a dubious translation:
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-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {s : Set.{u1} E} {x : E} {a : 𝕜} {b : 𝕜}, (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) s) -> (Eq.{1} Real (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) a) (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) b)) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) a x) s) (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) b x) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align balanced.mem_smul_iff Balanced.mem_smul_iffₓ'. -/
 theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s :=
   by
@@ -608,10 +602,7 @@ theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
 #align absorbent_nhds_zero absorbent_nhds_zero
 
 /- warning: balanced_zero_union_interior -> balanced_zero_union_interior is a dubious translation:
-lean 3 declaration is
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(AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (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_4)))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) (OfNat.ofNat.{u2} (Set.{u2} E) 0 (OfNat.mk.{u2} (Set.{u2} E) 0 (Zero.zero.{u2} (Set.{u2} E) (Set.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_4))))))))) (interior.{u2} E _inst_8 A)))
-but is expected to have type
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(SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_8], (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (Union.union.{u1} (Set.{u1} E) (Set.instUnionSet.{u1} E) (OfNat.ofNat.{u1} (Set.{u1} E) 0 (Zero.toOfNat0.{u1} (Set.{u1} E) (Set.zero.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4)))))))) (interior.{u1} E _inst_8 A)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align balanced_zero_union_interior balanced_zero_union_interiorₓ'. -/
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
 theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0 : Set E) ∪ interior A) :=
@@ -632,10 +623,7 @@ theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0
 #align balanced_zero_union_interior balanced_zero_union_interior
 
 /- warning: balanced.interior -> Balanced.interior is a dubious translation:
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(AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (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_4)))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (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_4)))))))) (interior.{u2} E _inst_8 A)) -> (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (interior.{u2} E _inst_8 A))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {A : Set.{u1} E} [_inst_8 : TopologicalSpace.{u1} E] [_inst_9 : ContinuousSMul.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_8], (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))))) (interior.{u1} E _inst_8 A)) -> (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (interior.{u1} E _inst_8 A))
+<too large>
 Case conversion may be inaccurate. Consider using '#align balanced.interior Balanced.interiorₓ'. -/
 /-- The interior of a balanced set is balanced if it contains the origin. -/
 theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
@@ -646,10 +634,7 @@ theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
 #align balanced.interior Balanced.interior
 
 /- warning: balanced.closure -> Balanced.closure is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : 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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (closure.{u2} E _inst_8 A))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {A : Set.{u1} E} [_inst_8 : TopologicalSpace.{u1} E] [_inst_9 : ContinuousSMul.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_8], (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (closure.{u1} E _inst_8 A))
+<too large>
 Case conversion may be inaccurate. Consider using '#align balanced.closure Balanced.closureₓ'. -/
 theorem Balanced.closure (hA : Balanced 𝕜 A) : Balanced 𝕜 (closure A) := fun a ha =>
   (image_closure_subset_closure_image <| continuous_id.const_smul _).trans <|
@@ -691,10 +676,7 @@ theorem Absorbent.zero_mem (hs : Absorbent 𝕜 s) : (0 : E) ∈ s :=
 variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
 
 /- warning: balanced_convex_hull_of_balanced -> balanced_convexHull_of_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)] {s : Set.{u2} E} [_inst_4 : Module.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : SMulCommClass.{0, u1, u2} Real 𝕜 E (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (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))))], (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) -> (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)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{0, u2} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E} [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : SMulCommClass.{0, u2, u1} Real 𝕜 E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))], (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s) -> (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (OrderHom.toFun.{u1, u1} (Set.{u1} E) (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (ClosureOperator.toOrderHom.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (convexHull.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align balanced_convex_hull_of_balanced balanced_convexHull_of_balancedₓ'. -/
 theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -522,8 +522,8 @@ theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a
   · rw [norm_zero, norm_eq_zero] at h
     rw [h]
   have ha : a ≠ 0 := norm_ne_zero_iff.1 (ne_of_eq_of_ne h <| norm_ne_zero_iff.2 hb)
-  constructor <;> intro h' <;> [rw [← inv_mul_cancel_right₀ ha b],
-      rw [← inv_mul_cancel_right₀ hb a]] <;>
+  constructor <;> intro h' <;>
+      [rw [← inv_mul_cancel_right₀ ha b];rw [← inv_mul_cancel_right₀ hb a]] <;>
     · rw [← smul_eq_mul, smul_assoc]
       refine' hs.smul_mem _ h'
       simp [← h, ha]

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

@@ -134,32 +134,32 @@ theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorb
     fun h => h.1.union h.2⟩
 #align absorbs_union absorbs_union
 
-#print absorbs_unionᵢ_finset /-
-theorem absorbs_unionᵢ_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
+#print absorbs_iUnion_finset /-
+theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
     Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   classical
     induction' t using Finset.induction_on with i t ht hi
     ·
-      simp only [Finset.not_mem_empty, Set.unionᵢ_false, Set.unionᵢ_empty, absorbs_empty,
+      simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
         IsEmpty.forall_iff, imp_true_iff]
-    rw [Finset.set_bunionᵢ_insert, absorbs_union, hi]
+    rw [Finset.set_biUnion_insert, absorbs_union, hi]
     constructor <;> intro h
     · refine' fun _ hi' => (finset.mem_insert.mp hi').elim _ (h.2 _)
       exact fun hi'' => by
         rw [hi'']
         exact h.1
     exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
-#align absorbs_Union_finset absorbs_unionᵢ_finset
+#align absorbs_Union_finset absorbs_iUnion_finset
 -/
 
-#print Set.Finite.absorbs_unionᵢ /-
-theorem Set.Finite.absorbs_unionᵢ {ι : Type _} {s : Set E} {t : Set ι} {f : ι → Set E}
+#print Set.Finite.absorbs_iUnion /-
+theorem Set.Finite.absorbs_iUnion {ι : Type _} {s : Set E} {t : Set ι} {f : ι → Set E}
     (hi : t.Finite) : Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) :=
   by
   lift t to Finset ι using hi
   simp only [Finset.mem_coe]
-  exact absorbs_unionᵢ_finset
-#align set.finite.absorbs_Union Set.Finite.absorbs_unionᵢ
+  exact absorbs_iUnion_finset
+#align set.finite.absorbs_Union Set.Finite.absorbs_iUnion
 -/
 
 variable (𝕜)
@@ -222,7 +222,7 @@ theorem absorbent_iff_nonneg_lt :
 #print Absorbent.absorbs_finite /-
 theorem Absorbent.absorbs_finite {s : Set E} (hs : Absorbent 𝕜 s) {v : Set E} (hv : v.Finite) :
     Absorbs 𝕜 s v := by
-  rw [← Set.bunionᵢ_of_singleton v]
+  rw [← Set.biUnion_of_singleton v]
   exact hv.absorbs_Union.mpr fun _ _ => hs.absorbs
 #align absorbent.absorbs_finite Absorbent.absorbs_finite
 -/
@@ -297,49 +297,49 @@ theorem Balanced.inter (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced
   smul_set_inter_subset.trans <| inter_subset_inter (hA _ ha) <| hB _ ha
 #align balanced.inter Balanced.inter
 
-/- warning: balanced_Union -> balanced_unionᵢ is a dubious translation:
+/- warning: balanced_Union -> balanced_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : ι -> (Set.{u2} E)}, (forall (i : ι), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.unionᵢ.{u2, u3} E ι (fun (i : ι) => f i)))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : ι -> (Set.{u2} E)}, (forall (i : ι), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.iUnion.{u2, u3} E ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u3} 𝕜 E] {f : ι -> (Set.{u3} E)}, (forall (i : ι), Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (Set.unionᵢ.{u3, u1} E ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align balanced_Union balanced_unionᵢₓ'. -/
-theorem balanced_unionᵢ {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋃ i, f i) :=
-  fun a ha => (smul_set_Union _ _).Subset.trans <| unionᵢ_mono fun _ => h _ _ ha
-#align balanced_Union balanced_unionᵢ
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u3} 𝕜 E] {f : ι -> (Set.{u3} E)}, (forall (i : ι), Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (Set.iUnion.{u3, u1} E ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align balanced_Union balanced_iUnionₓ'. -/
+theorem balanced_iUnion {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋃ i, f i) :=
+  fun a ha => (smul_set_Union _ _).Subset.trans <| iUnion_mono fun _ => h _ _ ha
+#align balanced_Union balanced_iUnion
 
-/- warning: balanced_Union₂ -> balanced_unionᵢ₂ is a dubious translation:
+/- warning: balanced_Union₂ -> balanced_iUnion₂ is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u2} E)}, (forall (i : ι) (j : κ i), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.unionᵢ.{u2, u3} E ι (fun (i : ι) => Set.unionᵢ.{u2, u4} E (κ i) (fun (j : κ i) => f i j))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u2} E)}, (forall (i : ι) (j : κ i), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.iUnion.{u2, u3} E ι (fun (i : ι) => Set.iUnion.{u2, u4} E (κ i) (fun (j : κ i) => f i j))))
 but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u4} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u4} E)}, (forall (i : ι) (j : κ i), Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (Set.unionᵢ.{u4, u2} E ι (fun (i : ι) => Set.unionᵢ.{u4, u1} E (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align balanced_Union₂ balanced_unionᵢ₂ₓ'. -/
+  forall {𝕜 : Type.{u3}} {E : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u4} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u4} E)}, (forall (i : ι) (j : κ i), Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (Set.iUnion.{u4, u2} E ι (fun (i : ι) => Set.iUnion.{u4, u1} E (κ i) (fun (j : κ i) => f i j))))
+Case conversion may be inaccurate. Consider using '#align balanced_Union₂ balanced_iUnion₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem balanced_unionᵢ₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
+theorem balanced_iUnion₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋃ (i) (j), f i j) :=
-  balanced_unionᵢ fun _ => balanced_unionᵢ <| h _
-#align balanced_Union₂ balanced_unionᵢ₂
+  balanced_iUnion fun _ => balanced_iUnion <| h _
+#align balanced_Union₂ balanced_iUnion₂
 
-/- warning: balanced_Inter -> balanced_interᵢ is a dubious translation:
+/- warning: balanced_Inter -> balanced_iInter is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : ι -> (Set.{u2} E)}, (forall (i : ι), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.interᵢ.{u2, u3} E ι (fun (i : ι) => f i)))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : ι -> (Set.{u2} E)}, (forall (i : ι), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.iInter.{u2, u3} E ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u3} 𝕜 E] {f : ι -> (Set.{u3} E)}, (forall (i : ι), Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (Set.interᵢ.{u3, u1} E ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align balanced_Inter balanced_interᵢₓ'. -/
-theorem balanced_interᵢ {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋂ i, f i) :=
-  fun a ha => (smul_set_interᵢ_subset _ _).trans <| interᵢ_mono fun _ => h _ _ ha
-#align balanced_Inter balanced_interᵢ
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u3} 𝕜 E] {f : ι -> (Set.{u3} E)}, (forall (i : ι), Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (Set.iInter.{u3, u1} E ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align balanced_Inter balanced_iInterₓ'. -/
+theorem balanced_iInter {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋂ i, f i) :=
+  fun a ha => (smul_set_iInter_subset _ _).trans <| iInter_mono fun _ => h _ _ ha
+#align balanced_Inter balanced_iInter
 
-/- warning: balanced_Inter₂ -> balanced_interᵢ₂ is a dubious translation:
+/- warning: balanced_Inter₂ -> balanced_iInter₂ is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u2} E)}, (forall (i : ι) (j : κ i), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.interᵢ.{u2, u3} E ι (fun (i : ι) => Set.interᵢ.{u2, u4} E (κ i) (fun (j : κ i) => f i j))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u2} E)}, (forall (i : ι) (j : κ i), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.iInter.{u2, u3} E ι (fun (i : ι) => Set.iInter.{u2, u4} E (κ i) (fun (j : κ i) => f i j))))
 but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u4} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u4} E)}, (forall (i : ι) (j : κ i), Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (Set.interᵢ.{u4, u2} E ι (fun (i : ι) => Set.interᵢ.{u4, u1} E (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align balanced_Inter₂ balanced_interᵢ₂ₓ'. -/
+  forall {𝕜 : Type.{u3}} {E : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u4} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u4} E)}, (forall (i : ι) (j : κ i), Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (Set.iInter.{u4, u2} E ι (fun (i : ι) => Set.iInter.{u4, u1} E (κ i) (fun (j : κ i) => f i j))))
+Case conversion may be inaccurate. Consider using '#align balanced_Inter₂ balanced_iInter₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem balanced_interᵢ₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
+theorem balanced_iInter₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋂ (i) (j), f i j) :=
-  balanced_interᵢ fun _ => balanced_interᵢ <| h _
-#align balanced_Inter₂ balanced_interᵢ₂
+  balanced_iInter fun _ => balanced_iInter <| h _
+#align balanced_Inter₂ balanced_iInter₂
 
 variable [SMul 𝕝 E] [SMulCommClass 𝕜 𝕝 E]
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo, Bhavik Mehta, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.locally_convex.basic
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 9a48a083b390d9b84a71efbdc4e8dfa26a687104
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.NormedSpace.Basic
 /-!
 # Local convexity
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines absorbent and balanced sets.
 
 An absorbent set is one that "surrounds" the origin. The idea is made precise by requiring that any

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -56,32 +56,60 @@ section SMul
 
 variable (𝕜) [SMul 𝕜 E]
 
+#print Absorbs /-
 /-- A set `A` absorbs another set `B` if `B` is contained in all scalings of `A` by elements of
 sufficiently large norm. -/
 def Absorbs (A B : Set E) :=
   ∃ r, 0 < r ∧ ∀ a : 𝕜, r ≤ ‖a‖ → B ⊆ a • A
 #align absorbs Absorbs
+-/
 
 variable {𝕜} {s t u v A B : Set E}
 
+#print absorbs_empty /-
 @[simp]
 theorem absorbs_empty {s : Set E} : Absorbs 𝕜 s (∅ : Set E) :=
   ⟨1, one_pos, fun a ha => Set.empty_subset _⟩
 #align absorbs_empty absorbs_empty
+-/
 
+/- warning: absorbs.mono -> Absorbs.mono 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} {u : Set.{u2} E} {v : Set.{u2} E}, (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s u) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s t) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) v u) -> (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 t v)
+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} {u : Set.{u1} E} {v : Set.{u1} E}, (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s u) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s t) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) v u) -> (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 t v)
+Case conversion may be inaccurate. Consider using '#align absorbs.mono Absorbs.monoₓ'. -/
 theorem Absorbs.mono (hs : Absorbs 𝕜 s u) (hst : s ⊆ t) (hvu : v ⊆ u) : Absorbs 𝕜 t v :=
   let ⟨r, hr, h⟩ := hs
   ⟨r, hr, fun a ha => hvu.trans <| (h _ ha).trans <| smul_set_mono hst⟩
 #align absorbs.mono Absorbs.mono
 
+/- warning: absorbs.mono_left -> Absorbs.mono_left 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} {u : Set.{u2} E}, (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s u) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s t) -> (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 t u)
+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} {u : Set.{u1} E}, (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s u) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) s t) -> (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 t u)
+Case conversion may be inaccurate. Consider using '#align absorbs.mono_left Absorbs.mono_leftₓ'. -/
 theorem Absorbs.mono_left (hs : Absorbs 𝕜 s u) (h : s ⊆ t) : Absorbs 𝕜 t u :=
   hs.mono h Subset.rfl
 #align absorbs.mono_left Absorbs.mono_left
 
+/- warning: absorbs.mono_right -> Absorbs.mono_right 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} {u : Set.{u2} E} {v : Set.{u2} E}, (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s u) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) v u) -> (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s v)
+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} {u : Set.{u1} E} {v : Set.{u1} E}, (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s u) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) v u) -> (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s v)
+Case conversion may be inaccurate. Consider using '#align absorbs.mono_right Absorbs.mono_rightₓ'. -/
 theorem Absorbs.mono_right (hs : Absorbs 𝕜 s u) (h : v ⊆ u) : Absorbs 𝕜 s v :=
   hs.mono Subset.rfl h
 #align absorbs.mono_right Absorbs.mono_right
 
+/- warning: absorbs.union -> Absorbs.union 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} {u : Set.{u2} E} {v : Set.{u2} E}, (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s u) -> (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s v) -> (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) u v))
+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} {u : Set.{u1} E} {v : Set.{u1} E}, (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s u) -> (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s v) -> (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s (Union.union.{u1} (Set.{u1} E) (Set.instUnionSet.{u1} E) u v))
+Case conversion may be inaccurate. Consider using '#align absorbs.union Absorbs.unionₓ'. -/
 theorem Absorbs.union (hu : Absorbs 𝕜 s u) (hv : Absorbs 𝕜 s v) : Absorbs 𝕜 s (u ∪ v) :=
   by
   obtain ⟨a, ha, hu⟩ := hu
@@ -91,12 +119,19 @@ theorem Absorbs.union (hu : Absorbs 𝕜 s u) (hv : Absorbs 𝕜 s v) : Absorbs
       union_subset (hu _ <| le_of_max_le_left hc) (hv _ <| le_of_max_le_right hc)⟩
 #align absorbs.union Absorbs.union
 
+/- warning: absorbs_union -> absorbs_union 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} {u : Set.{u2} E} {v : Set.{u2} E}, Iff (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) u v)) (And (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s u) (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s v))
+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} {u : Set.{u1} E} {v : Set.{u1} E}, Iff (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s (Union.union.{u1} (Set.{u1} E) (Set.instUnionSet.{u1} E) u v)) (And (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s u) (Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s v))
+Case conversion may be inaccurate. Consider using '#align absorbs_union absorbs_unionₓ'. -/
 @[simp]
 theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorbs 𝕜 s v :=
   ⟨fun h => ⟨h.mono_right <| subset_union_left _ _, h.mono_right <| subset_union_right _ _⟩,
     fun h => h.1.union h.2⟩
 #align absorbs_union absorbs_union
 
+#print absorbs_unionᵢ_finset /-
 theorem absorbs_unionᵢ_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
     Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   classical
@@ -112,7 +147,9 @@ theorem absorbs_unionᵢ_finset {ι : Type _} {t : Finset ι} {f : ι → Set E}
         exact h.1
     exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
 #align absorbs_Union_finset absorbs_unionᵢ_finset
+-/
 
+#print Set.Finite.absorbs_unionᵢ /-
 theorem Set.Finite.absorbs_unionᵢ {ι : Type _} {s : Set E} {t : Set ι} {f : ι → Set E}
     (hi : t.Finite) : Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) :=
   by
@@ -120,30 +157,57 @@ theorem Set.Finite.absorbs_unionᵢ {ι : Type _} {s : Set E} {t : Set ι} {f :
   simp only [Finset.mem_coe]
   exact absorbs_unionᵢ_finset
 #align set.finite.absorbs_Union Set.Finite.absorbs_unionᵢ
+-/
 
 variable (𝕜)
 
+#print Absorbent /-
 /-- A set is absorbent if it absorbs every singleton. -/
 def Absorbent (A : Set E) :=
   ∀ x, ∃ r, 0 < r ∧ ∀ a : 𝕜, r ≤ ‖a‖ → x ∈ a • A
 #align absorbent Absorbent
+-/
 
 variable {𝕜}
 
+/- warning: absorbent.subset -> Absorbent.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] {A : Set.{u2} E} {B : Set.{u2} E}, (Absorbent.{u1, u2} 𝕜 E _inst_1 _inst_2 A) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) A B) -> (Absorbent.{u1, u2} 𝕜 E _inst_1 _inst_2 B)
+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] {A : Set.{u1} E} {B : Set.{u1} E}, (Absorbent.{u2, u1} 𝕜 E _inst_1 _inst_2 A) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) A B) -> (Absorbent.{u2, u1} 𝕜 E _inst_1 _inst_2 B)
+Case conversion may be inaccurate. Consider using '#align absorbent.subset Absorbent.subsetₓ'. -/
 theorem Absorbent.subset (hA : Absorbent 𝕜 A) (hAB : A ⊆ B) : Absorbent 𝕜 B :=
   by
   refine' forall_imp (fun x => _) hA
   exact Exists.imp fun r => And.imp_right <| forall₂_imp fun a ha hx => Set.smul_set_mono hAB hx
 #align absorbent.subset Absorbent.subset
 
+/- warning: absorbent_iff_forall_absorbs_singleton -> absorbent_iff_forall_absorbs_singleton 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] {A : Set.{u2} E}, Iff (Absorbent.{u1, u2} 𝕜 E _inst_1 _inst_2 A) (forall (x : E), Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 A (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x))
+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] {A : Set.{u1} E}, Iff (Absorbent.{u2, u1} 𝕜 E _inst_1 _inst_2 A) (forall (x : E), Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 A (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x))
+Case conversion may be inaccurate. Consider using '#align absorbent_iff_forall_absorbs_singleton absorbent_iff_forall_absorbs_singletonₓ'. -/
 theorem absorbent_iff_forall_absorbs_singleton : Absorbent 𝕜 A ↔ ∀ x, Absorbs 𝕜 A {x} := by
   simp_rw [Absorbs, Absorbent, singleton_subset_iff]
 #align absorbent_iff_forall_absorbs_singleton absorbent_iff_forall_absorbs_singleton
 
+/- warning: absorbent.absorbs -> Absorbent.absorbs 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}, (Absorbent.{u1, u2} 𝕜 E _inst_1 _inst_2 s) -> (forall {x : E}, Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 s (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x))
+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}, (Absorbent.{u2, u1} 𝕜 E _inst_1 _inst_2 s) -> (forall {x : E}, Absorbs.{u2, u1} 𝕜 E _inst_1 _inst_2 s (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x))
+Case conversion may be inaccurate. Consider using '#align absorbent.absorbs Absorbent.absorbsₓ'. -/
 theorem Absorbent.absorbs (hs : Absorbent 𝕜 s) {x : E} : Absorbs 𝕜 s {x} :=
   absorbent_iff_forall_absorbs_singleton.1 hs _
 #align absorbent.absorbs Absorbent.absorbs
 
+/- warning: absorbent_iff_nonneg_lt -> absorbent_iff_nonneg_lt 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] {A : Set.{u2} E}, Iff (Absorbent.{u1, u2} 𝕜 E _inst_1 _inst_2 A) (forall (x : E), Exists.{1} Real (fun (r : Real) => And (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) (forall {{a : 𝕜}}, (LT.lt.{0} Real Real.hasLt r (Norm.norm.{u1} 𝕜 (SeminormedRing.toHasNorm.{u1} 𝕜 _inst_1) a)) -> (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) a A)))))
+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] {A : Set.{u1} E}, Iff (Absorbent.{u2, u1} 𝕜 E _inst_1 _inst_2 A) (forall (x : E), Exists.{1} Real (fun (r : Real) => And (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) (forall {{a : 𝕜}}, (LT.lt.{0} Real Real.instLTReal r (Norm.norm.{u2} 𝕜 (SeminormedRing.toNorm.{u2} 𝕜 _inst_1) a)) -> (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E _inst_2)) a A)))))
+Case conversion may be inaccurate. Consider using '#align absorbent_iff_nonneg_lt absorbent_iff_nonneg_ltₓ'. -/
 theorem absorbent_iff_nonneg_lt :
     Absorbent 𝕜 A ↔ ∀ x, ∃ r, 0 ≤ r ∧ ∀ ⦃a : 𝕜⦄, r < ‖a‖ → x ∈ a • A :=
   forall_congr' fun x =>
@@ -152,66 +216,136 @@ theorem absorbent_iff_nonneg_lt :
         hx ((lt_add_of_pos_right r zero_lt_one).trans_le ha)⟩⟩
 #align absorbent_iff_nonneg_lt absorbent_iff_nonneg_lt
 
+#print Absorbent.absorbs_finite /-
 theorem Absorbent.absorbs_finite {s : Set E} (hs : Absorbent 𝕜 s) {v : Set E} (hv : v.Finite) :
     Absorbs 𝕜 s v := by
   rw [← Set.bunionᵢ_of_singleton v]
   exact hv.absorbs_Union.mpr fun _ _ => hs.absorbs
 #align absorbent.absorbs_finite Absorbent.absorbs_finite
+-/
 
 variable (𝕜)
 
+#print Balanced /-
 /-- A set `A` is balanced if `a • A` is contained in `A` whenever `a` has norm at most `1`. -/
 def Balanced (A : Set E) :=
   ∀ a : 𝕜, ‖a‖ ≤ 1 → a • A ⊆ A
 #align balanced Balanced
+-/
 
 variable {𝕜}
 
+/- warning: balanced_iff_smul_mem -> balanced_iff_smul_mem 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}, Iff (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 s) (forall {{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)))) -> (forall {{x : E}}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (SMul.smul.{u1, u2} 𝕜 E _inst_2 a x) s)))
+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}, Iff (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 s) (forall {{a : 𝕜}}, (LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} 𝕜 (SeminormedRing.toNorm.{u2} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall {{x : E}}, (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s) -> (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E _inst_2) a x) s)))
+Case conversion may be inaccurate. Consider using '#align balanced_iff_smul_mem balanced_iff_smul_memₓ'. -/
 theorem balanced_iff_smul_mem : Balanced 𝕜 s ↔ ∀ ⦃a : 𝕜⦄, ‖a‖ ≤ 1 → ∀ ⦃x : E⦄, x ∈ s → a • x ∈ s :=
   forall₂_congr fun a ha => smul_set_subset_iff
 #align balanced_iff_smul_mem balanced_iff_smul_mem
 
+/- warning: balanced.smul_mem -> Balanced.smul_mem 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}, (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 s) -> (forall {{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)))) -> (forall {{x : E}}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (SMul.smul.{u1, u2} 𝕜 E _inst_2 a x) s)))
+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}, (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 s) -> (forall {{a : 𝕜}}, (LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} 𝕜 (SeminormedRing.toNorm.{u2} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (forall {{x : E}}, (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s) -> (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E _inst_2) a x) s)))
+Case conversion may be inaccurate. Consider using '#align balanced.smul_mem Balanced.smul_memₓ'. -/
 alias balanced_iff_smul_mem ↔ Balanced.smul_mem _
 #align balanced.smul_mem Balanced.smul_mem
 
+/- warning: balanced_empty -> balanced_empty 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], Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (EmptyCollection.emptyCollection.{u2} (Set.{u2} E) (Set.hasEmptyc.{u2} E))
+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], Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))
+Case conversion may be inaccurate. Consider using '#align balanced_empty balanced_emptyₓ'. -/
 @[simp]
 theorem balanced_empty : Balanced 𝕜 (∅ : Set E) := fun _ _ => by rw [smul_set_empty]
 #align balanced_empty balanced_empty
 
+/- warning: balanced_univ -> balanced_univ 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], Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.univ.{u2} E)
+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], Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 (Set.univ.{u1} E)
+Case conversion may be inaccurate. Consider using '#align balanced_univ balanced_univₓ'. -/
 @[simp]
 theorem balanced_univ : Balanced 𝕜 (univ : Set E) := fun a ha => subset_univ _
 #align balanced_univ balanced_univ
 
+/- warning: balanced.union -> Balanced.union 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] {A : Set.{u2} E} {B : Set.{u2} E}, (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 A) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 B) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) A B))
+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] {A : Set.{u1} E} {B : Set.{u1} E}, (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 A) -> (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 B) -> (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 (Union.union.{u1} (Set.{u1} E) (Set.instUnionSet.{u1} E) A B))
+Case conversion may be inaccurate. Consider using '#align balanced.union Balanced.unionₓ'. -/
 theorem Balanced.union (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced 𝕜 (A ∪ B) := fun a ha =>
   smul_set_union.Subset.trans <| union_subset_union (hA _ ha) <| hB _ ha
 #align balanced.union Balanced.union
 
+/- warning: balanced.inter -> Balanced.inter 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] {A : Set.{u2} E} {B : Set.{u2} E}, (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 A) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 B) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) A B))
+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] {A : Set.{u1} E} {B : Set.{u1} E}, (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 A) -> (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 B) -> (Balanced.{u2, u1} 𝕜 E _inst_1 _inst_2 (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) A B))
+Case conversion may be inaccurate. Consider using '#align balanced.inter Balanced.interₓ'. -/
 theorem Balanced.inter (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced 𝕜 (A ∩ B) := fun a ha =>
   smul_set_inter_subset.trans <| inter_subset_inter (hA _ ha) <| hB _ ha
 #align balanced.inter Balanced.inter
 
+/- warning: balanced_Union -> balanced_unionᵢ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : ι -> (Set.{u2} E)}, (forall (i : ι), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.unionᵢ.{u2, u3} E ι (fun (i : ι) => f i)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u3} 𝕜 E] {f : ι -> (Set.{u3} E)}, (forall (i : ι), Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (Set.unionᵢ.{u3, u1} E ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align balanced_Union balanced_unionᵢₓ'. -/
 theorem balanced_unionᵢ {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋃ i, f i) :=
   fun a ha => (smul_set_Union _ _).Subset.trans <| unionᵢ_mono fun _ => h _ _ ha
 #align balanced_Union balanced_unionᵢ
 
+/- warning: balanced_Union₂ -> balanced_unionᵢ₂ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u2} E)}, (forall (i : ι) (j : κ i), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.unionᵢ.{u2, u3} E ι (fun (i : ι) => Set.unionᵢ.{u2, u4} E (κ i) (fun (j : κ i) => f i j))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u4} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u4} E)}, (forall (i : ι) (j : κ i), Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (Set.unionᵢ.{u4, u2} E ι (fun (i : ι) => Set.unionᵢ.{u4, u1} E (κ i) (fun (j : κ i) => f i j))))
+Case conversion may be inaccurate. Consider using '#align balanced_Union₂ balanced_unionᵢ₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem balanced_Union₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
+theorem balanced_unionᵢ₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋃ (i) (j), f i j) :=
   balanced_unionᵢ fun _ => balanced_unionᵢ <| h _
-#align balanced_Union₂ balanced_Union₂
-
+#align balanced_Union₂ balanced_unionᵢ₂
+
+/- warning: balanced_Inter -> balanced_interᵢ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : ι -> (Set.{u2} E)}, (forall (i : ι), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.interᵢ.{u2, u3} E ι (fun (i : ι) => f i)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : SeminormedRing.{u2} 𝕜] [_inst_2 : SMul.{u2, u3} 𝕜 E] {f : ι -> (Set.{u3} E)}, (forall (i : ι), Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (f i)) -> (Balanced.{u2, u3} 𝕜 E _inst_1 _inst_2 (Set.interᵢ.{u3, u1} E ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align balanced_Inter balanced_interᵢₓ'. -/
 theorem balanced_interᵢ {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋂ i, f i) :=
   fun a ha => (smul_set_interᵢ_subset _ _).trans <| interᵢ_mono fun _ => h _ _ ha
 #align balanced_Inter balanced_interᵢ
 
+/- warning: balanced_Inter₂ -> balanced_interᵢ₂ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u2} E)}, (forall (i : ι) (j : κ i), Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u1, u2} 𝕜 E _inst_1 _inst_2 (Set.interᵢ.{u2, u3} E ι (fun (i : ι) => Set.interᵢ.{u2, u4} E (κ i) (fun (j : κ i) => f i j))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u4} 𝕜 E] {f : forall (i : ι), (κ i) -> (Set.{u4} E)}, (forall (i : ι) (j : κ i), Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (f i j)) -> (Balanced.{u3, u4} 𝕜 E _inst_1 _inst_2 (Set.interᵢ.{u4, u2} E ι (fun (i : ι) => Set.interᵢ.{u4, u1} E (κ i) (fun (j : κ i) => f i j))))
+Case conversion may be inaccurate. Consider using '#align balanced_Inter₂ balanced_interᵢ₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem balanced_Inter₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
+theorem balanced_interᵢ₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋂ (i) (j), f i j) :=
   balanced_interᵢ fun _ => balanced_interᵢ <| h _
-#align balanced_Inter₂ balanced_Inter₂
+#align balanced_Inter₂ balanced_interᵢ₂
 
 variable [SMul 𝕝 E] [SMulCommClass 𝕜 𝕝 E]
 
+/- warning: balanced.smul -> Balanced.smul is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕝 : Type.{u2}} {E : Type.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u3} 𝕜 E] {s : Set.{u3} E} [_inst_3 : SMul.{u2, u3} 𝕝 E] [_inst_4 : SMulCommClass.{u1, u2, u3} 𝕜 𝕝 E _inst_2 _inst_3] (a : 𝕝), (Balanced.{u1, u3} 𝕜 E _inst_1 _inst_2 s) -> (Balanced.{u1, u3} 𝕜 E _inst_1 _inst_2 (SMul.smul.{u2, u3} 𝕝 (Set.{u3} E) (Set.smulSet.{u2, u3} 𝕝 E _inst_3) a s))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {𝕝 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u3} 𝕜] [_inst_2 : SMul.{u3, u2} 𝕜 E] {s : Set.{u2} E} [_inst_3 : SMul.{u1, u2} 𝕝 E] [_inst_4 : SMulCommClass.{u3, u1, u2} 𝕜 𝕝 E _inst_2 _inst_3] (a : 𝕝), (Balanced.{u3, u2} 𝕜 E _inst_1 _inst_2 s) -> (Balanced.{u3, u2} 𝕜 E _inst_1 _inst_2 (HSMul.hSMul.{u1, u2, u2} 𝕝 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u1, u2} 𝕝 (Set.{u2} E) (Set.smulSet.{u1, u2} 𝕝 E _inst_3)) a s))
+Case conversion may be inaccurate. Consider using '#align balanced.smul Balanced.smulₓ'. -/
 theorem Balanced.smul (a : 𝕝) (hs : Balanced 𝕜 s) : Balanced 𝕜 (a • s) := fun b hb =>
   (smul_comm _ _ _).Subset.trans <| smul_set_mono <| hs _ hb
 #align balanced.smul Balanced.smul
@@ -222,15 +356,33 @@ section Module
 
 variable [AddCommGroup E] [Module 𝕜 E] {s s₁ s₂ t t₁ t₂ : Set E}
 
+/- warning: absorbs.neg -> Absorbs.neg 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} {t : Set.{u2} E}, (Absorbs.{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 t) -> (Absorbs.{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)))) (Neg.neg.{u2} (Set.{u2} E) (Set.neg.{u2} E (SubNegMonoid.toHasNeg.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) s) (Neg.neg.{u2} (Set.{u2} E) (Set.neg.{u2} E (SubNegMonoid.toHasNeg.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) t))
+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)] {s : Set.{u1} E} {t : Set.{u1} E}, (Absorbs.{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 t) -> (Absorbs.{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)))) (Neg.neg.{u1} (Set.{u1} E) (Set.neg.{u1} E (NegZeroClass.toNeg.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2)))))) s) (Neg.neg.{u1} (Set.{u1} E) (Set.neg.{u1} E (NegZeroClass.toNeg.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2)))))) t))
+Case conversion may be inaccurate. Consider using '#align absorbs.neg Absorbs.negₓ'. -/
 theorem Absorbs.neg : Absorbs 𝕜 s t → Absorbs 𝕜 (-s) (-t) :=
   Exists.imp fun r =>
     And.imp_right <| forall₂_imp fun _ _ h => (neg_subset_neg.2 h).trans (smul_set_neg _ _).Superset
 #align absorbs.neg Absorbs.neg
 
+/- warning: balanced.neg -> Balanced.neg 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}, (Balanced.{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) -> (Balanced.{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)))) (Neg.neg.{u2} (Set.{u2} E) (Set.neg.{u2} E (SubNegMonoid.toHasNeg.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) 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)] {s : Set.{u1} E}, (Balanced.{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) -> (Balanced.{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)))) (Neg.neg.{u1} (Set.{u1} E) (Set.neg.{u1} E (NegZeroClass.toNeg.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2)))))) s))
+Case conversion may be inaccurate. Consider using '#align balanced.neg Balanced.negₓ'. -/
 theorem Balanced.neg : Balanced 𝕜 s → Balanced 𝕜 (-s) :=
   forall₂_imp fun _ _ h => (smul_set_neg _ _).Subset.trans <| neg_subset_neg.2 h
 #align balanced.neg Balanced.neg
 
+/- warning: absorbs.add -> Absorbs.add 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)] {s₁ : Set.{u2} E} {s₂ : Set.{u2} E} {t₁ : Set.{u2} E} {t₂ : Set.{u2} E}, (Absorbs.{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)))) s₁ t₁) -> (Absorbs.{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)))) s₂ t₂) -> (Absorbs.{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)))) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHAdd.{u2} (Set.{u2} E) (Set.add.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))))) s₁ s₂) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHAdd.{u2} (Set.{u2} E) (Set.add.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))))) t₁ t₂))
+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)] {s₁ : Set.{u1} E} {s₂ : Set.{u1} E} {t₁ : Set.{u1} E} {t₂ : Set.{u1} E}, (Absorbs.{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)))) s₁ t₁) -> (Absorbs.{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)))) s₂ t₂) -> (Absorbs.{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)))) (HAdd.hAdd.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHAdd.{u1} (Set.{u1} E) (Set.add.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))))) s₁ s₂) (HAdd.hAdd.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHAdd.{u1} (Set.{u1} E) (Set.add.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))))) t₁ t₂))
+Case conversion may be inaccurate. Consider using '#align absorbs.add Absorbs.addₓ'. -/
 theorem Absorbs.add : Absorbs 𝕜 s₁ t₁ → Absorbs 𝕜 s₂ t₂ → Absorbs 𝕜 (s₁ + s₂) (t₁ + t₂) :=
   fun ⟨r₁, hr₁, h₁⟩ ⟨r₂, hr₂, h₂⟩ =>
   ⟨max r₁ r₂, lt_max_of_lt_left hr₁, fun a ha =>
@@ -238,22 +390,46 @@ theorem Absorbs.add : Absorbs 𝕜 s₁ t₁ → Absorbs 𝕜 s₂ t₂ → Abso
       (smul_add _ _ _).Superset⟩
 #align absorbs.add Absorbs.add
 
+/- warning: balanced.add -> Balanced.add 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} {t : Set.{u2} E}, (Balanced.{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) -> (Balanced.{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)))) t) -> (Balanced.{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)))) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHAdd.{u2} (Set.{u2} E) (Set.add.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))))) s t))
+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)] {s : Set.{u1} E} {t : Set.{u1} E}, (Balanced.{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) -> (Balanced.{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)))) t) -> (Balanced.{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)))) (HAdd.hAdd.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHAdd.{u1} (Set.{u1} E) (Set.add.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))))) s t))
+Case conversion may be inaccurate. Consider using '#align balanced.add Balanced.addₓ'. -/
 theorem Balanced.add (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s + t) := fun a ha =>
   (smul_add _ _ _).Subset.trans <| add_subset_add (hs _ ha) <| ht _ ha
 #align balanced.add Balanced.add
 
+/- warning: absorbs.sub -> Absorbs.sub 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)] {s₁ : Set.{u2} E} {s₂ : Set.{u2} E} {t₁ : Set.{u2} E} {t₂ : Set.{u2} E}, (Absorbs.{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)))) s₁ t₁) -> (Absorbs.{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)))) s₂ t₂) -> (Absorbs.{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)))) (HSub.hSub.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHSub.{u2} (Set.{u2} E) (Set.sub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) s₁ s₂) (HSub.hSub.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHSub.{u2} (Set.{u2} E) (Set.sub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) t₁ t₂))
+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)] {s₁ : Set.{u1} E} {s₂ : Set.{u1} E} {t₁ : Set.{u1} E} {t₂ : Set.{u1} E}, (Absorbs.{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)))) s₁ t₁) -> (Absorbs.{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)))) s₂ t₂) -> (Absorbs.{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)))) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))) s₁ s₂) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))) t₁ t₂))
+Case conversion may be inaccurate. Consider using '#align absorbs.sub Absorbs.subₓ'. -/
 theorem Absorbs.sub (h₁ : Absorbs 𝕜 s₁ t₁) (h₂ : Absorbs 𝕜 s₂ t₂) : Absorbs 𝕜 (s₁ - s₂) (t₁ - t₂) :=
   by
   simp_rw [sub_eq_add_neg]
   exact h₁.add h₂.neg
 #align absorbs.sub Absorbs.sub
 
+/- warning: balanced.sub -> Balanced.sub 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} {t : Set.{u2} E}, (Balanced.{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) -> (Balanced.{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)))) t) -> (Balanced.{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)))) (HSub.hSub.{u2, u2, u2} (Set.{u2} E) (Set.{u2} E) (Set.{u2} E) (instHSub.{u2} (Set.{u2} E) (Set.sub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) s t))
+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)] {s : Set.{u1} E} {t : Set.{u1} E}, (Balanced.{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) -> (Balanced.{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)))) t) -> (Balanced.{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)))) (HSub.hSub.{u1, u1, u1} (Set.{u1} E) (Set.{u1} E) (Set.{u1} E) (instHSub.{u1} (Set.{u1} E) (Set.sub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2))))) s t))
+Case conversion may be inaccurate. Consider using '#align balanced.sub Balanced.subₓ'. -/
 theorem Balanced.sub (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s - t) :=
   by
   simp_rw [sub_eq_add_neg]
   exact hs.add ht.neg
 #align balanced.sub Balanced.sub
 
+/- warning: balanced_zero -> balanced_zero 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)], Balanced.{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)))) (OfNat.ofNat.{u2} (Set.{u2} E) 0 (OfNat.mk.{u2} (Set.{u2} E) 0 (Zero.zero.{u2} (Set.{u2} E) (Set.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.{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)], Balanced.{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)))) (OfNat.ofNat.{u1} (Set.{u1} E) 0 (Zero.toOfNat0.{u1} (Set.{u1} E) (Set.zero.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align balanced_zero balanced_zeroₓ'. -/
 theorem balanced_zero : Balanced 𝕜 (0 : Set E) := fun a ha => (smul_zero _).Subset
 #align balanced_zero balanced_zero
 
@@ -266,6 +442,12 @@ section NormedField
 variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGroup E] [Module 𝕜 E]
   [SMulWithZero 𝕝 E] [IsScalarTower 𝕜 𝕝 E] {s t u v A B : Set E} {x : E} {a b : 𝕜}
 
+/- warning: balanced.smul_mono -> Balanced.smul_mono is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {𝕝 : Type.{u2}} {E : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedRing.{u2} 𝕝] [_inst_3 : NormedSpace.{u1, u2} 𝕜 𝕝 _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2)))] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)] [_inst_6 : SMulWithZero.{u2, u3} 𝕝 E (MulZeroClass.toHasZero.{u2} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕝 (Ring.toNonAssocRing.{u2} 𝕝 (NormedRing.toRing.{u2} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4)))))] [_inst_7 : IsScalarTower.{u1, u2, u3} 𝕜 𝕝 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 𝕝 (AddZeroClass.toHasZero.{u2} 𝕝 (AddMonoid.toAddZeroClass.{u2} 𝕝 (AddCommMonoid.toAddMonoid.{u2} 𝕝 (AddCommGroup.toAddCommMonoid.{u2} 𝕝 (SeminormedAddCommGroup.toAddCommGroup.{u2} 𝕝 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 𝕝 (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} 𝕝 (AddMonoid.toAddZeroClass.{u2} 𝕝 (AddCommMonoid.toAddMonoid.{u2} 𝕝 (AddCommGroup.toAddCommMonoid.{u2} 𝕝 (SeminormedAddCommGroup.toAddCommGroup.{u2} 𝕝 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 𝕝 (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} 𝕝 (AddMonoid.toAddZeroClass.{u2} 𝕝 (AddCommMonoid.toAddMonoid.{u2} 𝕝 (AddCommGroup.toAddCommMonoid.{u2} 𝕝 (SeminormedAddCommGroup.toAddCommGroup.{u2} 𝕝 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 𝕝 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕝 (SeminormedAddCommGroup.toAddCommGroup.{u2} 𝕝 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2))))) (NormedSpace.toModule.{u1, u2} 𝕜 𝕝 _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕝 (NormedRing.toNonUnitalNormedRing.{u2} 𝕝 _inst_2))) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕝 E (MulZeroClass.toHasZero.{u2} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕝 (Ring.toNonAssocRing.{u2} 𝕝 (NormedRing.toRing.{u2} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) _inst_6)) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))] {s : Set.{u3} E}, (Balanced.{u2, u3} 𝕝 E (NormedRing.toSeminormedRing.{u2} 𝕝 _inst_2) (SMulZeroClass.toHasSmul.{u2, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕝 E (MulZeroClass.toHasZero.{u2} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕝 (Ring.toNonAssocRing.{u2} 𝕝 (NormedRing.toRing.{u2} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) _inst_6)) s) -> (forall {a : 𝕝} {b : 𝕜}, (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} 𝕝 (NormedRing.toHasNorm.{u2} 𝕝 _inst_2) a) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) b)) -> (HasSubset.Subset.{u3} (Set.{u3} E) (Set.hasSubset.{u3} E) (SMul.smul.{u2, u3} 𝕝 (Set.{u3} E) (Set.smulSet.{u2, u3} 𝕝 E (SMulZeroClass.toHasSmul.{u2, u3} 𝕝 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u2, u3} 𝕝 E (MulZeroClass.toHasZero.{u2} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕝 (Ring.toNonAssocRing.{u2} 𝕝 (NormedRing.toRing.{u2} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) _inst_6))) a s) (SMul.smul.{u1, u3} 𝕜 (Set.{u3} E) (Set.smulSet.{u1, u3} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 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.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) b s)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {𝕝 : Type.{u3}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : NormedRing.{u3} 𝕝] [_inst_3 : NormedSpace.{u1, u3} 𝕜 𝕝 _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u3} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u3} 𝕝 (NormedRing.toNonUnitalNormedRing.{u3} 𝕝 _inst_2)))] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] [_inst_6 : SMulWithZero.{u3, u2} 𝕝 E (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4)))))] [_inst_7 : IsScalarTower.{u1, u3, u2} 𝕜 𝕝 E (SMulZeroClass.toSMul.{u1, u3} 𝕜 𝕝 (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 𝕝 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 𝕝 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 𝕝 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2))))) (NormedSpace.toModule.{u1, u3} 𝕜 𝕝 _inst_1 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u3} 𝕝 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u3} 𝕝 (NormedRing.toNonUnitalNormedRing.{u3} 𝕝 _inst_2))) _inst_3))))) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) _inst_6)) (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5))))] {s : Set.{u2} E}, (Balanced.{u3, u2} 𝕝 E (NormedRing.toSeminormedRing.{u3} 𝕝 _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) _inst_6)) s) -> (forall {a : 𝕝} {b : 𝕜}, (LE.le.{0} Real Real.instLEReal (Norm.norm.{u3} 𝕝 (NormedRing.toNorm.{u3} 𝕝 _inst_2) a) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) b)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (HSMul.hSMul.{u3, u2, u2} 𝕝 (Set.{u2} E) (Set.{u2} E) (instHSMul.{u3, u2} 𝕝 (Set.{u2} E) (Set.smulSet.{u3, u2} 𝕝 E (SMulZeroClass.toSMul.{u3, u2} 𝕝 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕝 E (MonoidWithZero.toZero.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 _inst_2)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_4))))) _inst_6)))) a s) (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))))) b s)))
+Case conversion may be inaccurate. Consider using '#align balanced.smul_mono Balanced.smul_monoₓ'. -/
 /-- Scalar multiplication (by possibly different types) of a balanced set is monotone. -/
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s :=
   by
@@ -283,6 +465,12 @@ theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖
   exact div_le_one_of_le h (norm_nonneg _)
 #align balanced.smul_mono Balanced.smul_mono
 
+/- warning: balanced.absorbs_self -> Balanced.absorbs_self is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E}, (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A A)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {A : Set.{u1} E}, (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A A)
+Case conversion may be inaccurate. Consider using '#align balanced.absorbs_self Balanced.absorbs_selfₓ'. -/
 /-- A balanced set absorbs itself. -/
 theorem Balanced.absorbs_self (hA : Balanced 𝕜 A) : Absorbs 𝕜 A A :=
   by
@@ -293,6 +481,12 @@ theorem Balanced.absorbs_self (hA : Balanced 𝕜 A) : Absorbs 𝕜 A A :=
   exact inv_le_one ha
 #align balanced.absorbs_self Balanced.absorbs_self
 
+/- warning: balanced.subset_smul -> Balanced.subset_smul is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} {a : 𝕜}, (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (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) a)) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) A (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5))))) a A))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {A : Set.{u1} E} {a : 𝕜}, (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) a)) -> (HasSubset.Subset.{u1} (Set.{u1} E) (Set.instHasSubsetSet.{u1} E) A (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))))) a A))
+Case conversion may be inaccurate. Consider using '#align balanced.subset_smul Balanced.subset_smulₓ'. -/
 theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆ a • A :=
   by
   refine' (subset_set_smul_iff₀ _).2 (hA a⁻¹ _)
@@ -303,10 +497,22 @@ theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆
     exact inv_le_one ha
 #align balanced.subset_smul Balanced.subset_smul
 
+/- warning: balanced.smul_eq -> Balanced.smul_eq is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} {a : 𝕜}, (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (Eq.{1} Real (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)))) -> (Eq.{succ u2} (Set.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5))))) a A) A)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {A : Set.{u1} E} {a : 𝕜}, (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (Eq.{1} Real (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) a) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) -> (Eq.{succ u1} (Set.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 (Set.{u1} E) (Set.{u1} E) (instHSMul.{u2, u1} 𝕜 (Set.{u1} E) (Set.smulSet.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))))) a A) A)
+Case conversion may be inaccurate. Consider using '#align balanced.smul_eq Balanced.smul_eqₓ'. -/
 theorem Balanced.smul_eq (hA : Balanced 𝕜 A) (ha : ‖a‖ = 1) : a • A = A :=
   (hA _ ha.le).antisymm <| hA.subset_smul ha.ge
 #align balanced.smul_eq Balanced.smul_eq
 
+/- warning: balanced.mem_smul_iff -> Balanced.mem_smul_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {s : Set.{u2} E} {x : E} {a : 𝕜} {b : 𝕜}, (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) s) -> (Eq.{1} Real (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) a) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) b)) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) a x) s) (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) b x) s))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {s : Set.{u1} E} {x : E} {a : 𝕜} {b : 𝕜}, (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) s) -> (Eq.{1} Real (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) a) (Norm.norm.{u2} 𝕜 (NormedField.toNorm.{u2} 𝕜 _inst_1) b)) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) a x) s) (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) b x) s))
+Case conversion may be inaccurate. Consider using '#align balanced.mem_smul_iff Balanced.mem_smul_iffₓ'. -/
 theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s :=
   by
   obtain rfl | hb := eq_or_ne b 0
@@ -320,10 +526,22 @@ theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a
       simp [← h, ha]
 #align balanced.mem_smul_iff Balanced.mem_smul_iff
 
+/- warning: balanced.neg_mem_iff -> Balanced.neg_mem_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {s : Set.{u2} E} {x : E}, (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) s) -> (Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (Neg.neg.{u2} E (SubNegMonoid.toHasNeg.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_4))) x) s) (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {s : Set.{u1} E} {x : E}, (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) s) -> (Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (Neg.neg.{u1} E (NegZeroClass.toNeg.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) x) s) (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s))
+Case conversion may be inaccurate. Consider using '#align balanced.neg_mem_iff Balanced.neg_mem_iffₓ'. -/
 theorem Balanced.neg_mem_iff (hs : Balanced 𝕜 s) : -x ∈ s ↔ x ∈ s := by
   convert hs.mem_smul_iff (norm_neg 1) <;> simp only [neg_smul, one_smul]
 #align balanced.neg_mem_iff Balanced.neg_mem_iff
 
+/- warning: absorbs.inter -> Absorbs.inter is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {s : Set.{u2} E} {t : Set.{u2} E} {u : Set.{u2} E}, (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) s u) -> (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) t u) -> (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) u)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {s : Set.{u1} E} {t : Set.{u1} E} {u : Set.{u1} E}, (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) s u) -> (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) t u) -> (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t) u)
+Case conversion may be inaccurate. Consider using '#align absorbs.inter Absorbs.interₓ'. -/
 theorem Absorbs.inter (hs : Absorbs 𝕜 s u) (ht : Absorbs 𝕜 t u) : Absorbs 𝕜 (s ∩ t) u :=
   by
   obtain ⟨a, ha, hs⟩ := hs
@@ -334,12 +552,24 @@ theorem Absorbs.inter (hs : Absorbs 𝕜 s u) (ht : Absorbs 𝕜 t u) : Absorbs
   exact subset_inter (hs _ <| le_of_max_le_left hc) (ht _ <| le_of_max_le_right hc)
 #align absorbs.inter Absorbs.inter
 
+/- warning: absorbs_inter -> absorbs_inter is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {s : Set.{u2} E} {t : Set.{u2} E} {u : Set.{u2} E}, Iff (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (Inter.inter.{u2} (Set.{u2} E) (Set.hasInter.{u2} E) s t) u) (And (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) s u) (Absorbs.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) t u))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {s : Set.{u1} E} {t : Set.{u1} E} {u : Set.{u1} E}, Iff (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (Inter.inter.{u1} (Set.{u1} E) (Set.instInterSet.{u1} E) s t) u) (And (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) s u) (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) t u))
+Case conversion may be inaccurate. Consider using '#align absorbs_inter absorbs_interₓ'. -/
 @[simp]
 theorem absorbs_inter : Absorbs 𝕜 (s ∩ t) u ↔ Absorbs 𝕜 s u ∧ Absorbs 𝕜 t u :=
   ⟨fun h => ⟨h.mono_left <| inter_subset_left _ _, h.mono_left <| inter_subset_right _ _⟩, fun h =>
     h.1.inter h.2⟩
 #align absorbs_inter absorbs_inter
 
+/- warning: absorbent_univ -> absorbent_univ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)], Absorbent.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (Set.univ.{u2} E)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)], Absorbent.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (Set.univ.{u1} E)
+Case conversion may be inaccurate. Consider using '#align absorbent_univ absorbent_univₓ'. -/
 theorem absorbent_univ : Absorbent 𝕜 (univ : Set E) :=
   by
   refine' fun x => ⟨1, zero_lt_one, fun a ha => _⟩
@@ -349,6 +579,12 @@ theorem absorbent_univ : Absorbent 𝕜 (univ : Set E) :=
 
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
+/- warning: absorbent_nhds_zero -> absorbent_nhds_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : 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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (Membership.Mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (Filter.hasMem.{u2} E) A (nhds.{u2} E _inst_8 (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_4)))))))))) -> (Absorbent.{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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : 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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (Membership.mem.{u2, u2} (Set.{u2} E) (Filter.{u2} E) (instMembershipSetFilter.{u2} E) A (nhds.{u2} E _inst_8 (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_4))))))))) -> (Absorbent.{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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) A)
+Case conversion may be inaccurate. Consider using '#align absorbent_nhds_zero absorbent_nhds_zeroₓ'. -/
 /-- Every neighbourhood of the origin is absorbent. -/
 theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
   by
@@ -368,6 +604,12 @@ theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
     
 #align absorbent_nhds_zero absorbent_nhds_zero
 
+/- warning: balanced_zero_union_interior -> balanced_zero_union_interior is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : 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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) (OfNat.ofNat.{u2} (Set.{u2} E) 0 (OfNat.mk.{u2} (Set.{u2} E) 0 (Zero.zero.{u2} (Set.{u2} E) (Set.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_4))))))))) (interior.{u2} E _inst_8 A)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {A : Set.{u1} E} [_inst_8 : TopologicalSpace.{u1} E] [_inst_9 : ContinuousSMul.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_8], (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (Union.union.{u1} (Set.{u1} E) (Set.instUnionSet.{u1} E) (OfNat.ofNat.{u1} (Set.{u1} E) 0 (Zero.toOfNat0.{u1} (Set.{u1} E) (Set.zero.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4)))))))) (interior.{u1} E _inst_8 A)))
+Case conversion may be inaccurate. Consider using '#align balanced_zero_union_interior balanced_zero_union_interiorₓ'. -/
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
 theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0 : Set E) ∪ interior A) :=
   by
@@ -386,6 +628,12 @@ theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0
         
 #align balanced_zero_union_interior balanced_zero_union_interior
 
+/- warning: balanced.interior -> Balanced.interior is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : 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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (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_4)))))))) (interior.{u2} E _inst_8 A)) -> (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (interior.{u2} E _inst_8 A))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {A : Set.{u1} E} [_inst_8 : TopologicalSpace.{u1} E] [_inst_9 : ContinuousSMul.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_8], (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))))) (interior.{u1} E _inst_8 A)) -> (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (interior.{u1} E _inst_8 A))
+Case conversion may be inaccurate. Consider using '#align balanced.interior Balanced.interiorₓ'. -/
 /-- The interior of a balanced set is balanced if it contains the origin. -/
 theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
     Balanced 𝕜 (interior A) :=
@@ -394,6 +642,12 @@ theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
   exact balanced_zero_union_interior hA
 #align balanced.interior Balanced.interior
 
+/- warning: balanced.closure -> Balanced.closure is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u2} E] [_inst_5 : 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_4)] {A : Set.{u2} E} [_inst_8 : TopologicalSpace.{u2} E] [_inst_9 : 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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_8], (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) A) -> (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_4)))) (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_4)))) (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_4)))) (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_4) _inst_5)))) (closure.{u2} E _inst_8 A))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] {A : Set.{u1} E} [_inst_8 : TopologicalSpace.{u1} E] [_inst_9 : ContinuousSMul.{u2, u1} 𝕜 E (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_8], (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) A) -> (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{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_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (closure.{u1} E _inst_8 A))
+Case conversion may be inaccurate. Consider using '#align balanced.closure Balanced.closureₓ'. -/
 theorem Balanced.closure (hA : Balanced 𝕜 A) : Balanced 𝕜 (closure A) := fun a ha =>
   (image_closure_subset_closure_image <| continuous_id.const_smul _).trans <|
     closure_mono <| hA _ ha
@@ -405,6 +659,12 @@ section NontriviallyNormedField
 
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {s : Set E}
 
+/- warning: absorbs_zero_iff -> absorbs_zero_iff 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)] {s : Set.{u2} E}, Iff (Absorbs.{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 (OfNat.ofNat.{u2} (Set.{u2} E) 0 (OfNat.mk.{u2} (Set.{u2} E) 0 (Zero.zero.{u2} (Set.{u2} E) (Set.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} 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.{u2}} {E : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E}, Iff (Absorbs.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s (OfNat.ofNat.{u1} (Set.{u1} E) 0 (Zero.toOfNat0.{u1} (Set.{u1} E) (Set.zero.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))))))) (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))))) s)
+Case conversion may be inaccurate. Consider using '#align absorbs_zero_iff absorbs_zero_iffₓ'. -/
 theorem absorbs_zero_iff : Absorbs 𝕜 s 0 ↔ (0 : E) ∈ s :=
   by
   refine' ⟨_, fun h => ⟨1, zero_lt_one, fun a _ => zero_subset.2 <| zero_mem_smul_set h⟩⟩
@@ -415,12 +675,24 @@ theorem absorbs_zero_iff : Absorbs 𝕜 s 0 ↔ (0 : E) ∈ s :=
   exact norm_ne_zero_iff.1 (hr.trans ha).ne'
 #align absorbs_zero_iff absorbs_zero_iff
 
+/- warning: absorbent.zero_mem -> Absorbent.zero_mem 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)] {s : Set.{u2} E}, (Absorbent.{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) -> (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.{u2}} {E : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E}, (Absorbent.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s) -> (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))))) s)
+Case conversion may be inaccurate. Consider using '#align absorbent.zero_mem Absorbent.zero_memₓ'. -/
 theorem Absorbent.zero_mem (hs : Absorbent 𝕜 s) : (0 : E) ∈ s :=
   absorbs_zero_iff.1 <| absorbent_iff_forall_absorbs_singleton.1 hs _
 #align absorbent.zero_mem Absorbent.zero_mem
 
 variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
 
+/- warning: balanced_convex_hull_of_balanced -> balanced_convexHull_of_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)] {s : Set.{u2} E} [_inst_4 : Module.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_5 : SMulCommClass.{0, u1, u2} Real 𝕜 E (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4)))) (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))))], (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) -> (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)))) (coeFn.{succ u2, succ u2} (ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (fun (_x : ClosureOperator.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) => (Set.{u2} E) -> (Set.{u2} E)) (ClosureOperator.hasCoeToFun.{u2} (Set.{u2} E) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E)))))))) (convexHull.{0, u2} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_4) s))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {s : Set.{u1} E} [_inst_4 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_5 : SMulCommClass.{0, u2, u1} Real 𝕜 E (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)))) (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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))], (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) s) -> (Balanced.{u2, u1} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _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 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (OrderHom.toFun.{u1, u1} (Set.{u1} E) (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (ClosureOperator.toOrderHom.{u1} (Set.{u1} E) (PartialOrder.toPreorder.{u1} (Set.{u1} E) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} E) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} E) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} E) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} E) (Set.instCompleteBooleanAlgebraSet.{u1} E))))))) (convexHull.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_4)) s))
+Case conversion may be inaccurate. Consider using '#align balanced_convex_hull_of_balanced balanced_convexHull_of_balancedₓ'. -/
 theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) :=
   by
   suffices Convex ℝ { x | ∀ a : 𝕜, ‖a‖ ≤ 1 → a • x ∈ convexHull ℝ s }
@@ -439,6 +711,12 @@ section Real
 
 variable [AddCommGroup E] [Module ℝ E] {s : Set E}
 
+/- warning: balanced_iff_neg_mem -> balanced_iff_neg_mem is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] {s : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) -> (Iff (Balanced.{0, u1} Real E (SeminormedCommRing.toSemiNormedRing.{0} Real (NormedCommRing.toSeminormedCommRing.{0} Real Real.normedCommRing)) (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) (forall {{x : E}}, (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) x s) -> (Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) (Neg.neg.{u1} E (SubNegMonoid.toHasNeg.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_1))) x) s)))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] {s : Set.{u1} E}, (Convex.{0, u1} Real E Real.orderedSemiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) -> (Iff (Balanced.{0, u1} Real E (SeminormedCommRing.toSeminormedRing.{0} Real (NormedCommRing.toSeminormedCommRing.{0} Real Real.normedCommRing)) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) s) (forall {{x : E}}, (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x s) -> (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (Neg.neg.{u1} E (NegZeroClass.toNeg.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) x) s)))
+Case conversion may be inaccurate. Consider using '#align balanced_iff_neg_mem balanced_iff_neg_memₓ'. -/
 theorem balanced_iff_neg_mem (hs : Convex ℝ s) : Balanced ℝ s ↔ ∀ ⦃x⦄, x ∈ s → -x ∈ s :=
   by
   refine' ⟨fun h x => h.neg_mem_iff.2, fun h a ha => smul_set_subset_iff.2 fun x hx => _⟩

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

@@ -48,9 +48,9 @@ open Pointwise Topology
 
 variable {𝕜 𝕝 E : Type _} {ι : Sort _} {κ : ι → Sort _}
 
-section SemiNormedRing
+section SeminormedRing
 
-variable [SemiNormedRing 𝕜]
+variable [SeminormedRing 𝕜]
 
 section SMul
 
@@ -259,7 +259,7 @@ theorem balanced_zero : Balanced 𝕜 (0 : Set E) := fun a ha => (smul_zero _).S
 
 end Module
 
-end SemiNormedRing
+end SeminormedRing
 
 section NormedField
 

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

• consistently use the YYYY-MM-DD format
• when easily possible, put the date on the same line as the deprecated attribute
• when easily possible, format the entire declaration on the same line

Why these changes?

• consistency makes it easier for tools to parse this information
• compactness: I don't see a good reason for these declarations taking up more space than needed; as I understand it, deprecated lemmas are not supposed to be used in mathlib anyway
• putting the date on the same line as the attribute makes it easier to discover un-dated deprecations; they also ease writing a tool to replace these by a machine-readable version using leanprover/lean4#3968

@@ -236,8 +236,7 @@ theorem Balanced.smul_mem_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a
   ⟨(hs.smul_mem_mono · h.ge), (hs.smul_mem_mono · h.le)⟩
 #align balanced.mem_smul_iff Balanced.smul_mem_iff
 
-@[deprecated] -- Since 2024/02/02
-alias Balanced.mem_smul_iff := Balanced.smul_mem_iff
+@[deprecated] alias Balanced.mem_smul_iff := Balanced.smul_mem_iff -- since 2024-02-02
 
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
@@ -281,7 +280,7 @@ section NontriviallyNormedField
 
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {s : Set E}
 
-@[deprecated Absorbent.zero_mem] -- Since 2024/02/02
+@[deprecated Absorbent.zero_mem] -- Since 2024-02-02
 theorem Absorbent.zero_mem' (hs : Absorbent 𝕜 s) : (0 : E) ∈ s := hs.zero_mem
 
 variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
@@ -296,8 +295,7 @@ protected theorem Balanced.convexHull (hs : Balanced 𝕜 s) : Balanced 𝕜 (co
   exact convex_convexHull ℝ s (hx a ha) (hy a ha) hu hv huv
 #align balanced_convex_hull_of_balanced Balanced.convexHull
 
-@[deprecated] -- Since 2024/02/02
-alias balanced_convexHull_of_balanced := Balanced.convexHull
+@[deprecated] alias balanced_convexHull_of_balanced := Balanced.convexHull -- Since 2024-02-02
 
 end NontriviallyNormedField
 

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

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

@@ -105,7 +105,7 @@ protected lemma sUnion (hT : T.Finite) (hs : ∀ t ∈ T, Absorbs M s t) :
 @[simp]
 lemma _root_.absorbs_iUnion {ι : Sort*} [Finite ι] {t : ι → Set α} :
     Absorbs M s (⋃ i, t i) ↔ ∀ i, Absorbs M s (t i) :=
-  (finite_range t).absorbs_sUnion.trans forall_range_iff
+  (finite_range t).absorbs_sUnion.trans forall_mem_range
 
 protected alias ⟨_, iUnion⟩ := absorbs_iUnion
 
@@ -180,13 +180,13 @@ protected lemma inter (hs : Absorbs G₀ s u) (ht : Absorbs G₀ t u) : Absorbs
 @[simp]
 lemma _root_.absorbs_iInter {ι : Sort*} [Finite ι] {s : ι → Set α} :
     Absorbs G₀ (⋂ i, s i) t ↔ ∀ i, Absorbs G₀ (s i) t :=
-  (finite_range s).absorbs_sInter.trans forall_range_iff
+  (finite_range s).absorbs_sInter.trans forall_mem_range
 
 protected alias ⟨_, iInter⟩ := absorbs_iInter
 
 lemma _root_.Set.Finite.absorbs_biInter {ι : Type*} {I : Set ι} (hI : I.Finite) {s : ι → Set α} :
     Absorbs G₀ (⋂ i ∈ I, s i) t ↔ ∀ i ∈ I, Absorbs G₀ (s i) t := by
-  simpa only [sInter_image, ball_image_iff] using (hI.image s).absorbs_sInter
+  simpa only [sInter_image, forall_mem_image] using (hI.image s).absorbs_sInter
 
 protected alias ⟨_, biInter⟩ := Set.Finite.absorbs_biInter
 

• add absorbs_iff_eventually_nhds_zero, isVonNBounded_iff_tendsto_smallSets_nhds, and isVonNBounded_pi_iff;
• generalize some lemmas from NormedField to NormedDivisionRing;
• use new lemmas to golf 2 proofs

@@ -159,10 +159,9 @@ end Module
 
 end SeminormedRing
 
-section NormedField
+section NormedDivisionRing
 
-variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGroup E] [Module 𝕜 E]
-  [SMulWithZero 𝕝 E] [IsScalarTower 𝕜 𝕝 E] {s t u v A B : Set E} {x : E} {a b : 𝕜}
+variable [NormedDivisionRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {s t : Set E} {x : E} {a b : 𝕜}
 
 theorem absorbs_iff_eventually_nhdsWithin_zero :
     Absorbs 𝕜 s t ↔ ∀ᶠ c : 𝕜 in 𝓝[≠] 0, MapsTo (c • ·) t s := by
@@ -170,19 +169,30 @@ theorem absorbs_iff_eventually_nhdsWithin_zero :
 
 alias ⟨Absorbs.eventually_nhdsWithin_zero, _⟩ := absorbs_iff_eventually_nhdsWithin_zero
 
-theorem Absorbs.eventually_nhds_zero (h : Absorbs 𝕜 s t) (h₀ : 0 ∈ s) :
-    ∀ᶠ c : 𝕜 in 𝓝 0, MapsTo (c • ·) t s := by
-  rw [← nhdsWithin_compl_singleton_sup_pure, Filter.eventually_sup, Filter.eventually_pure,
-    ← absorbs_iff_eventually_nhdsWithin_zero]
-  refine ⟨h, fun x _ ↦ ?_⟩
-  simpa only [zero_smul]
-
 theorem absorbent_iff_eventually_nhdsWithin_zero :
     Absorbent 𝕜 s ↔ ∀ x : E, ∀ᶠ c : 𝕜 in 𝓝[≠] 0, c • x ∈ s :=
   forall_congr' fun x ↦ by simp only [absorbs_iff_eventually_nhdsWithin_zero, mapsTo_singleton]
 
 alias ⟨Absorbent.eventually_nhdsWithin_zero, _⟩ := absorbent_iff_eventually_nhdsWithin_zero
 
+theorem absorbs_iff_eventually_nhds_zero (h₀ : 0 ∈ s) :
+    Absorbs 𝕜 s t ↔ ∀ᶠ c : 𝕜 in 𝓝 0, MapsTo (c • ·) t s := by
+  rw [← nhdsWithin_compl_singleton_sup_pure, Filter.eventually_sup, Filter.eventually_pure,
+    ← absorbs_iff_eventually_nhdsWithin_zero, and_iff_left]
+  intro x _
+  simpa only [zero_smul]
+
+theorem Absorbs.eventually_nhds_zero (h : Absorbs 𝕜 s t) (h₀ : 0 ∈ s) :
+    ∀ᶠ c : 𝕜 in 𝓝 0, MapsTo (c • ·) t s :=
+  (absorbs_iff_eventually_nhds_zero h₀).1 h
+
+end NormedDivisionRing
+
+section NormedField
+
+variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGroup E] [Module 𝕜 E]
+  [SMulWithZero 𝕝 E] [IsScalarTower 𝕜 𝕝 E] {s t u v A B : Set E} {x : E} {a b : 𝕜}
+
 /-- Scalar multiplication (by possibly different types) of a balanced set is monotone. -/
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s := by
   obtain rfl | hb := eq_or_ne b 0

• Add absorbent_iff_eventually_nhdsWithin_zero.
• Use it to golf Seminorm.bddAbove_of_absorbent.

@@ -177,6 +177,12 @@ theorem Absorbs.eventually_nhds_zero (h : Absorbs 𝕜 s t) (h₀ : 0 ∈ s) :
   refine ⟨h, fun x _ ↦ ?_⟩
   simpa only [zero_smul]
 
+theorem absorbent_iff_eventually_nhdsWithin_zero :
+    Absorbent 𝕜 s ↔ ∀ x : E, ∀ᶠ c : 𝕜 in 𝓝[≠] 0, c • x ∈ s :=
+  forall_congr' fun x ↦ by simp only [absorbs_iff_eventually_nhdsWithin_zero, mapsTo_singleton]
+
+alias ⟨Absorbent.eventually_nhdsWithin_zero, _⟩ := absorbent_iff_eventually_nhdsWithin_zero
+
 /-- Scalar multiplication (by possibly different types) of a balanced set is monotone. -/
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s := by
   obtain rfl | hb := eq_or_ne b 0

• Prove a version of UniformOnFun.continuousSMul_induced_of_image_bounded for UniformFuns.
• Deal with φ : H →ₗ[𝕜] (α → E) and ofFun ∘ φ, not φ : H →ₗ[𝕜] (α →ᵤ[𝔖] E).
• Drop unneeded assumptions (nonempty, directed).

@@ -164,6 +164,19 @@ section NormedField
 variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGroup E] [Module 𝕜 E]
   [SMulWithZero 𝕝 E] [IsScalarTower 𝕜 𝕝 E] {s t u v A B : Set E} {x : E} {a b : 𝕜}
 
+theorem absorbs_iff_eventually_nhdsWithin_zero :
+    Absorbs 𝕜 s t ↔ ∀ᶠ c : 𝕜 in 𝓝[≠] 0, MapsTo (c • ·) t s := by
+  rw [absorbs_iff_eventually_cobounded_mapsTo, ← Filter.inv_cobounded₀]; rfl
+
+alias ⟨Absorbs.eventually_nhdsWithin_zero, _⟩ := absorbs_iff_eventually_nhdsWithin_zero
+
+theorem Absorbs.eventually_nhds_zero (h : Absorbs 𝕜 s t) (h₀ : 0 ∈ s) :
+    ∀ᶠ c : 𝕜 in 𝓝 0, MapsTo (c • ·) t s := by
+  rw [← nhdsWithin_compl_singleton_sup_pure, Filter.eventually_sup, Filter.eventually_pure,
+    ← absorbs_iff_eventually_nhdsWithin_zero]
+  refine ⟨h, fun x _ ↦ ?_⟩
+  simpa only [zero_smul]
+
 /-- Scalar multiplication (by possibly different types) of a balanced set is monotone. -/
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s := by
   obtain rfl | hb := eq_or_ne b 0

• add balanced_iff_closedBall_smul, balanced_neg;
• generalize Balanced.neg_mem_iff to a SeminormedRing + NormOneClass, add Balanced.neg_eq
• add Balanced.smul_mem_mono and Balanced.smul_congr;
• rename Balanced.mem_smul_iff to Balanced.smul_mem_iff;
• rename balanced_zero_union_interior to Balanced.zero_insert_interior, use insert 0 (interior A) instead of 0 ∪ interior A;
• make Balanced.interior and Balanced.closure protected;
• deprecate Absorbs.zero_mem';
• rename balanced_convexHull_of_balanced to Balanced.convexHull;
• add absorbs_iff_eventually_cobounded_mapsTo, use it to golf some proofs.

@@ -155,11 +155,16 @@ variable {G₀ α : Type*} [GroupWithZero G₀] [Bornology G₀] [MulAction G₀
 protected lemma univ : Absorbs G₀ univ s :=
   (eventually_ne_cobounded 0).mono fun a ha ↦ by rw [smul_set_univ₀ ha]; apply subset_univ
 
+lemma _root_.absorbs_iff_eventually_cobounded_mapsTo :
+    Absorbs G₀ s t ↔ ∀ᶠ c in cobounded G₀, MapsTo (c⁻¹ • ·) t s :=
+  eventually_congr <| (eventually_ne_cobounded 0).mono fun c hc ↦ by
+    rw [← preimage_smul_inv₀ hc]; rfl
+
+alias ⟨eventually_cobounded_mapsTo, _⟩ := absorbs_iff_eventually_cobounded_mapsTo
+
 lemma _root_.Set.Finite.absorbs_sInter (hS : S.Finite) :
     Absorbs G₀ (⋂₀ S) t ↔ ∀ s ∈ S, Absorbs G₀ s t := by
-  simp only [Absorbs, ← hS.eventually_all]
-  refine eventually_congr <| (eventually_ne_cobounded 0).mono fun a ha ↦ ?_
-  simp only [← preimage_smul_inv₀ ha, preimage_sInter, subset_iInter_iff]
+  simp only [absorbs_iff_eventually_cobounded_mapsTo, mapsTo_sInter, hS.eventually_all]
 
 protected alias ⟨_, sInter⟩ := Set.Finite.absorbs_sInter
 
@@ -188,10 +193,8 @@ protected alias ⟨_, biInter⟩ := Set.Finite.absorbs_biInter
 @[simp]
 lemma _root_.absorbs_zero_iff [NeBot (cobounded G₀)] {E : Type*} [AddMonoid E]
     [DistribMulAction G₀ E] {s : Set E} : Absorbs G₀ s 0 ↔ 0 ∈ s := by
-  refine ⟨fun h ↦ ?_, .zero⟩
-  rcases (h.and (eventually_ne_cobounded 0)).exists with ⟨c, hc, hc₀⟩
-  rcases hc rfl with ⟨x, hx, hx₀⟩
-  rwa [← smul_zero c⁻¹, ← hx₀, inv_smul_smul₀ hc₀]
+  simp only [absorbs_iff_eventually_cobounded_mapsTo, ← singleton_zero,
+    mapsTo_singleton, smul_zero, eventually_const]
 #align absorbs_zero_iff absorbs_zero_iff
 
 end GroupWithZero
@@ -259,8 +262,7 @@ lemma absorbent_univ : Absorbent G₀ (univ : Set α) := fun _ ↦ .univ
 
 lemma absorbent_iff_inv_smul {s : Set α} :
     Absorbent G₀ s ↔ ∀ x, ∀ᶠ c in cobounded G₀, c⁻¹ • x ∈ s :=
-  forall_congr' fun x ↦ eventually_congr <| (eventually_ne_cobounded 0).mono fun c hc ↦ by
-    rw [singleton_subset_iff, ← preimage_smul_inv₀ hc, mem_preimage]
+  forall_congr' fun x ↦ by simp only [absorbs_iff_eventually_cobounded_mapsTo, mapsTo_singleton]
 
 lemma Absorbent.zero_mem [NeBot (cobounded G₀)] [AddMonoid E] [DistribMulAction G₀ E]
     {s : Set E} (hs : Absorbent G₀ s) : (0 : E) ∈ s :=

• add balanced_iff_closedBall_smul, balanced_neg;
• generalize Balanced.neg_mem_iff to a SeminormedRing + NormOneClass, add Balanced.neg_eq
• add Balanced.smul_mem_mono and Balanced.smul_congr;
• rename Balanced.mem_smul_iff to Balanced.smul_mem_iff;
• rename balanced_zero_union_interior to Balanced.zero_insert_interior, use insert 0 (interior A) instead of 0 ∪ interior A;
• make Balanced.interior and Balanced.closure protected;
• deprecate Absorbs.zero_mem';
• rename balanced_convexHull_of_balanced to Balanced.convexHull;
• add absorbs_iff_eventually_cobounded_mapsTo, use it to golf some proofs.

@@ -78,6 +78,9 @@ theorem balanced_iff_smul_mem : Balanced 𝕜 s ↔ ∀ ⦃a : 𝕜⦄, ‖a‖
 alias ⟨Balanced.smul_mem, _⟩ := balanced_iff_smul_mem
 #align balanced.smul_mem Balanced.smul_mem
 
+theorem balanced_iff_closedBall_smul : Balanced 𝕜 s ↔ Metric.closedBall (0 : 𝕜) 1 • s ⊆ s := by
+  simp [balanced_iff_smul_mem, smul_subset_iff]
+
 @[simp]
 theorem balanced_empty : Balanced 𝕜 (∅ : Set E) := fun _ _ => by rw [smul_set_empty]
 #align balanced_empty balanced_empty
@@ -128,6 +131,18 @@ theorem Balanced.neg : Balanced 𝕜 s → Balanced 𝕜 (-s) :=
   forall₂_imp fun _ _ h => (smul_set_neg _ _).subset.trans <| neg_subset_neg.2 h
 #align balanced.neg Balanced.neg
 
+@[simp]
+theorem balanced_neg : Balanced 𝕜 (-s) ↔ Balanced 𝕜 s :=
+  ⟨fun h ↦ neg_neg s ▸ h.neg, fun h ↦ h.neg⟩
+
+theorem Balanced.neg_mem_iff [NormOneClass 𝕜] (h : Balanced 𝕜 s) {x : E} : -x ∈ s ↔ x ∈ s :=
+  ⟨fun hx ↦ by simpa using h.smul_mem (a := -1) (by simp) hx,
+    fun hx ↦ by simpa using h.smul_mem (a := -1) (by simp) hx⟩
+#align balanced.neg_mem_iff Balanced.neg_mem_iff
+
+theorem Balanced.neg_eq [NormOneClass 𝕜] (h : Balanced 𝕜 s) : -s = s :=
+  Set.ext fun _ ↦ h.neg_mem_iff
+
 theorem Balanced.add (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s + t) := fun _a ha =>
   (smul_add _ _ _).subset.trans <| add_subset_add (hs _ ha) <| ht _ ha
 #align balanced.add Balanced.add
@@ -152,23 +167,33 @@ variable [NormedField 𝕜] [NormedRing 𝕝] [NormedSpace 𝕜 𝕝] [AddCommGr
 /-- Scalar multiplication (by possibly different types) of a balanced set is monotone. -/
 theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖a‖ ≤ ‖b‖) : a • s ⊆ b • s := by
   obtain rfl | hb := eq_or_ne b 0
-  · rw [norm_zero] at h
-    rw [norm_eq_zero.1 (h.antisymm <| norm_nonneg _)]
-    obtain rfl | h := s.eq_empty_or_nonempty
-    · simp_rw [smul_set_empty]; rfl
-    · simp_rw [zero_smul_set h]; rfl
-  rintro _ ⟨x, hx, rfl⟩
-  refine' ⟨b⁻¹ • a • x, _, smul_inv_smul₀ hb _⟩
-  rw [← smul_assoc]
-  refine' hs _ _ (smul_mem_smul_set hx)
-  rw [norm_smul, norm_inv, ← div_eq_inv_mul]
-  exact div_le_one_of_le h (norm_nonneg _)
+  · rw [norm_zero, norm_le_zero_iff] at h
+    simp only [h, ← image_smul, zero_smul, Subset.rfl]
+  · calc
+      a • s = b • (b⁻¹ • a) • s := by rw [smul_assoc, smul_inv_smul₀ hb]
+      _ ⊆ b • s := smul_set_mono <| hs _ <| by
+        rw [norm_smul, norm_inv, ← div_eq_inv_mul]
+        exact div_le_one_of_le h (norm_nonneg _)
 #align balanced.smul_mono Balanced.smul_mono
 
+theorem Balanced.smul_mem_mono [SMulCommClass 𝕝 𝕜 E] (hs : Balanced 𝕝 s) {a : 𝕜} {b : 𝕝}
+    (ha : a • x ∈ s) (hba : ‖b‖ ≤ ‖a‖) : b • x ∈ s := by
+  rcases eq_or_ne a 0 with rfl | ha₀
+  · simp_all
+  · calc
+      b • x = (a⁻¹ • b) • a • x := by rw [smul_comm, smul_assoc, smul_inv_smul₀ ha₀]
+      _ ∈ s := by
+        refine hs.smul_mem ?_ ha
+        rw [norm_smul, norm_inv, ← div_eq_inv_mul]
+        exact div_le_one_of_le hba (norm_nonneg _)
+
 theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆ a • A := by
   rw [← @norm_one 𝕜] at ha; simpa using hA.smul_mono ha
 #align balanced.subset_smul Balanced.subset_smul
 
+theorem Balanced.smul_congr (hs : Balanced 𝕜 A) (h : ‖a‖ = ‖b‖) : a • A = b • A :=
+  (hs.smul_mono h.le).antisymm (hs.smul_mono h.ge)
+
 theorem Balanced.smul_eq (hA : Balanced 𝕜 A) (ha : ‖a‖ = 1) : a • A = A :=
   (hA _ ha.le).antisymm <| hA.subset_smul ha.ge
 #align balanced.smul_eq Balanced.smul_eq
@@ -178,22 +203,12 @@ theorem Balanced.absorbs_self (hA : Balanced 𝕜 A) : Absorbs 𝕜 A A :=
   .of_norm ⟨1, fun _ => hA.subset_smul⟩
 #align balanced.absorbs_self Balanced.absorbs_self
 
-theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s := by
-  obtain rfl | hb := eq_or_ne b 0
-  · rw [norm_zero, norm_eq_zero] at h
-    rw [h]
-  have ha : a ≠ 0 := norm_ne_zero_iff.1 (ne_of_eq_of_ne h <| norm_ne_zero_iff.2 hb)
-  constructor <;> intro h' <;> [rw [← inv_mul_cancel_right₀ ha b];
-      rw [← inv_mul_cancel_right₀ hb a]] <;>
-    · rw [← smul_eq_mul, smul_assoc]
-      refine' hs.smul_mem _ h'
-      simp [← h, ha]
-#align balanced.mem_smul_iff Balanced.mem_smul_iff
-
-theorem Balanced.neg_mem_iff (hs : Balanced 𝕜 s) : -x ∈ s ↔ x ∈ s := by
-  convert hs.mem_smul_iff (x := x) (norm_neg 1) using 0;
-  simp only [neg_smul, one_smul 𝕜 x]
-#align balanced.neg_mem_iff Balanced.neg_mem_iff
+theorem Balanced.smul_mem_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s :=
+  ⟨(hs.smul_mem_mono · h.ge), (hs.smul_mem_mono · h.le)⟩
+#align balanced.mem_smul_iff Balanced.smul_mem_iff
+
+@[deprecated] -- Since 2024/02/02
+alias Balanced.mem_smul_iff := Balanced.smul_mem_iff
 
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
@@ -204,30 +219,30 @@ theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
 #align absorbent_nhds_zero absorbent_nhds_zero
 
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
-theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) :
-    Balanced 𝕜 ((0 : Set E) ∪ interior A) := by
+theorem Balanced.zero_insert_interior (hA : Balanced 𝕜 A) :
+    Balanced 𝕜 (insert 0 (interior A)) := by
   intro a ha
   obtain rfl | h := eq_or_ne a 0
   · rw [zero_smul_set]
     exacts [subset_union_left _ _, ⟨0, Or.inl rfl⟩]
-  · rw [← image_smul, image_union]
-    apply union_subset_union
-    · rw [image_zero, smul_zero]
-      rfl
-    · calc
-        a • interior A ⊆ interior (a • A) := (isOpenMap_smul₀ h).image_interior_subset A
-        _ ⊆ interior A := interior_mono (hA _ ha)
-#align balanced_zero_union_interior balanced_zero_union_interior
+  · rw [← image_smul, image_insert_eq, smul_zero]
+    apply insert_subset_insert
+    exact ((isOpenMap_smul₀ h).mapsTo_interior <| hA.smul_mem ha).image_subset
+#align balanced_zero_union_interior Balanced.zero_insert_interior
+
+@[deprecated Balanced.zero_insert_interior]
+theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0 : Set E) ∪ interior A) :=
+  hA.zero_insert_interior
 
 /-- The interior of a balanced set is balanced if it contains the origin. -/
-theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
+protected theorem Balanced.interior (hA : Balanced 𝕜 A) (h : (0 : E) ∈ interior A) :
     Balanced 𝕜 (interior A) := by
-  rw [← union_eq_self_of_subset_left (singleton_subset_iff.2 h)]
-  exact balanced_zero_union_interior hA
+  rw [← insert_eq_self.2 h]
+  exact hA.zero_insert_interior
 #align balanced.interior Balanced.interior
 
-theorem Balanced.closure (hA : Balanced 𝕜 A) : Balanced 𝕜 (closure A) := fun _a ha =>
-  (image_closure_subset_closure_image <| continuous_id.const_smul _).trans <|
+protected theorem Balanced.closure (hA : Balanced 𝕜 A) : Balanced 𝕜 (closure A) := fun _a ha =>
+  (image_closure_subset_closure_image <| continuous_const_smul _).trans <|
     closure_mono <| hA _ ha
 #align balanced.closure Balanced.closure
 
@@ -237,11 +252,12 @@ section NontriviallyNormedField
 
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {s : Set E}
 
+@[deprecated Absorbent.zero_mem] -- Since 2024/02/02
 theorem Absorbent.zero_mem' (hs : Absorbent 𝕜 s) : (0 : E) ∈ s := hs.zero_mem
 
 variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
 
-theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) := by
+protected theorem Balanced.convexHull (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) := by
   suffices Convex ℝ { x | ∀ a : 𝕜, ‖a‖ ≤ 1 → a • x ∈ convexHull ℝ s } by
     rw [balanced_iff_smul_mem] at hs ⊢
     refine' fun a ha x hx => convexHull_min _ this hx a ha
@@ -249,7 +265,10 @@ theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (
   intro x hx y hy u v hu hv huv a ha
   simp only [smul_add, ← smul_comm]
   exact convex_convexHull ℝ s (hx a ha) (hy a ha) hu hv huv
-#align balanced_convex_hull_of_balanced balanced_convexHull_of_balanced
+#align balanced_convex_hull_of_balanced Balanced.convexHull
+
+@[deprecated] -- Since 2024/02/02
+alias balanced_convexHull_of_balanced := Balanced.convexHull
 
 end NontriviallyNormedField
 

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo, Yury Kudryashov
 -/
 import Mathlib.Data.Set.Pointwise.SMul
-import Mathlib.Topology.Bornology.Constructions
+import Mathlib.Topology.Bornology.Basic
 
 #align_import analysis.locally_convex.basic from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

Redefine Absorbs and Absorbent in terms of the cobounded filter.

Redefine Absorbs and Absorbent in terms of the cobounded filter.

@@ -6,6 +6,7 @@ Authors: Jean Lo, Bhavik Mehta, Yaël Dillies
 import Mathlib.Analysis.Convex.Basic
 import Mathlib.Analysis.Convex.Hull
 import Mathlib.Analysis.NormedSpace.Basic
+import Mathlib.Topology.Bornology.Absorbs
 
 #align_import analysis.locally_convex.basic from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 
@@ -51,106 +52,7 @@ variable [SeminormedRing 𝕜]
 
 section SMul
 
-variable (𝕜) [SMul 𝕜 E]
-
-/-- A set `A` absorbs another set `B` if `B` is contained in all scalings of `A` by elements of
-sufficiently large norm. -/
-def Absorbs (A B : Set E) :=
-  ∃ r, 0 < r ∧ ∀ a : 𝕜, r ≤ ‖a‖ → B ⊆ a • A
-#align absorbs Absorbs
-
-variable {𝕜} {s t u v A B : Set E}
-
-@[simp]
-theorem absorbs_empty {s : Set E} : Absorbs 𝕜 s (∅ : Set E) :=
-  ⟨1, one_pos, fun _a _ha => Set.empty_subset _⟩
-#align absorbs_empty absorbs_empty
-
-theorem Absorbs.mono (hs : Absorbs 𝕜 s u) (hst : s ⊆ t) (hvu : v ⊆ u) : Absorbs 𝕜 t v :=
-  let ⟨r, hr, h⟩ := hs
-  ⟨r, hr, fun _a ha => hvu.trans <| (h _ ha).trans <| smul_set_mono hst⟩
-#align absorbs.mono Absorbs.mono
-
-theorem Absorbs.mono_left (hs : Absorbs 𝕜 s u) (h : s ⊆ t) : Absorbs 𝕜 t u :=
-  hs.mono h Subset.rfl
-#align absorbs.mono_left Absorbs.mono_left
-
-theorem Absorbs.mono_right (hs : Absorbs 𝕜 s u) (h : v ⊆ u) : Absorbs 𝕜 s v :=
-  hs.mono Subset.rfl h
-#align absorbs.mono_right Absorbs.mono_right
-
-theorem Absorbs.union (hu : Absorbs 𝕜 s u) (hv : Absorbs 𝕜 s v) : Absorbs 𝕜 s (u ∪ v) := by
-  obtain ⟨a, ha, hu⟩ := hu
-  obtain ⟨b, _hb, hv⟩ := hv
-  exact
-    ⟨max a b, lt_max_of_lt_left ha, fun c hc =>
-      union_subset (hu _ <| le_of_max_le_left hc) (hv _ <| le_of_max_le_right hc)⟩
-#align absorbs.union Absorbs.union
-
-@[simp]
-theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorbs 𝕜 s v :=
-  ⟨fun h => ⟨h.mono_right <| subset_union_left _ _, h.mono_right <| subset_union_right _ _⟩,
-    fun h => h.1.union h.2⟩
-#align absorbs_union absorbs_union
-
-theorem absorbs_iUnion_finset {ι : Type*} {t : Finset ι} {f : ι → Set E} :
-    Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
-  classical
-    induction' t using Finset.induction_on with i t _ht hi
-    · simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
-        IsEmpty.forall_iff, imp_true_iff]
-    rw [Finset.set_biUnion_insert, absorbs_union, hi]
-    constructor <;> intro h
-    · refine' fun _ hi' => (Finset.mem_insert.mp hi').elim _ (h.2 _)
-      exact fun hi'' => by
-        rw [hi'']
-        exact h.1
-    exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
-#align absorbs_Union_finset absorbs_iUnion_finset
-
-theorem Set.Finite.absorbs_iUnion {ι : Type*} {s : Set E} {t : Set ι} {f : ι → Set E}
-    (hi : t.Finite) : Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
-  lift t to Finset ι using hi
-  simp only [Finset.mem_coe]
-  exact absorbs_iUnion_finset
-#align set.finite.absorbs_Union Set.Finite.absorbs_iUnion
-
-variable (𝕜)
-
-/-- A set is absorbent if it absorbs every singleton. -/
-def Absorbent (A : Set E) :=
-  ∀ x, ∃ r, 0 < r ∧ ∀ a : 𝕜, r ≤ ‖a‖ → x ∈ a • A
-#align absorbent Absorbent
-
-variable {𝕜}
-
-theorem Absorbent.subset (hA : Absorbent 𝕜 A) (hAB : A ⊆ B) : Absorbent 𝕜 B := by
-  refine' forall_imp (fun x => _) hA
-  exact Exists.imp fun r => And.imp_right <| forall₂_imp fun a _ha hx => Set.smul_set_mono hAB hx
-#align absorbent.subset Absorbent.subset
-
-theorem absorbent_iff_forall_absorbs_singleton : Absorbent 𝕜 A ↔ ∀ x, Absorbs 𝕜 A {x} := by
-  simp_rw [Absorbs, Absorbent, singleton_subset_iff]
-#align absorbent_iff_forall_absorbs_singleton absorbent_iff_forall_absorbs_singleton
-
-theorem Absorbent.absorbs (hs : Absorbent 𝕜 s) {x : E} : Absorbs 𝕜 s {x} :=
-  absorbent_iff_forall_absorbs_singleton.1 hs _
-#align absorbent.absorbs Absorbent.absorbs
-
-theorem absorbent_iff_nonneg_lt :
-    Absorbent 𝕜 A ↔ ∀ x, ∃ r, 0 ≤ r ∧ ∀ ⦃a : 𝕜⦄, r < ‖a‖ → x ∈ a • A :=
-  forall_congr' fun _x =>
-    ⟨fun ⟨r, hr, hx⟩ => ⟨r, hr.le, fun a ha => hx a ha.le⟩, fun ⟨r, hr, hx⟩ =>
-      ⟨r + 1, add_pos_of_nonneg_of_pos hr zero_lt_one, fun _a ha =>
-        hx ((lt_add_of_pos_right r zero_lt_one).trans_le ha)⟩⟩
-#align absorbent_iff_nonneg_lt absorbent_iff_nonneg_lt
-
-theorem Absorbent.absorbs_finite {s : Set E} (hs : Absorbent 𝕜 s) {v : Set E} (hv : v.Finite) :
-    Absorbs 𝕜 s v := by
-  rw [← Set.biUnion_of_singleton v]
-  exact hv.absorbs_iUnion.mpr fun _ _ => hs.absorbs
-#align absorbent.absorbs_finite Absorbent.absorbs_finite
-
+variable [SMul 𝕜 E] {s t u v A B : Set E}
 variable (𝕜)
 
 /-- A set `A` is balanced if `a • A` is contained in `A` whenever `a` has norm at most `1`. -/
@@ -160,6 +62,15 @@ def Balanced (A : Set E) :=
 
 variable {𝕜}
 
+lemma absorbs_iff_norm : Absorbs 𝕜 A B ↔ ∃ r, ∀ c : 𝕜, r ≤ ‖c‖ → B ⊆ c • A :=
+  Filter.atTop_basis.cobounded_of_norm.eventually_iff.trans <| by simp only [true_and]; rfl
+
+alias ⟨_, Absorbs.of_norm⟩ := absorbs_iff_norm
+
+lemma Absorbs.exists_pos (h : Absorbs 𝕜 A B) : ∃ r > 0, ∀ c : 𝕜, r ≤ ‖c‖ → B ⊆ c • A :=
+  let ⟨r, hr₁, hr⟩ := (Filter.atTop_basis' 1).cobounded_of_norm.eventually_iff.1 h
+  ⟨r, one_pos.trans_le hr₁, hr⟩
+
 theorem balanced_iff_smul_mem : Balanced 𝕜 s ↔ ∀ ⦃a : 𝕜⦄, ‖a‖ ≤ 1 → ∀ ⦃x : E⦄, x ∈ s → a • x ∈ s :=
   forall₂_congr fun _a _ha => smul_set_subset_iff
 #align balanced_iff_smul_mem balanced_iff_smul_mem
@@ -213,32 +124,14 @@ section Module
 
 variable [AddCommGroup E] [Module 𝕜 E] {s s₁ s₂ t t₁ t₂ : Set E}
 
-theorem Absorbs.neg : Absorbs 𝕜 s t → Absorbs 𝕜 (-s) (-t) :=
-  Exists.imp fun _r =>
-    And.imp_right <| forall₂_imp fun _ _ h => (neg_subset_neg.2 h).trans (smul_set_neg _ _).superset
-#align absorbs.neg Absorbs.neg
-
 theorem Balanced.neg : Balanced 𝕜 s → Balanced 𝕜 (-s) :=
   forall₂_imp fun _ _ h => (smul_set_neg _ _).subset.trans <| neg_subset_neg.2 h
 #align balanced.neg Balanced.neg
 
-theorem Absorbs.add : Absorbs 𝕜 s₁ t₁ → Absorbs 𝕜 s₂ t₂ → Absorbs 𝕜 (s₁ + s₂) (t₁ + t₂) :=
-  fun ⟨r₁, hr₁, h₁⟩ ⟨r₂, _hr₂, h₂⟩ =>
-  ⟨max r₁ r₂, lt_max_of_lt_left hr₁, fun _a ha =>
-    (add_subset_add (h₁ _ <| le_of_max_le_left ha) <| h₂ _ <| le_of_max_le_right ha).trans
-      (smul_add _ _ _).superset⟩
-#align absorbs.add Absorbs.add
-
 theorem Balanced.add (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s + t) := fun _a ha =>
   (smul_add _ _ _).subset.trans <| add_subset_add (hs _ ha) <| ht _ ha
 #align balanced.add Balanced.add
 
-theorem Absorbs.sub (h₁ : Absorbs 𝕜 s₁ t₁) (h₂ : Absorbs 𝕜 s₂ t₂) :
-    Absorbs 𝕜 (s₁ - s₂) (t₁ - t₂) := by
-  simp_rw [sub_eq_add_neg]
-  exact h₁.add h₂.neg
-#align absorbs.sub Absorbs.sub
-
 theorem Balanced.sub (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 𝕜 (s - t) := by
   simp_rw [sub_eq_add_neg]
   exact hs.add ht.neg
@@ -272,28 +165,19 @@ theorem Balanced.smul_mono (hs : Balanced 𝕝 s) {a : 𝕝} {b : 𝕜} (h : ‖
   exact div_le_one_of_le h (norm_nonneg _)
 #align balanced.smul_mono Balanced.smul_mono
 
-/-- A balanced set absorbs itself. -/
-theorem Balanced.absorbs_self (hA : Balanced 𝕜 A) : Absorbs 𝕜 A A := by
-  refine' ⟨1, zero_lt_one, fun a ha x hx => _⟩
-  rw [mem_smul_set_iff_inv_smul_mem₀ (norm_pos_iff.1 <| zero_lt_one.trans_le ha)]
-  refine' hA a⁻¹ _ (smul_mem_smul_set hx)
-  rw [norm_inv]
-  exact inv_le_one ha
-#align balanced.absorbs_self Balanced.absorbs_self
-
 theorem Balanced.subset_smul (hA : Balanced 𝕜 A) (ha : 1 ≤ ‖a‖) : A ⊆ a • A := by
-  refine' (subset_set_smul_iff₀ _).2 (hA a⁻¹ _)
-  · rintro rfl
-    rw [norm_zero] at ha
-    exact zero_lt_one.not_le ha
-  · rw [norm_inv]
-    exact inv_le_one ha
+  rw [← @norm_one 𝕜] at ha; simpa using hA.smul_mono ha
 #align balanced.subset_smul Balanced.subset_smul
 
 theorem Balanced.smul_eq (hA : Balanced 𝕜 A) (ha : ‖a‖ = 1) : a • A = A :=
   (hA _ ha.le).antisymm <| hA.subset_smul ha.ge
 #align balanced.smul_eq Balanced.smul_eq
 
+/-- A balanced set absorbs itself. -/
+theorem Balanced.absorbs_self (hA : Balanced 𝕜 A) : Absorbs 𝕜 A A :=
+  .of_norm ⟨1, fun _ => hA.subset_smul⟩
+#align balanced.absorbs_self Balanced.absorbs_self
+
 theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a • x ∈ s ↔ b • x ∈ s := by
   obtain rfl | hb := eq_or_ne b 0
   · rw [norm_zero, norm_eq_zero] at h
@@ -311,44 +195,12 @@ theorem Balanced.neg_mem_iff (hs : Balanced 𝕜 s) : -x ∈ s ↔ x ∈ s := by
   simp only [neg_smul, one_smul 𝕜 x]
 #align balanced.neg_mem_iff Balanced.neg_mem_iff
 
-theorem Absorbs.inter (hs : Absorbs 𝕜 s u) (ht : Absorbs 𝕜 t u) : Absorbs 𝕜 (s ∩ t) u := by
-  obtain ⟨a, ha, hs⟩ := hs
-  obtain ⟨b, _hb, ht⟩ := ht
-  have h : 0 < max a b := lt_max_of_lt_left ha
-  refine' ⟨max a b, lt_max_of_lt_left ha, fun c hc => _⟩
-  rw [smul_set_inter₀ (norm_pos_iff.1 <| h.trans_le hc)]
-  exact subset_inter (hs _ <| le_of_max_le_left hc) (ht _ <| le_of_max_le_right hc)
-#align absorbs.inter Absorbs.inter
-
-@[simp]
-theorem absorbs_inter : Absorbs 𝕜 (s ∩ t) u ↔ Absorbs 𝕜 s u ∧ Absorbs 𝕜 t u :=
-  ⟨fun h => ⟨h.mono_left <| inter_subset_left _ _, h.mono_left <| inter_subset_right _ _⟩, fun h =>
-    h.1.inter h.2⟩
-#align absorbs_inter absorbs_inter
-
-theorem absorbent_univ : Absorbent 𝕜 (univ : Set E) := by
-  refine' fun x => ⟨1, zero_lt_one, fun a ha => _⟩
-  rw [smul_set_univ₀ (norm_pos_iff.1 <| zero_lt_one.trans_le ha)]
-  exact trivial
-#align absorbent_univ absorbent_univ
-
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
 /-- Every neighbourhood of the origin is absorbent. -/
-theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A := by
-  intro x
-  obtain ⟨w, hw₁, hw₂, hw₃⟩ := mem_nhds_iff.mp hA
-  have hc : Continuous fun t : 𝕜 => t • x := continuous_id.smul continuous_const
-  obtain ⟨r, hr₁, hr₂⟩ :=
-    Metric.isOpen_iff.mp (hw₂.preimage hc) 0 (by rwa [mem_preimage, zero_smul])
-  have hr₃ := inv_pos.mpr (half_pos hr₁)
-  refine' ⟨(r / 2)⁻¹, hr₃, fun a ha₁ => _⟩
-  have ha₂ : 0 < ‖a‖ := hr₃.trans_le ha₁
-  refine' (mem_smul_set_iff_inv_smul_mem₀ (norm_pos_iff.mp ha₂) _ _).2 (hw₁ <| hr₂ _)
-  rw [Metric.mem_ball, dist_zero_right, norm_inv]
-  calc
-    ‖a‖⁻¹ ≤ r / 2 := (inv_le (half_pos hr₁) ha₂).mp ha₁
-    _ < r := half_lt_self hr₁
+theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A :=
+  absorbent_iff_inv_smul.2 fun x ↦ Filter.tendsto_inv₀_cobounded.smul tendsto_const_nhds <| by
+    rwa [zero_smul]
 #align absorbent_nhds_zero absorbent_nhds_zero
 
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
@@ -385,18 +237,7 @@ section NontriviallyNormedField
 
 variable [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {s : Set E}
 
-theorem absorbs_zero_iff : Absorbs 𝕜 s 0 ↔ (0 : E) ∈ s := by
-  refine' ⟨_, fun h => ⟨1, zero_lt_one, fun a _ => zero_subset.2 <| zero_mem_smul_set h⟩⟩
-  rintro ⟨r, hr, h⟩
-  obtain ⟨a, ha⟩ := NormedSpace.exists_lt_norm 𝕜 𝕜 r
-  have := h _ ha.le
-  rwa [zero_subset, zero_mem_smul_set_iff] at this
-  exact norm_ne_zero_iff.1 (hr.trans ha).ne'
-#align absorbs_zero_iff absorbs_zero_iff
-
-theorem Absorbent.zero_mem (hs : Absorbent 𝕜 s) : (0 : E) ∈ s :=
-  absorbs_zero_iff.1 <| absorbent_iff_forall_absorbs_singleton.1 hs _
-#align absorbent.zero_mem Absorbent.zero_mem
+theorem Absorbent.zero_mem' (hs : Absorbent 𝕜 s) : (0 : E) ∈ s := hs.zero_mem
 
 variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
 
@@ -420,9 +261,8 @@ theorem balanced_iff_neg_mem (hs : Convex ℝ s) : Balanced ℝ s ↔ ∀ ⦃x
   refine' ⟨fun h x => h.neg_mem_iff.2, fun h a ha => smul_set_subset_iff.2 fun x hx => _⟩
   rw [Real.norm_eq_abs, abs_le] at ha
   rw [show a = -((1 - a) / 2) + (a - -1) / 2 by ring, add_smul, neg_smul, ← smul_neg]
-  exact
-    hs (h hx) hx (div_nonneg (sub_nonneg_of_le ha.2) zero_le_two)
-      (div_nonneg (sub_nonneg_of_le ha.1) zero_le_two) (by ring)
+  exact hs (h hx) hx (div_nonneg (sub_nonneg_of_le ha.2) zero_le_two)
+    (div_nonneg (sub_nonneg_of_le ha.1) zero_le_two) (by ring)
 #align balanced_iff_neg_mem balanced_iff_neg_mem
 
 end Real

@@ -184,7 +184,7 @@ theorem Balanced.inter (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced
 #align balanced.inter Balanced.inter
 
 theorem balanced_iUnion {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋃ i, f i) :=
-  fun _a ha => (smul_set_Union _ _).subset.trans <| iUnion_mono fun _ => h _ _ ha
+  fun _a ha => (smul_set_iUnion _ _).subset.trans <| iUnion_mono fun _ => h _ _ ha
 #align balanced_Union balanced_iUnion
 
 theorem balanced_iUnion₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :

@@ -164,7 +164,7 @@ theorem balanced_iff_smul_mem : Balanced 𝕜 s ↔ ∀ ⦃a : 𝕜⦄, ‖a‖
   forall₂_congr fun _a _ha => smul_set_subset_iff
 #align balanced_iff_smul_mem balanced_iff_smul_mem
 
-alias balanced_iff_smul_mem ↔ Balanced.smul_mem _
+alias ⟨Balanced.smul_mem, _⟩ := balanced_iff_smul_mem
 #align balanced.smul_mem Balanced.smul_mem
 
 @[simp]

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

This has nice performance benefits.

@@ -43,7 +43,7 @@ open Set
 
 open Pointwise Topology
 
-variable {𝕜 𝕝 E : Type _} {ι : Sort _} {κ : ι → Sort _}
+variable {𝕜 𝕝 E : Type*} {ι : Sort*} {κ : ι → Sort*}
 
 section SeminormedRing
 
@@ -93,7 +93,7 @@ theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorb
     fun h => h.1.union h.2⟩
 #align absorbs_union absorbs_union
 
-theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
+theorem absorbs_iUnion_finset {ι : Type*} {t : Finset ι} {f : ι → Set E} :
     Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   classical
     induction' t using Finset.induction_on with i t _ht hi
@@ -108,7 +108,7 @@ theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
     exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
 #align absorbs_Union_finset absorbs_iUnion_finset
 
-theorem Set.Finite.absorbs_iUnion {ι : Type _} {s : Set E} {t : Set ι} {f : ι → Set E}
+theorem Set.Finite.absorbs_iUnion {ι : Type*} {s : Set E} {t : Set ι} {f : ι → Set E}
     (hi : t.Finite) : Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   lift t to Finset ι using hi
   simp only [Finset.mem_coe]

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Jean Lo. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jean Lo, Bhavik Mehta, Yaël Dillies
-
-! This file was ported from Lean 3 source module analysis.locally_convex.basic
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Convex.Basic
 import Mathlib.Analysis.Convex.Hull
 import Mathlib.Analysis.NormedSpace.Basic
 
+#align_import analysis.locally_convex.basic from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Local convexity
 

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -100,8 +100,7 @@ theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
     Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   classical
     induction' t using Finset.induction_on with i t _ht hi
-    ·
-      simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
+    · simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
         IsEmpty.forall_iff, imp_true_iff]
     rw [Finset.set_biUnion_insert, absorbs_union, hi]
     constructor <;> intro h

Changes are of the form

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

@@ -406,7 +406,7 @@ variable [Module ℝ E] [SMulCommClass ℝ 𝕜 E]
 
 theorem balanced_convexHull_of_balanced (hs : Balanced 𝕜 s) : Balanced 𝕜 (convexHull ℝ s) := by
   suffices Convex ℝ { x | ∀ a : 𝕜, ‖a‖ ≤ 1 → a • x ∈ convexHull ℝ s } by
-    rw [balanced_iff_smul_mem] at hs⊢
+    rw [balanced_iff_smul_mem] at hs ⊢
     refine' fun a ha x hx => convexHull_min _ this hx a ha
     exact fun y hy a ha => subset_convexHull ℝ s (hs ha hy)
   intro x hx y hy u v hu hv huv a ha

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -361,7 +361,7 @@ theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) :
   intro a ha
   obtain rfl | h := eq_or_ne a 0
   · rw [zero_smul_set]
-    exacts[subset_union_left _ _, ⟨0, Or.inl rfl⟩]
+    exacts [subset_union_left _ _, ⟨0, Or.inl rfl⟩]
   · rw [← image_smul, image_union]
     apply union_subset_union
     · rw [image_zero, smul_zero]

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

@@ -303,7 +303,7 @@ theorem Balanced.mem_smul_iff (hs : Balanced 𝕜 s) (h : ‖a‖ = ‖b‖) : a
   · rw [norm_zero, norm_eq_zero] at h
     rw [h]
   have ha : a ≠ 0 := norm_ne_zero_iff.1 (ne_of_eq_of_ne h <| norm_ne_zero_iff.2 hb)
-  constructor <;> intro h' <;> [rw [← inv_mul_cancel_right₀ ha b],
+  constructor <;> intro h' <;> [rw [← inv_mul_cancel_right₀ ha b];
       rw [← inv_mul_cancel_right₀ hb a]] <;>
     · rw [← smul_eq_mul, smul_assoc]
       refine' hs.smul_mem _ h'

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>

@@ -96,28 +96,28 @@ theorem absorbs_union : Absorbs 𝕜 s (u ∪ v) ↔ Absorbs 𝕜 s u ∧ Absorb
     fun h => h.1.union h.2⟩
 #align absorbs_union absorbs_union
 
-theorem absorbs_unionᵢ_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
+theorem absorbs_iUnion_finset {ι : Type _} {t : Finset ι} {f : ι → Set E} :
     Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   classical
     induction' t using Finset.induction_on with i t _ht hi
     ·
-      simp only [Finset.not_mem_empty, Set.unionᵢ_false, Set.unionᵢ_empty, absorbs_empty,
+      simp only [Finset.not_mem_empty, Set.iUnion_false, Set.iUnion_empty, absorbs_empty,
         IsEmpty.forall_iff, imp_true_iff]
-    rw [Finset.set_bunionᵢ_insert, absorbs_union, hi]
+    rw [Finset.set_biUnion_insert, absorbs_union, hi]
     constructor <;> intro h
     · refine' fun _ hi' => (Finset.mem_insert.mp hi').elim _ (h.2 _)
       exact fun hi'' => by
         rw [hi'']
         exact h.1
     exact ⟨h i (Finset.mem_insert_self i t), fun i' hi' => h i' (Finset.mem_insert_of_mem hi')⟩
-#align absorbs_Union_finset absorbs_unionᵢ_finset
+#align absorbs_Union_finset absorbs_iUnion_finset
 
-theorem Set.Finite.absorbs_unionᵢ {ι : Type _} {s : Set E} {t : Set ι} {f : ι → Set E}
+theorem Set.Finite.absorbs_iUnion {ι : Type _} {s : Set E} {t : Set ι} {f : ι → Set E}
     (hi : t.Finite) : Absorbs 𝕜 s (⋃ i ∈ t, f i) ↔ ∀ i ∈ t, Absorbs 𝕜 s (f i) := by
   lift t to Finset ι using hi
   simp only [Finset.mem_coe]
-  exact absorbs_unionᵢ_finset
-#align set.finite.absorbs_Union Set.Finite.absorbs_unionᵢ
+  exact absorbs_iUnion_finset
+#align set.finite.absorbs_Union Set.Finite.absorbs_iUnion
 
 variable (𝕜)
 
@@ -151,8 +151,8 @@ theorem absorbent_iff_nonneg_lt :
 
 theorem Absorbent.absorbs_finite {s : Set E} (hs : Absorbent 𝕜 s) {v : Set E} (hv : v.Finite) :
     Absorbs 𝕜 s v := by
-  rw [← Set.bunionᵢ_of_singleton v]
-  exact hv.absorbs_unionᵢ.mpr fun _ _ => hs.absorbs
+  rw [← Set.biUnion_of_singleton v]
+  exact hv.absorbs_iUnion.mpr fun _ _ => hs.absorbs
 #align absorbent.absorbs_finite Absorbent.absorbs_finite
 
 variable (𝕜)
@@ -187,23 +187,23 @@ theorem Balanced.inter (hA : Balanced 𝕜 A) (hB : Balanced 𝕜 B) : Balanced
   smul_set_inter_subset.trans <| inter_subset_inter (hA _ ha) <| hB _ ha
 #align balanced.inter Balanced.inter
 
-theorem balanced_unionᵢ {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋃ i, f i) :=
-  fun _a ha => (smul_set_Union _ _).subset.trans <| unionᵢ_mono fun _ => h _ _ ha
-#align balanced_Union balanced_unionᵢ
+theorem balanced_iUnion {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋃ i, f i) :=
+  fun _a ha => (smul_set_Union _ _).subset.trans <| iUnion_mono fun _ => h _ _ ha
+#align balanced_Union balanced_iUnion
 
-theorem balanced_unionᵢ₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
+theorem balanced_iUnion₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋃ (i) (j), f i j) :=
-  balanced_unionᵢ fun _ => balanced_unionᵢ <| h _
-#align balanced_Union₂ balanced_unionᵢ₂
+  balanced_iUnion fun _ => balanced_iUnion <| h _
+#align balanced_Union₂ balanced_iUnion₂
 
-theorem balanced_interᵢ {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋂ i, f i) :=
-  fun _a ha => (smul_set_interᵢ_subset _ _).trans <| interᵢ_mono fun _ => h _ _ ha
-#align balanced_Inter balanced_interᵢ
+theorem balanced_iInter {f : ι → Set E} (h : ∀ i, Balanced 𝕜 (f i)) : Balanced 𝕜 (⋂ i, f i) :=
+  fun _a ha => (smul_set_iInter_subset _ _).trans <| iInter_mono fun _ => h _ _ ha
+#align balanced_Inter balanced_iInter
 
-theorem balanced_interᵢ₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
+theorem balanced_iInter₂ {f : ∀ i, κ i → Set E} (h : ∀ i j, Balanced 𝕜 (f i j)) :
     Balanced 𝕜 (⋂ (i) (j), f i j) :=
-  balanced_interᵢ fun _ => balanced_interᵢ <| h _
-#align balanced_Inter₂ balanced_interᵢ₂
+  balanced_iInter fun _ => balanced_iInter <| h _
+#align balanced_Inter₂ balanced_iInter₂
 
 variable [SMul 𝕝 E] [SMulCommClass 𝕜 𝕝 E]
 

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".

@@ -237,8 +237,8 @@ theorem Balanced.add (hs : Balanced 𝕜 s) (ht : Balanced 𝕜 t) : Balanced 
   (smul_add _ _ _).subset.trans <| add_subset_add (hs _ ha) <| ht _ ha
 #align balanced.add Balanced.add
 
-theorem Absorbs.sub (h₁ : Absorbs 𝕜 s₁ t₁) (h₂ : Absorbs 𝕜 s₂ t₂) : Absorbs 𝕜 (s₁ - s₂) (t₁ - t₂) :=
-  by
+theorem Absorbs.sub (h₁ : Absorbs 𝕜 s₁ t₁) (h₂ : Absorbs 𝕜 s₂ t₂) :
+    Absorbs 𝕜 (s₁ - s₂) (t₁ - t₂) := by
   simp_rw [sub_eq_add_neg]
   exact h₁.add h₂.neg
 #align absorbs.sub Absorbs.sub
@@ -356,8 +356,8 @@ theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A := by
 #align absorbent_nhds_zero absorbent_nhds_zero
 
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
-theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0 : Set E) ∪ interior A) :=
-  by
+theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) :
+    Balanced 𝕜 ((0 : Set E) ∪ interior A) := by
   intro a ha
   obtain rfl | h := eq_or_ne a 0
   · rw [zero_smul_set]

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -353,7 +353,6 @@ theorem absorbent_nhds_zero (hA : A ∈ 𝓝 (0 : E)) : Absorbent 𝕜 A := by
   calc
     ‖a‖⁻¹ ≤ r / 2 := (inv_le (half_pos hr₁) ha₂).mp ha₁
     _ < r := half_lt_self hr₁
-
 #align absorbent_nhds_zero absorbent_nhds_zero
 
 /-- The union of `{0}` with the interior of a balanced set is balanced. -/
@@ -367,11 +366,9 @@ theorem balanced_zero_union_interior (hA : Balanced 𝕜 A) : Balanced 𝕜 ((0
     apply union_subset_union
     · rw [image_zero, smul_zero]
       rfl
-    ·
-      calc
+    · calc
         a • interior A ⊆ interior (a • A) := (isOpenMap_smul₀ h).image_interior_subset A
         _ ⊆ interior A := interior_mono (hA _ ha)
-
 #align balanced_zero_union_interior balanced_zero_union_interior
 
 /-- The interior of a balanced set is balanced if it contains the origin. -/