analysis.locally_convex.bounded ⟷ Mathlib.Analysis.LocallyConvex.Bounded

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

@@ -150,7 +150,7 @@ theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ]
   have hanz : a ≠ 0 := norm_pos_iff.mp (hrpos.trans_le ha)
   have : σ'.symm a ≠ 0 := (map_ne_zero σ'.symm.to_ring_hom).mpr hanz
   change _ ⊆ σ _ • _
-  rw [Set.image_subset_iff, preimage_smul_setₛₗ _ _ _ f this.is_unit]
+  rw [Set.image_subset_iff, preimage_smul_setₛₗ_of_units _ _ _ f this.is_unit]
   refine' hr (σ'.symm a) _
   rwa [σ'_symm_iso.norm_map_of_map_zero (map_zero _)]
 #align bornology.is_vonN_bounded.image Bornology.IsVonNBounded.image

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
-import Analysis.LocallyConvex.Basic
+import Topology.Bornology.Absorbs
 import Analysis.LocallyConvex.BalancedCoreHull
 import Analysis.Seminorm
 import Topology.Bornology.Basic

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

@@ -142,7 +142,7 @@ theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ]
   have σ_iso : Isometry σ := AddMonoidHomClass.isometry_of_norm σ fun x => RingHomIsometric.is_iso
   have σ'_symm_iso : Isometry σ'.symm := σ_iso.right_inv σ'.right_inv
   have f_tendsto_zero := f.continuous.tendsto 0
-  rw [map_zero] at f_tendsto_zero 
+  rw [map_zero] at f_tendsto_zero
   intro V hV
   rcases hs (f_tendsto_zero hV) with ⟨r, hrpos, hr⟩
   refine' ⟨r, hrpos, fun a ha => _⟩
@@ -173,7 +173,7 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
   filter_upwards [hxS, hε _ (Metric.ball_mem_nhds 0 <| inv_pos.mpr r_pos)] with n hnS hnr
   by_cases this : ε n = 0
   · simp [this, mem_of_mem_nhds hV]
-  · rw [mem_preimage, mem_ball_zero_iff, lt_inv (norm_pos_iff.mpr this) r_pos, ← norm_inv] at hnr 
+  · rw [mem_preimage, mem_ball_zero_iff, lt_inv (norm_pos_iff.mpr this) r_pos, ← norm_inv] at hnr
     rw [mem_preimage, Pi.smul_apply', ← Set.mem_inv_smul_set_iff₀ this]
     exact hrS _ hnr.le hnS
 #align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zero
@@ -190,12 +190,12 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V :=
     by
     filter_upwards [hε] with n hn
-    rw [Absorbs] at hVS 
-    push_neg at hVS 
+    rw [Absorbs] at hVS
+    push_neg at hVS
     rcases hVS _ (norm_pos_iff.mpr <| inv_ne_zero hn) with ⟨a, haε, haS⟩
     rcases set.not_subset.mp haS with ⟨x, hxS, hx⟩
     refine' ⟨⟨x, hxS⟩, fun hnx => _⟩
-    rw [← Set.mem_inv_smul_set_iff₀ hn] at hnx 
+    rw [← Set.mem_inv_smul_set_iff₀ hn] at hnx
     exact hx (hVb.smul_mono haε hnx)
   rcases this.choice with ⟨x, hx⟩
   refine' Filter.frequently_false l (Filter.Eventually.frequently _)
@@ -280,13 +280,13 @@ variable [UniformSpace E] [UniformAddGroup E] [ContinuousSMul 𝕜 E]
 theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
     Bornology.IsVonNBounded 𝕜 s :=
   by
-  rw [totallyBounded_iff_subset_finite_iUnion_nhds_zero] at hs 
+  rw [totallyBounded_iff_subset_finite_iUnion_nhds_zero] at hs
   intro U hU
   have h : Filter.Tendsto (fun x : E × E => x.fst + x.snd) (𝓝 (0, 0)) (𝓝 ((0 : E) + (0 : E))) :=
     tendsto_add
-  rw [add_zero] at h 
+  rw [add_zero] at h
   have h' := (nhds_basis_balanced 𝕜 E).Prod (nhds_basis_balanced 𝕜 E)
-  simp_rw [← nhds_prod_eq, id.def] at h' 
+  simp_rw [← nhds_prod_eq, id.def] at h'
   rcases h.basis_left h' U hU with ⟨x, hx, h''⟩
   rcases hs x.snd hx.2.1 with ⟨t, ht, hs⟩
   refine' Absorbs.mono_right _ hs
@@ -335,7 +335,7 @@ theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Borno
     rcases NormedField.exists_lt_norm 𝕜 ρ with ⟨a, ha⟩
     specialize hρball a ha.le
     rw [← ball_normSeminorm 𝕜 E, Seminorm.smul_ball_zero (norm_pos_iff.1 <| hρ.trans ha),
-      ball_normSeminorm, mul_one] at hρball 
+      ball_normSeminorm, mul_one] at hρball
     exact ⟨‖a‖, hρball.trans Metric.ball_subset_closedBall⟩
   · exact fun ⟨C, hC⟩ => (is_vonN_bounded_closed_ball 𝕜 E C).Subset hC
 #align normed_space.is_vonN_bounded_iff NormedSpace.isVonNBounded_iff
@@ -351,7 +351,7 @@ theorem isVonNBounded_iff' (s : Set E) :
 #print NormedSpace.image_isVonNBounded_iff /-
 theorem image_isVonNBounded_iff (f : E' → E) (s : Set E') :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∃ r : ℝ, ∀ (x : E') (hx : x ∈ s), ‖f x‖ ≤ r := by
-  simp_rw [is_vonN_bounded_iff', Set.ball_image_iff]
+  simp_rw [is_vonN_bounded_iff', Set.forall_mem_image]
 #align normed_space.image_is_vonN_bounded_iff NormedSpace.image_isVonNBounded_iff
 -/
 

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

@@ -73,7 +73,7 @@ variable (E)
 
 #print Bornology.isVonNBounded_empty /-
 @[simp]
-theorem isVonNBounded_empty : IsVonNBounded 𝕜 (∅ : Set E) := fun _ _ => absorbs_empty
+theorem isVonNBounded_empty : IsVonNBounded 𝕜 (∅ : Set E) := fun _ _ => Absorbs.empty
 #align bornology.is_vonN_bounded_empty Bornology.isVonNBounded_empty
 -/
 

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

@@ -85,14 +85,14 @@ theorem isVonNBounded_iff (s : Set E) : IsVonNBounded 𝕜 s ↔ ∀ V ∈ 𝓝
 #align bornology.is_vonN_bounded_iff Bornology.isVonNBounded_iff
 -/
 
-#print Filter.HasBasis.isVonNBounded_basis_iff /-
-theorem Filter.HasBasis.isVonNBounded_basis_iff {q : ι → Prop} {s : ι → Set E} {A : Set E}
+#print Filter.HasBasis.isVonNBounded_iff /-
+theorem Filter.HasBasis.isVonNBounded_iff {q : ι → Prop} {s : ι → Set E} {A : Set E}
     (h : (𝓝 (0 : E)).HasBasis q s) : IsVonNBounded 𝕜 A ↔ ∀ (i) (hi : q i), Absorbs 𝕜 (s i) A :=
   by
   refine' ⟨fun hA i hi => hA (h.mem_of_mem hi), fun hA V hV => _⟩
   rcases h.mem_iff.mp hV with ⟨i, hi, hV⟩
   exact (hA i hi).mono_left hV
-#align filter.has_basis.is_vonN_bounded_basis_iff Filter.HasBasis.isVonNBounded_basis_iff
+#align filter.has_basis.is_vonN_bounded_basis_iff Filter.HasBasis.isVonNBounded_iff
 -/
 
 #print Bornology.IsVonNBounded.subset /-
@@ -184,7 +184,7 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
     (hε : ∀ᶠ n in l, ε n ≠ 0) {S : Set E}
     (H : ∀ x : ι → E, (∀ n, x n ∈ S) → Tendsto (ε • x) l (𝓝 0)) : IsVonNBounded 𝕝 S :=
   by
-  rw [(nhds_basis_balanced 𝕝 E).isVonNBounded_basis_iff]
+  rw [(nhds_basis_balanced 𝕝 E).isVonNBounded_iff]
   by_contra! H'
   rcases H' with ⟨V, ⟨hV, hVb⟩, hVS⟩
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V :=

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

@@ -185,7 +185,7 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
     (H : ∀ x : ι → E, (∀ n, x n ∈ S) → Tendsto (ε • x) l (𝓝 0)) : IsVonNBounded 𝕝 S :=
   by
   rw [(nhds_basis_balanced 𝕝 E).isVonNBounded_basis_iff]
-  by_contra' H'
+  by_contra! H'
   rcases H' with ⟨V, ⟨hV, hVb⟩, hVS⟩
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V :=
     by

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

@@ -3,12 +3,12 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
-import Mathbin.Analysis.LocallyConvex.Basic
-import Mathbin.Analysis.LocallyConvex.BalancedCoreHull
-import Mathbin.Analysis.Seminorm
-import Mathbin.Topology.Bornology.Basic
-import Mathbin.Topology.Algebra.UniformGroup
-import Mathbin.Topology.UniformSpace.Cauchy
+import Analysis.LocallyConvex.Basic
+import Analysis.LocallyConvex.BalancedCoreHull
+import Analysis.Seminorm
+import Topology.Bornology.Basic
+import Topology.Algebra.UniformGroup
+import Topology.UniformSpace.Cauchy
 
 #align_import analysis.locally_convex.bounded from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
 

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

@@ -328,7 +328,7 @@ theorem isVonNBounded_closedBall (r : ℝ) :
 #print NormedSpace.isVonNBounded_iff /-
 theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Bornology.IsBounded s :=
   by
-  rw [← Metric.bounded_iff_isBounded, Metric.bounded_iff_subset_ball (0 : E)]
+  rw [← Metric.isBounded_iff_isBounded, Metric.isBounded_iff_subset_closedBall (0 : E)]
   constructor
   · intro h
     rcases h (Metric.ball_mem_nhds 0 zero_lt_one) with ⟨ρ, hρ, hρball⟩
@@ -344,7 +344,7 @@ theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Borno
 #print NormedSpace.isVonNBounded_iff' /-
 theorem isVonNBounded_iff' (s : Set E) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∃ r : ℝ, ∀ (x : E) (hx : x ∈ s), ‖x‖ ≤ r := by
-  rw [NormedSpace.isVonNBounded_iff, ← Metric.bounded_iff_isBounded, bounded_iff_forall_norm_le]
+  rw [NormedSpace.isVonNBounded_iff, ← Metric.isBounded_iff_isBounded, isBounded_iff_forall_norm_le]
 #align normed_space.is_vonN_bounded_iff' NormedSpace.isVonNBounded_iff'
 -/
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module analysis.locally_convex.bounded
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.LocallyConvex.Basic
 import Mathbin.Analysis.LocallyConvex.BalancedCoreHull
@@ -15,6 +10,8 @@ import Mathbin.Topology.Bornology.Basic
 import Mathbin.Topology.Algebra.UniformGroup
 import Mathbin.Topology.UniformSpace.Cauchy
 
+#align_import analysis.locally_convex.bounded from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 # Von Neumann Boundedness
 

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

@@ -74,9 +74,11 @@ def IsVonNBounded (s : Set E) : Prop :=
 
 variable (E)
 
+#print Bornology.isVonNBounded_empty /-
 @[simp]
 theorem isVonNBounded_empty : IsVonNBounded 𝕜 (∅ : Set E) := fun _ _ => absorbs_empty
 #align bornology.is_vonN_bounded_empty Bornology.isVonNBounded_empty
+-/
 
 variable {𝕜 E}
 
@@ -86,6 +88,7 @@ theorem isVonNBounded_iff (s : Set E) : IsVonNBounded 𝕜 s ↔ ∀ V ∈ 𝓝
 #align bornology.is_vonN_bounded_iff Bornology.isVonNBounded_iff
 -/
 
+#print Filter.HasBasis.isVonNBounded_basis_iff /-
 theorem Filter.HasBasis.isVonNBounded_basis_iff {q : ι → Prop} {s : ι → Set E} {A : Set E}
     (h : (𝓝 (0 : E)).HasBasis q s) : IsVonNBounded 𝕜 A ↔ ∀ (i) (hi : q i), Absorbs 𝕜 (s i) A :=
   by
@@ -93,6 +96,7 @@ theorem Filter.HasBasis.isVonNBounded_basis_iff {q : ι → Prop} {s : ι → Se
   rcases h.mem_iff.mp hV with ⟨i, hi, hV⟩
   exact (hA i hi).mono_left hV
 #align filter.has_basis.is_vonN_bounded_basis_iff Filter.HasBasis.isVonNBounded_basis_iff
+-/
 
 #print Bornology.IsVonNBounded.subset /-
 /-- Subsets of bounded sets are bounded. -/
@@ -101,10 +105,12 @@ theorem IsVonNBounded.subset {s₁ s₂ : Set E} (h : s₁ ⊆ s₂) (hs₂ : Is
 #align bornology.is_vonN_bounded.subset Bornology.IsVonNBounded.subset
 -/
 
+#print Bornology.IsVonNBounded.union /-
 /-- The union of two bounded sets is bounded. -/
 theorem IsVonNBounded.union {s₁ s₂ : Set E} (hs₁ : IsVonNBounded 𝕜 s₁) (hs₂ : IsVonNBounded 𝕜 s₂) :
     IsVonNBounded 𝕜 (s₁ ∪ s₂) := fun V hV => (hs₁ hV).union (hs₂ hV)
 #align bornology.is_vonN_bounded.union Bornology.IsVonNBounded.union
+-/
 
 end Zero
 
@@ -114,12 +120,14 @@ section MultipleTopologies
 
 variable [SeminormedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
+#print Bornology.IsVonNBounded.of_topologicalSpace_le /-
 /-- If a topology `t'` is coarser than `t`, then any set `s` that is bounded with respect to
 `t` is bounded with respect to `t'`. -/
 theorem IsVonNBounded.of_topologicalSpace_le {t t' : TopologicalSpace E} (h : t ≤ t') {s : Set E}
     (hs : @IsVonNBounded 𝕜 E _ _ _ t s) : @IsVonNBounded 𝕜 E _ _ _ t' s := fun V hV =>
   hs <| (le_iff_nhds t t').mp h 0 hV
 #align bornology.is_vonN_bounded.of_topological_space_le Bornology.IsVonNBounded.of_topologicalSpace_le
+-/
 
 end MultipleTopologies
 
@@ -128,6 +136,7 @@ section Image
 variable {𝕜₁ 𝕜₂ : Type _} [NormedDivisionRing 𝕜₁] [NormedDivisionRing 𝕜₂] [AddCommGroup E]
   [Module 𝕜₁ E] [AddCommGroup F] [Module 𝕜₂ F] [TopologicalSpace E] [TopologicalSpace F]
 
+#print Bornology.IsVonNBounded.image /-
 /-- A continuous linear image of a bounded set is bounded. -/
 theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ] [RingHomIsometric σ] {s : Set E}
     (hs : IsVonNBounded 𝕜₁ s) (f : E →SL[σ] F) : IsVonNBounded 𝕜₂ (f '' s) :=
@@ -148,6 +157,7 @@ theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ]
   refine' hr (σ'.symm a) _
   rwa [σ'_symm_iso.norm_map_of_map_zero (map_zero _)]
 #align bornology.is_vonN_bounded.image Bornology.IsVonNBounded.image
+-/
 
 end Image
 
@@ -156,6 +166,7 @@ section sequence
 variable {𝕝 : Type _} [NormedField 𝕜] [NontriviallyNormedField 𝕝] [AddCommGroup E] [Module 𝕜 E]
   [Module 𝕝 E] [TopologicalSpace E] [ContinuousSMul 𝕝 E]
 
+#print Bornology.IsVonNBounded.smul_tendsto_zero /-
 theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι → E} {l : Filter ι}
     (hS : IsVonNBounded 𝕜 S) (hxS : ∀ᶠ n in l, x n ∈ S) (hε : Tendsto ε l (𝓝 0)) :
     Tendsto (ε • x) l (𝓝 0) := by
@@ -169,7 +180,9 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
     rw [mem_preimage, Pi.smul_apply', ← Set.mem_inv_smul_set_iff₀ this]
     exact hrS _ hnr.le hnS
 #align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zero
+-/
 
+#print Bornology.isVonNBounded_of_smul_tendsto_zero /-
 theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l.ne_bot]
     (hε : ∀ᶠ n in l, ε n ≠ 0) {S : Set E}
     (H : ∀ x : ι → E, (∀ n, x n ∈ S) → Tendsto (ε • x) l (𝓝 0)) : IsVonNBounded 𝕝 S :=
@@ -192,7 +205,9 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
   filter_upwards [hx, (H (coe ∘ x) fun n => (x n).2).Eventually (eventually_mem_set.mpr hV)] using
     fun n => id
 #align bornology.is_vonN_bounded_of_smul_tendsto_zero Bornology.isVonNBounded_of_smul_tendsto_zero
+-/
 
+#print Bornology.isVonNBounded_iff_smul_tendsto_zero /-
 /-- Given any sequence `ε` of scalars which tends to `𝓝[≠] 0`, we have that a set `S` is bounded
   if and only if for any sequence `x : ℕ → S`, `ε • x` tends to 0. This actually works for any
   indexing type `ι`, but in the special case `ι = ℕ` we get the important fact that convergent
@@ -203,6 +218,7 @@ theorem isVonNBounded_iff_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [
   ⟨fun hS x hxS => hS.smul_tendsto_zero (eventually_of_forall hxS) (le_trans hε nhdsWithin_le_nhds),
     isVonNBounded_of_smul_tendsto_zero (hε self_mem_nhdsWithin)⟩
 #align bornology.is_vonN_bounded_iff_smul_tendsto_zero Bornology.isVonNBounded_iff_smul_tendsto_zero
+-/
 
 end sequence
 
@@ -212,16 +228,20 @@ variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
+#print Bornology.isVonNBounded_singleton /-
 /-- Singletons are bounded. -/
 theorem isVonNBounded_singleton (x : E) : IsVonNBounded 𝕜 ({x} : Set E) := fun V hV =>
   (absorbent_nhds_zero hV).Absorbs
 #align bornology.is_vonN_bounded_singleton Bornology.isVonNBounded_singleton
+-/
 
+#print Bornology.isVonNBounded_covers /-
 /-- The union of all bounded set is the whole space. -/
 theorem isVonNBounded_covers : ⋃₀ setOf (IsVonNBounded 𝕜) = (Set.univ : Set E) :=
   Set.eq_univ_iff_forall.mpr fun x =>
     Set.mem_sUnion.mpr ⟨{x}, isVonNBounded_singleton _, Set.mem_singleton _⟩
 #align bornology.is_vonN_bounded_covers Bornology.isVonNBounded_covers
+-/
 
 variable (𝕜 E)
 
@@ -240,11 +260,13 @@ def vonNBornology : Bornology E :=
 
 variable {E}
 
+#print Bornology.isBounded_iff_isVonNBounded /-
 @[simp]
 theorem isBounded_iff_isVonNBounded {s : Set E} :
     @IsBounded _ (vonNBornology 𝕜 E) s ↔ IsVonNBounded 𝕜 s :=
   isBounded_ofBounded_iff _
 #align bornology.is_bounded_iff_is_vonN_bounded Bornology.isBounded_iff_isVonNBounded
+-/
 
 end NormedField
 
@@ -257,6 +279,7 @@ variable (𝕜) [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
 variable [UniformSpace E] [UniformAddGroup E] [ContinuousSMul 𝕜 E]
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print TotallyBounded.isVonNBounded /-
 theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
     Bornology.IsVonNBounded 𝕜 s :=
   by
@@ -280,6 +303,7 @@ theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
   rw [← Set.singleton_vadd, vadd_eq_add]
   exact (absorbent_nhds_zero hx.1.1).Absorbs.add hx.2.2.absorbs_self
 #align totally_bounded.is_vonN_bounded TotallyBounded.isVonNBounded
+-/
 
 end UniformAddGroup
 
@@ -289,17 +313,22 @@ variable (𝕜 E) [NontriviallyNormedField 𝕜] [SeminormedAddCommGroup E] [Nor
 
 namespace NormedSpace
 
+#print NormedSpace.isVonNBounded_ball /-
 theorem isVonNBounded_ball (r : ℝ) : Bornology.IsVonNBounded 𝕜 (Metric.ball (0 : E) r) :=
   by
   rw [metric.nhds_basis_ball.is_vonN_bounded_basis_iff, ← ball_normSeminorm 𝕜 E]
   exact fun ε hε => (normSeminorm 𝕜 E).ball_zero_absorbs_ball_zero hε
 #align normed_space.is_vonN_bounded_ball NormedSpace.isVonNBounded_ball
+-/
 
+#print NormedSpace.isVonNBounded_closedBall /-
 theorem isVonNBounded_closedBall (r : ℝ) :
     Bornology.IsVonNBounded 𝕜 (Metric.closedBall (0 : E) r) :=
   (isVonNBounded_ball 𝕜 E (r + 1)).Subset (Metric.closedBall_subset_ball <| by linarith)
 #align normed_space.is_vonN_bounded_closed_ball NormedSpace.isVonNBounded_closedBall
+-/
 
+#print NormedSpace.isVonNBounded_iff /-
 theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Bornology.IsBounded s :=
   by
   rw [← Metric.bounded_iff_isBounded, Metric.bounded_iff_subset_ball (0 : E)]
@@ -313,16 +342,21 @@ theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Borno
     exact ⟨‖a‖, hρball.trans Metric.ball_subset_closedBall⟩
   · exact fun ⟨C, hC⟩ => (is_vonN_bounded_closed_ball 𝕜 E C).Subset hC
 #align normed_space.is_vonN_bounded_iff NormedSpace.isVonNBounded_iff
+-/
 
+#print NormedSpace.isVonNBounded_iff' /-
 theorem isVonNBounded_iff' (s : Set E) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∃ r : ℝ, ∀ (x : E) (hx : x ∈ s), ‖x‖ ≤ r := by
   rw [NormedSpace.isVonNBounded_iff, ← Metric.bounded_iff_isBounded, bounded_iff_forall_norm_le]
 #align normed_space.is_vonN_bounded_iff' NormedSpace.isVonNBounded_iff'
+-/
 
+#print NormedSpace.image_isVonNBounded_iff /-
 theorem image_isVonNBounded_iff (f : E' → E) (s : Set E') :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∃ r : ℝ, ∀ (x : E') (hx : x ∈ s), ‖f x‖ ≤ r := by
   simp_rw [is_vonN_bounded_iff', Set.ball_image_iff]
 #align normed_space.image_is_vonN_bounded_iff NormedSpace.image_isVonNBounded_iff
+-/
 
 #print NormedSpace.vonNBornology_eq /-
 /-- In a normed space, the von Neumann bornology (`bornology.vonN_bornology`) is equal to the
@@ -338,6 +372,7 @@ theorem vonNBornology_eq : Bornology.vonNBornology 𝕜 E = PseudoMetricSpace.to
 
 variable (𝕜)
 
+#print NormedSpace.isBounded_iff_subset_smul_ball /-
 theorem isBounded_iff_subset_smul_ball {s : Set E} :
     Bornology.IsBounded s ↔ ∃ a : 𝕜, s ⊆ a • Metric.ball 0 1 :=
   by
@@ -350,7 +385,9 @@ theorem isBounded_iff_subset_smul_ball {s : Set E} :
   · rintro ⟨a, ha⟩
     exact ((is_vonN_bounded_ball 𝕜 E 1).image (a • 1 : E →L[𝕜] E)).Subset ha
 #align normed_space.is_bounded_iff_subset_smul_ball NormedSpace.isBounded_iff_subset_smul_ball
+-/
 
+#print NormedSpace.isBounded_iff_subset_smul_closedBall /-
 theorem isBounded_iff_subset_smul_closedBall {s : Set E} :
     Bornology.IsBounded s ↔ ∃ a : 𝕜, s ⊆ a • Metric.closedBall 0 1 :=
   by
@@ -361,6 +398,7 @@ theorem isBounded_iff_subset_smul_closedBall {s : Set E} :
     rintro ⟨a, ha⟩
     exact ((is_vonN_bounded_closed_ball 𝕜 E 1).image (a • 1 : E →L[𝕜] E)).Subset ha
 #align normed_space.is_bounded_iff_subset_smul_closed_ball NormedSpace.isBounded_iff_subset_smul_closedBall
+-/
 
 end NormedSpace
 

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

@@ -162,7 +162,7 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
   rw [tendsto_def] at *
   intro V hV
   rcases hS hV with ⟨r, r_pos, hrS⟩
-  filter_upwards [hxS, hε _ (Metric.ball_mem_nhds 0 <| inv_pos.mpr r_pos)]with n hnS hnr
+  filter_upwards [hxS, hε _ (Metric.ball_mem_nhds 0 <| inv_pos.mpr r_pos)] with n hnS hnr
   by_cases this : ε n = 0
   · simp [this, mem_of_mem_nhds hV]
   · rw [mem_preimage, mem_ball_zero_iff, lt_inv (norm_pos_iff.mpr this) r_pos, ← norm_inv] at hnr 
@@ -179,9 +179,9 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
   rcases H' with ⟨V, ⟨hV, hVb⟩, hVS⟩
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V :=
     by
-    filter_upwards [hε]with n hn
+    filter_upwards [hε] with n hn
     rw [Absorbs] at hVS 
-    push_neg  at hVS 
+    push_neg at hVS 
     rcases hVS _ (norm_pos_iff.mpr <| inv_ne_zero hn) with ⟨a, haε, haS⟩
     rcases set.not_subset.mp haS with ⟨x, hxS, hx⟩
     refine' ⟨⟨x, hxS⟩, fun hnx => _⟩
@@ -189,8 +189,8 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
     exact hx (hVb.smul_mono haε hnx)
   rcases this.choice with ⟨x, hx⟩
   refine' Filter.frequently_false l (Filter.Eventually.frequently _)
-  filter_upwards [hx,
-    (H (coe ∘ x) fun n => (x n).2).Eventually (eventually_mem_set.mpr hV)]using fun n => id
+  filter_upwards [hx, (H (coe ∘ x) fun n => (x n).2).Eventually (eventually_mem_set.mpr hV)] using
+    fun n => id
 #align bornology.is_vonN_bounded_of_smul_tendsto_zero Bornology.isVonNBounded_of_smul_tendsto_zero
 
 /-- Given any sequence `ε` of scalars which tends to `𝓝[≠] 0`, we have that a set `S` is bounded

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

@@ -136,7 +136,7 @@ theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ]
   have σ_iso : Isometry σ := AddMonoidHomClass.isometry_of_norm σ fun x => RingHomIsometric.is_iso
   have σ'_symm_iso : Isometry σ'.symm := σ_iso.right_inv σ'.right_inv
   have f_tendsto_zero := f.continuous.tendsto 0
-  rw [map_zero] at f_tendsto_zero
+  rw [map_zero] at f_tendsto_zero 
   intro V hV
   rcases hs (f_tendsto_zero hV) with ⟨r, hrpos, hr⟩
   refine' ⟨r, hrpos, fun a ha => _⟩
@@ -165,7 +165,7 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
   filter_upwards [hxS, hε _ (Metric.ball_mem_nhds 0 <| inv_pos.mpr r_pos)]with n hnS hnr
   by_cases this : ε n = 0
   · simp [this, mem_of_mem_nhds hV]
-  · rw [mem_preimage, mem_ball_zero_iff, lt_inv (norm_pos_iff.mpr this) r_pos, ← norm_inv] at hnr
+  · rw [mem_preimage, mem_ball_zero_iff, lt_inv (norm_pos_iff.mpr this) r_pos, ← norm_inv] at hnr 
     rw [mem_preimage, Pi.smul_apply', ← Set.mem_inv_smul_set_iff₀ this]
     exact hrS _ hnr.le hnS
 #align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zero
@@ -180,12 +180,12 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V :=
     by
     filter_upwards [hε]with n hn
-    rw [Absorbs] at hVS
-    push_neg  at hVS
+    rw [Absorbs] at hVS 
+    push_neg  at hVS 
     rcases hVS _ (norm_pos_iff.mpr <| inv_ne_zero hn) with ⟨a, haε, haS⟩
     rcases set.not_subset.mp haS with ⟨x, hxS, hx⟩
     refine' ⟨⟨x, hxS⟩, fun hnx => _⟩
-    rw [← Set.mem_inv_smul_set_iff₀ hn] at hnx
+    rw [← Set.mem_inv_smul_set_iff₀ hn] at hnx 
     exact hx (hVb.smul_mono haε hnx)
   rcases this.choice with ⟨x, hx⟩
   refine' Filter.frequently_false l (Filter.Eventually.frequently _)
@@ -260,13 +260,13 @@ variable [UniformSpace E] [UniformAddGroup E] [ContinuousSMul 𝕜 E]
 theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
     Bornology.IsVonNBounded 𝕜 s :=
   by
-  rw [totallyBounded_iff_subset_finite_iUnion_nhds_zero] at hs
+  rw [totallyBounded_iff_subset_finite_iUnion_nhds_zero] at hs 
   intro U hU
   have h : Filter.Tendsto (fun x : E × E => x.fst + x.snd) (𝓝 (0, 0)) (𝓝 ((0 : E) + (0 : E))) :=
     tendsto_add
-  rw [add_zero] at h
+  rw [add_zero] at h 
   have h' := (nhds_basis_balanced 𝕜 E).Prod (nhds_basis_balanced 𝕜 E)
-  simp_rw [← nhds_prod_eq, id.def] at h'
+  simp_rw [← nhds_prod_eq, id.def] at h' 
   rcases h.basis_left h' U hU with ⟨x, hx, h''⟩
   rcases hs x.snd hx.2.1 with ⟨t, ht, hs⟩
   refine' Absorbs.mono_right _ hs
@@ -309,7 +309,7 @@ theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Borno
     rcases NormedField.exists_lt_norm 𝕜 ρ with ⟨a, ha⟩
     specialize hρball a ha.le
     rw [← ball_normSeminorm 𝕜 E, Seminorm.smul_ball_zero (norm_pos_iff.1 <| hρ.trans ha),
-      ball_normSeminorm, mul_one] at hρball
+      ball_normSeminorm, mul_one] at hρball 
     exact ⟨‖a‖, hρball.trans Metric.ball_subset_closedBall⟩
   · exact fun ⟨C, hC⟩ => (is_vonN_bounded_closed_ball 𝕜 E C).Subset hC
 #align normed_space.is_vonN_bounded_iff NormedSpace.isVonNBounded_iff

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

@@ -51,7 +51,7 @@ variable {𝕜 𝕜' E E' F ι : Type _}
 
 open Set Filter
 
-open Topology Pointwise
+open scoped Topology Pointwise
 
 namespace Bornology
 

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

@@ -74,12 +74,6 @@ def IsVonNBounded (s : Set E) : Prop :=
 
 variable (E)
 
-/- warning: bornology.is_vonN_bounded_empty -> Bornology.isVonNBounded_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] [_inst_3 : Zero.{u2} E] [_inst_4 : TopologicalSpace.{u2} E], Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 (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] [_inst_3 : Zero.{u1} E] [_inst_4 : TopologicalSpace.{u1} E], Bornology.IsVonNBounded.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))
-Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_empty Bornology.isVonNBounded_emptyₓ'. -/
 @[simp]
 theorem isVonNBounded_empty : IsVonNBounded 𝕜 (∅ : Set E) := fun _ _ => absorbs_empty
 #align bornology.is_vonN_bounded_empty Bornology.isVonNBounded_empty
@@ -92,12 +86,6 @@ theorem isVonNBounded_iff (s : Set E) : IsVonNBounded 𝕜 s ↔ ∀ V ∈ 𝓝
 #align bornology.is_vonN_bounded_iff Bornology.isVonNBounded_iff
 -/
 
-/- warning: filter.has_basis.is_vonN_bounded_basis_iff -> Filter.HasBasis.isVonNBounded_basis_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] [_inst_3 : Zero.{u2} E] [_inst_4 : TopologicalSpace.{u2} E] {q : ι -> Prop} {s : ι -> (Set.{u2} E)} {A : Set.{u2} E}, (Filter.HasBasis.{u2, succ u3} E ι (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E _inst_3)))) q s) -> (Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 A) (forall (i : ι), (q i) -> (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 (s i) A)))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {ι : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u3} 𝕜 E] [_inst_3 : Zero.{u3} E] [_inst_4 : TopologicalSpace.{u3} E] {q : ι -> Prop} {s : ι -> (Set.{u3} E)} {A : Set.{u3} E}, (Filter.HasBasis.{u3, succ u2} E ι (nhds.{u3} E _inst_4 (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E _inst_3))) q s) -> (Iff (Bornology.IsVonNBounded.{u1, u3} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 A) (forall (i : ι), (q i) -> (Absorbs.{u1, u3} 𝕜 E _inst_1 _inst_2 (s i) A)))
-Case conversion may be inaccurate. Consider using '#align filter.has_basis.is_vonN_bounded_basis_iff Filter.HasBasis.isVonNBounded_basis_iffₓ'. -/
 theorem Filter.HasBasis.isVonNBounded_basis_iff {q : ι → Prop} {s : ι → Set E} {A : Set E}
     (h : (𝓝 (0 : E)).HasBasis q s) : IsVonNBounded 𝕜 A ↔ ∀ (i) (hi : q i), Absorbs 𝕜 (s i) A :=
   by
@@ -113,12 +101,6 @@ theorem IsVonNBounded.subset {s₁ s₂ : Set E} (h : s₁ ⊆ s₂) (hs₂ : Is
 #align bornology.is_vonN_bounded.subset Bornology.IsVonNBounded.subset
 -/
 
-/- warning: bornology.is_vonN_bounded.union -> Bornology.IsVonNBounded.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] [_inst_3 : Zero.{u2} E] [_inst_4 : TopologicalSpace.{u2} E] {s₁ : Set.{u2} E} {s₂ : Set.{u2} E}, (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 s₁) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 s₂) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) s₁ s₂))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] [_inst_3 : Zero.{u2} E] [_inst_4 : TopologicalSpace.{u2} E] {s₁ : Set.{u2} E} {s₂ : Set.{u2} E}, (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 s₁) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 s₂) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 (Union.union.{u2} (Set.{u2} E) (Set.instUnionSet.{u2} E) s₁ s₂))
-Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.union Bornology.IsVonNBounded.unionₓ'. -/
 /-- The union of two bounded sets is bounded. -/
 theorem IsVonNBounded.union {s₁ s₂ : Set E} (hs₁ : IsVonNBounded 𝕜 s₁) (hs₂ : IsVonNBounded 𝕜 s₂) :
     IsVonNBounded 𝕜 (s₁ ∪ s₂) := fun V hV => (hs₁ hV).union (hs₂ hV)
@@ -132,12 +114,6 @@ section MultipleTopologies
 
 variable [SeminormedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
-/- warning: bornology.is_vonN_bounded.of_topological_space_le -> Bornology.IsVonNBounded.of_topologicalSpace_le 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)] {t : TopologicalSpace.{u2} E} {t' : TopologicalSpace.{u2} E}, (LE.le.{u2} (TopologicalSpace.{u2} E) (Preorder.toHasLe.{u2} (TopologicalSpace.{u2} E) (PartialOrder.toPreorder.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.partialOrder.{u2} E))) t t') -> (forall {s : Set.{u2} E}, (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) t s) -> (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) t' s))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {t : TopologicalSpace.{u2} E} {t' : TopologicalSpace.{u2} E}, (LE.le.{u2} (TopologicalSpace.{u2} E) (Preorder.toLE.{u2} (TopologicalSpace.{u2} E) (PartialOrder.toPreorder.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.instPartialOrderTopologicalSpace.{u2} E))) t t') -> (forall {s : Set.{u2} E}, (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) t s) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) t' s))
-Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.of_topological_space_le Bornology.IsVonNBounded.of_topologicalSpace_leₓ'. -/
 /-- If a topology `t'` is coarser than `t`, then any set `s` that is bounded with respect to
 `t` is bounded with respect to `t'`. -/
 theorem IsVonNBounded.of_topologicalSpace_le {t t' : TopologicalSpace E} (h : t ≤ t') {s : Set E}
@@ -152,9 +128,6 @@ section Image
 variable {𝕜₁ 𝕜₂ : Type _} [NormedDivisionRing 𝕜₁] [NormedDivisionRing 𝕜₂] [AddCommGroup E]
   [Module 𝕜₁ E] [AddCommGroup F] [Module 𝕜₂ F] [TopologicalSpace E] [TopologicalSpace F]
 
-/- warning: bornology.is_vonN_bounded.image -> Bornology.IsVonNBounded.image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.image Bornology.IsVonNBounded.imageₓ'. -/
 /-- A continuous linear image of a bounded set is bounded. -/
 theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ] [RingHomIsometric σ] {s : Set E}
     (hs : IsVonNBounded 𝕜₁ s) (f : E →SL[σ] F) : IsVonNBounded 𝕜₂ (f '' s) :=
@@ -183,9 +156,6 @@ section sequence
 variable {𝕝 : Type _} [NormedField 𝕜] [NontriviallyNormedField 𝕝] [AddCommGroup E] [Module 𝕜 E]
   [Module 𝕝 E] [TopologicalSpace E] [ContinuousSMul 𝕝 E]
 
-/- warning: bornology.is_vonN_bounded.smul_tendsto_zero -> Bornology.IsVonNBounded.smul_tendsto_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zeroₓ'. -/
 theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι → E} {l : Filter ι}
     (hS : IsVonNBounded 𝕜 S) (hxS : ∀ᶠ n in l, x n ∈ S) (hε : Tendsto ε l (𝓝 0)) :
     Tendsto (ε • x) l (𝓝 0) := by
@@ -200,9 +170,6 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
     exact hrS _ hnr.le hnS
 #align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zero
 
-/- warning: bornology.is_vonN_bounded_of_smul_tendsto_zero -> Bornology.isVonNBounded_of_smul_tendsto_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_of_smul_tendsto_zero Bornology.isVonNBounded_of_smul_tendsto_zeroₓ'. -/
 theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l.ne_bot]
     (hε : ∀ᶠ n in l, ε n ≠ 0) {S : Set E}
     (H : ∀ x : ι → E, (∀ n, x n ∈ S) → Tendsto (ε • x) l (𝓝 0)) : IsVonNBounded 𝕝 S :=
@@ -226,9 +193,6 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
     (H (coe ∘ x) fun n => (x n).2).Eventually (eventually_mem_set.mpr hV)]using fun n => id
 #align bornology.is_vonN_bounded_of_smul_tendsto_zero Bornology.isVonNBounded_of_smul_tendsto_zero
 
-/- warning: bornology.is_vonN_bounded_iff_smul_tendsto_zero -> Bornology.isVonNBounded_iff_smul_tendsto_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_iff_smul_tendsto_zero Bornology.isVonNBounded_iff_smul_tendsto_zeroₓ'. -/
 /-- Given any sequence `ε` of scalars which tends to `𝓝[≠] 0`, we have that a set `S` is bounded
   if and only if for any sequence `x : ℕ → S`, `ε • x` tends to 0. This actually works for any
   indexing type `ι`, but in the special case `ι = ℕ` we get the important fact that convergent
@@ -248,23 +212,11 @@ variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
-/- warning: bornology.is_vonN_bounded_singleton -> Bornology.isVonNBounded_singleton is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4] (x : E), Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_4 (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 : NormedField.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : TopologicalSpace.{u1} E] [_inst_5 : 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_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 _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 _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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (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_4] (x : E), Bornology.IsVonNBounded.{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_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 _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 _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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) _inst_4 (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x)
-Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_singleton Bornology.isVonNBounded_singletonₓ'. -/
 /-- Singletons are bounded. -/
 theorem isVonNBounded_singleton (x : E) : IsVonNBounded 𝕜 ({x} : Set E) := fun V hV =>
   (absorbent_nhds_zero hV).Absorbs
 #align bornology.is_vonN_bounded_singleton Bornology.isVonNBounded_singleton
 
-/- warning: bornology.is_vonN_bounded_covers -> Bornology.isVonNBounded_covers is a dubious translation:
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4], Eq.{succ u2} (Set.{u2} E) (Set.sUnion.{u2} E (setOf.{u2} (Set.{u2} E) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_4))) (Set.univ.{u2} E)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4], Eq.{succ u2} (Set.{u2} E) (Set.sUnion.{u2} E (setOf.{u2} (Set.{u2} E) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_4))) (Set.univ.{u2} E)
-Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_covers Bornology.isVonNBounded_coversₓ'. -/
 /-- The union of all bounded set is the whole space. -/
 theorem isVonNBounded_covers : ⋃₀ setOf (IsVonNBounded 𝕜) = (Set.univ : Set E) :=
   Set.eq_univ_iff_forall.mpr fun x =>
@@ -288,12 +240,6 @@ def vonNBornology : Bornology E :=
 
 variable {E}
 
-/- warning: bornology.is_bounded_iff_is_vonN_bounded -> Bornology.isBounded_iff_isVonNBounded is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4] {s : Set.{u2} E}, Iff (Bornology.IsBounded.{u2} E (Bornology.vonNBornology.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5) s) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_4 s)
-but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4] {s : Set.{u2} E}, Iff (Bornology.IsBounded.{u2} E (Bornology.vonNBornology.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5) s) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_4 s)
-Case conversion may be inaccurate. Consider using '#align bornology.is_bounded_iff_is_vonN_bounded Bornology.isBounded_iff_isVonNBoundedₓ'. -/
 @[simp]
 theorem isBounded_iff_isVonNBounded {s : Set E} :
     @IsBounded _ (vonNBornology 𝕜 E) s ↔ IsVonNBounded 𝕜 s :=
@@ -310,12 +256,6 @@ variable (𝕜) [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [UniformSpace E] [UniformAddGroup E] [ContinuousSMul 𝕜 E]
 
-/- warning: totally_bounded.is_vonN_bounded -> TotallyBounded.isVonNBounded is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : UniformSpace.{u2} E] [_inst_5 : UniformAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_6 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u2} E _inst_4)] {s : Set.{u2} E}, (TotallyBounded.{u2} E _inst_4 s) -> (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (UniformSpace.toTopologicalSpace.{u2} E _inst_4) s)
-but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : UniformSpace.{u2} E] [_inst_5 : UniformAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_6 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u2} E _inst_4)] {s : Set.{u2} E}, (TotallyBounded.{u2} E _inst_4 s) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (UniformSpace.toTopologicalSpace.{u2} E _inst_4) s)
-Case conversion may be inaccurate. Consider using '#align totally_bounded.is_vonN_bounded TotallyBounded.isVonNBoundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
     Bornology.IsVonNBounded 𝕜 s :=
@@ -349,35 +289,17 @@ variable (𝕜 E) [NontriviallyNormedField 𝕜] [SeminormedAddCommGroup E] [Nor
 
 namespace NormedSpace
 
-/- warning: normed_space.is_vonN_bounded_ball -> NormedSpace.isVonNBounded_ball is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] (r : Real), Bornology.IsVonNBounded.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (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 (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2))))))))) r)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align normed_space.is_vonN_bounded_ball NormedSpace.isVonNBounded_ballₓ'. -/
 theorem isVonNBounded_ball (r : ℝ) : Bornology.IsVonNBounded 𝕜 (Metric.ball (0 : E) r) :=
   by
   rw [metric.nhds_basis_ball.is_vonN_bounded_basis_iff, ← ball_normSeminorm 𝕜 E]
   exact fun ε hε => (normSeminorm 𝕜 E).ball_zero_absorbs_ball_zero hε
 #align normed_space.is_vonN_bounded_ball NormedSpace.isVonNBounded_ball
 
-/- warning: normed_space.is_vonN_bounded_closed_ball -> NormedSpace.isVonNBounded_closedBall is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align normed_space.is_vonN_bounded_closed_ball NormedSpace.isVonNBounded_closedBallₓ'. -/
 theorem isVonNBounded_closedBall (r : ℝ) :
     Bornology.IsVonNBounded 𝕜 (Metric.closedBall (0 : E) r) :=
   (isVonNBounded_ball 𝕜 E (r + 1)).Subset (Metric.closedBall_subset_ball <| by linarith)
 #align normed_space.is_vonN_bounded_closed_ball NormedSpace.isVonNBounded_closedBall
 
-/- warning: normed_space.is_vonN_bounded_iff -> NormedSpace.isVonNBounded_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align normed_space.is_vonN_bounded_iff NormedSpace.isVonNBounded_iffₓ'. -/
 theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Bornology.IsBounded s :=
   by
   rw [← Metric.bounded_iff_isBounded, Metric.bounded_iff_subset_ball (0 : E)]
@@ -392,23 +314,11 @@ theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Borno
   · exact fun ⟨C, hC⟩ => (is_vonN_bounded_closed_ball 𝕜 E C).Subset hC
 #align normed_space.is_vonN_bounded_iff NormedSpace.isVonNBounded_iff
 
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-Case conversion may be inaccurate. Consider using '#align normed_space.is_vonN_bounded_iff' NormedSpace.isVonNBounded_iff'ₓ'. -/
 theorem isVonNBounded_iff' (s : Set E) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∃ r : ℝ, ∀ (x : E) (hx : x ∈ s), ‖x‖ ≤ r := by
   rw [NormedSpace.isVonNBounded_iff, ← Metric.bounded_iff_isBounded, bounded_iff_forall_norm_le]
 #align normed_space.is_vonN_bounded_iff' NormedSpace.isVonNBounded_iff'
 
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-Case conversion may be inaccurate. Consider using '#align normed_space.image_is_vonN_bounded_iff NormedSpace.image_isVonNBounded_iffₓ'. -/
 theorem image_isVonNBounded_iff (f : E' → E) (s : Set E') :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∃ r : ℝ, ∀ (x : E') (hx : x ∈ s), ‖f x‖ ≤ r := by
   simp_rw [is_vonN_bounded_iff', Set.ball_image_iff]
@@ -428,12 +338,6 @@ theorem vonNBornology_eq : Bornology.vonNBornology 𝕜 E = PseudoMetricSpace.to
 
 variable (𝕜)
 
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-Case conversion may be inaccurate. Consider using '#align normed_space.is_bounded_iff_subset_smul_ball NormedSpace.isBounded_iff_subset_smul_ballₓ'. -/
 theorem isBounded_iff_subset_smul_ball {s : Set E} :
     Bornology.IsBounded s ↔ ∃ a : 𝕜, s ⊆ a • Metric.ball 0 1 :=
   by
@@ -447,12 +351,6 @@ theorem isBounded_iff_subset_smul_ball {s : Set E} :
     exact ((is_vonN_bounded_ball 𝕜 E 1).image (a • 1 : E →L[𝕜] E)).Subset ha
 #align normed_space.is_bounded_iff_subset_smul_ball NormedSpace.isBounded_iff_subset_smul_ball
 
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-Case conversion may be inaccurate. Consider using '#align normed_space.is_bounded_iff_subset_smul_closed_ball NormedSpace.isBounded_iff_subset_smul_closedBallₓ'. -/
 theorem isBounded_iff_subset_smul_closedBall {s : Set E} :
     Bornology.IsBounded s ↔ ∃ a : 𝕜, s ⊆ a • Metric.closedBall 0 1 :=
   by

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

@@ -153,10 +153,7 @@ variable {𝕜₁ 𝕜₂ : Type _} [NormedDivisionRing 𝕜₁] [NormedDivision
   [Module 𝕜₁ E] [AddCommGroup F] [Module 𝕜₂ F] [TopologicalSpace E] [TopologicalSpace F]
 
 /- warning: bornology.is_vonN_bounded.image -> Bornology.IsVonNBounded.image is a dubious translation:
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RingHomSurjective.{u3, u4} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ] [_inst_10 : RingHomIsometric.{u3, u4} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) (NormedDivisionRing.toHasNorm.{u3} 𝕜₁ _inst_1) (NormedDivisionRing.toHasNorm.{u4} 𝕜₂ _inst_2) σ] {s : Set.{u1} E}, (Bornology.IsVonNBounded.{u3, u1} 𝕜₁ E (NormedRing.toSeminormedRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1)) (SMulZeroClass.toHasSmul.{u3, u1} 𝕜₁ E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕜₁ E (MulZeroClass.toHasZero.{u3} 𝕜₁ (MulZeroOneClass.toMulZeroClass.{u3} 𝕜₁ (MonoidWithZero.toMulZeroOneClass.{u3} 𝕜₁ (Semiring.toMonoidWithZero.{u3} 𝕜₁ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜₁ E (Semiring.toMonoidWithZero.{u3} 𝕜₁ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕜₁ E (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_4)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))) _inst_7 s) -> (forall (f : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6), Bornology.IsVonNBounded.{u4, u2} 𝕜₂ F (NormedRing.toSeminormedRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2)) (SMulZeroClass.toHasSmul.{u4, u2} 𝕜₂ F (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (AddCommMonoid.toAddMonoid.{u2} F (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u4, u2} 𝕜₂ F (MulZeroClass.toHasZero.{u4} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u4} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u4} 𝕜₂ (Semiring.toMonoidWithZero.{u4} 𝕜₂ (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))))))) (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (AddCommMonoid.toAddMonoid.{u2} F (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜₂ F (Semiring.toMonoidWithZero.{u4} 𝕜₂ (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2)))) (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (AddCommMonoid.toAddMonoid.{u2} F (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)))) (Module.toMulActionWithZero.{u4, u2} 𝕜₂ F (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_6)))) (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (AddCommGroup.toAddGroup.{u2} F _inst_5))))) _inst_8 (Set.image.{u1, u2} E F (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6) (fun (_x : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6) => E -> F) (ContinuousLinearMap.toFun.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6) f) s))
-but is expected to have type
-  forall {E : Type.{u2}} {F : Type.{u1}} {𝕜₁ : Type.{u4}} {𝕜₂ : Type.{u3}} [_inst_1 : NormedDivisionRing.{u4} 𝕜₁] [_inst_2 : NormedDivisionRing.{u3} 𝕜₂] [_inst_3 : AddCommGroup.{u2} E] [_inst_4 : Module.{u4, u2} 𝕜₁ E (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_3)] [_inst_5 : AddCommGroup.{u1} F] [_inst_6 : Module.{u3, u1} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F _inst_5)] [_inst_7 : TopologicalSpace.{u2} E] [_inst_8 : TopologicalSpace.{u1} F] {σ : RingHom.{u4, u3} 𝕜₁ 𝕜₂ (Semiring.toNonAssocSemiring.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1)))) (Semiring.toNonAssocSemiring.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))))} [_inst_9 : RingHomSurjective.{u4, u3} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ] [_inst_10 : RingHomIsometric.{u4, u3} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (NormedDivisionRing.toNorm.{u4} 𝕜₁ _inst_1) (NormedDivisionRing.toNorm.{u3} 𝕜₂ _inst_2) σ] {s : Set.{u2} E}, (Bornology.IsVonNBounded.{u4, u2} 𝕜₁ E (NormedRing.toSeminormedRing.{u4} 𝕜₁ (NormedDivisionRing.toNormedRing.{u4} 𝕜₁ _inst_1)) (SMulZeroClass.toSMul.{u4, u2} 𝕜₁ E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜₁ E (MonoidWithZero.toZero.{u4} 𝕜₁ (Semiring.toMonoidWithZero.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜₁ E (Semiring.toMonoidWithZero.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜₁ E (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) _inst_4)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) _inst_7 s) -> (forall (f : ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6), Bornology.IsVonNBounded.{u3, u1} 𝕜₂ F (NormedRing.toSeminormedRing.{u3} 𝕜₂ (NormedDivisionRing.toNormedRing.{u3} 𝕜₂ _inst_2)) (SMulZeroClass.toSMul.{u3, u1} 𝕜₂ F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜₂ F (MonoidWithZero.toZero.{u3} 𝕜₂ (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜₂ F (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2)))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (Module.toMulActionWithZero.{u3, u1} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_6)))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) _inst_8 (Set.image.{u2, u1} E F (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) E F _inst_7 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6))) f) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.image Bornology.IsVonNBounded.imageₓ'. -/
 /-- A continuous linear image of a bounded set is bounded. -/
 theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ] [RingHomIsometric σ] {s : Set E}
@@ -187,10 +184,7 @@ variable {𝕝 : Type _} [NormedField 𝕜] [NontriviallyNormedField 𝕝] [AddC
   [Module 𝕝 E] [TopologicalSpace E] [ContinuousSMul 𝕝 E]
 
 /- warning: bornology.is_vonN_bounded.smul_tendsto_zero -> Bornology.IsVonNBounded.smul_tendsto_zero is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : AddCommGroup.{u2} E] [_inst_4 : 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_3)] [_inst_6 : TopologicalSpace.{u2} E] {S : Set.{u2} E} {ε : ι -> 𝕜} {x : ι -> E} {l : Filter.{u3} ι}, (Bornology.IsVonNBounded.{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_3)))) (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_3)))) (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_3)))) (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_3) _inst_4)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_3))))) _inst_6 S) -> (Filter.Eventually.{u3} ι (fun (n : ι) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (x n) S) l) -> (Filter.Tendsto.{u3, u1} ι 𝕜 ε l (nhds.{u1} 𝕜 (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)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))))))) -> (Filter.Tendsto.{u3, u2} ι E (SMul.smul.{max u3 u1, max u3 u2} (ι -> 𝕜) (ι -> E) (Pi.smul'.{u3, u1, u2} ι (fun (ᾰ : ι) => 𝕜) (fun (ᾰ : ι) => E) (fun (i : ι) => SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_3)))) (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_3)))) (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_3)))) (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_3) _inst_4))))) ε x) l (nhds.{u2} E _inst_6 (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_3))))))))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {ι : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : AddCommGroup.{u3} E] [_inst_4 : Module.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3)] [_inst_6 : TopologicalSpace.{u3} E] {S : Set.{u3} E} {ε : ι -> 𝕜} {x : ι -> E} {l : Filter.{u2} ι}, (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3) _inst_4)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) _inst_6 S) -> (Filter.Eventually.{u2} ι (fun (n : ι) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (x n) S) l) -> (Filter.Tendsto.{u2, u1} ι 𝕜 ε l (nhds.{u1} 𝕜 (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)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{u2, u3} ι E (HSMul.hSMul.{max u1 u2, max u3 u2, max u3 u2} (ι -> 𝕜) (ι -> E) (ι -> E) (instHSMul.{max u1 u2, max u3 u2} (ι -> 𝕜) (ι -> E) (Pi.smul'.{u2, u1, u3} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1071 : ι) => 𝕜) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1074 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3) _inst_4)))))) ε x) l (nhds.{u3} E _inst_6 (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3)))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zeroₓ'. -/
 theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι → E} {l : Filter ι}
     (hS : IsVonNBounded 𝕜 S) (hxS : ∀ᶠ n in l, x n ∈ S) (hε : Tendsto ε l (𝓝 0)) :
@@ -207,10 +201,7 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
 #align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zero
 
 /- warning: bornology.is_vonN_bounded_of_smul_tendsto_zero -> Bornology.isVonNBounded_of_smul_tendsto_zero is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} {ι : Type.{u2}} {𝕝 : Type.{u3}} [_inst_2 : NontriviallyNormedField.{u3} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u3, u1} 𝕝 E (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u3} 𝕝 (PseudoMetricSpace.toUniformSpace.{u3} 𝕝 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max u2 u1} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u2, u3, u1} ι (fun (ᾰ : ι) => 𝕝) (fun (ᾰ : ι) => E) (fun (i : ι) => SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5))))) ε x) l (nhds.{u1} E _inst_6 (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))))))))) -> (Bornology.IsVonNBounded.{u3, u1} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))) (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))) _inst_6 S))
-but is expected to have type
-  forall {E : Type.{u1}} {ι : Type.{u3}} {𝕝 : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u2, u1} 𝕝 E (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u3} ι} [_inst_8 : Filter.NeBot.{u3} ι l], (Filter.Eventually.{u3} ι (fun (n : ι) => Ne.{succ u2} 𝕝 (ε n) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))))) l) -> (forall {S : Set.{u1} E}, (forall (x : ι -> E), (forall (n : ι), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (x n) S) -> (Filter.Tendsto.{u3, u1} ι E (HSMul.hSMul.{max u3 u2, max u1 u3, max u1 u3} (ι -> 𝕝) (ι -> E) (ι -> E) (instHSMul.{max u3 u2, max u1 u3} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1362 : ι) => 𝕝) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1398 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))))) ε x) l (nhds.{u1} E _inst_6 (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_3)))))))))) -> (Bornology.IsVonNBounded.{u2, u1} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))) (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) _inst_6 S))
+<too large>
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_of_smul_tendsto_zero Bornology.isVonNBounded_of_smul_tendsto_zeroₓ'. -/
 theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l.ne_bot]
     (hε : ∀ᶠ n in l, ε n ≠ 0) {S : Set E}
@@ -236,10 +227,7 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
 #align bornology.is_vonN_bounded_of_smul_tendsto_zero Bornology.isVonNBounded_of_smul_tendsto_zero
 
 /- warning: bornology.is_vonN_bounded_iff_smul_tendsto_zero -> Bornology.isVonNBounded_iff_smul_tendsto_zero is a dubious translation:
-lean 3 declaration is
-  forall {E : Type.{u1}} {ι : Type.{u2}} {𝕝 : Type.{u3}} [_inst_2 : NontriviallyNormedField.{u3} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u3, u1} 𝕝 E (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u3} 𝕝 (PseudoMetricSpace.toUniformSpace.{u3} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u2} ι} [_inst_8 : Filter.NeBot.{u2} ι l], (Filter.Tendsto.{u2, u3} ι 𝕝 ε l (nhdsWithin.{u3} 𝕝 (UniformSpace.toTopologicalSpace.{u3} 𝕝 (PseudoMetricSpace.toUniformSpace.{u3} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))) (OfNat.ofNat.{u3} 𝕝 0 (OfNat.mk.{u3} 𝕝 0 (Zero.zero.{u3} 𝕝 (MulZeroClass.toHasZero.{u3} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))))))))) (HasCompl.compl.{u3} (Set.{u3} 𝕝) (BooleanAlgebra.toHasCompl.{u3} (Set.{u3} 𝕝) (Set.booleanAlgebra.{u3} 𝕝)) (Singleton.singleton.{u3, u3} 𝕝 (Set.{u3} 𝕝) (Set.hasSingleton.{u3} 𝕝) (OfNat.ofNat.{u3} 𝕝 0 (OfNat.mk.{u3} 𝕝 0 (Zero.zero.{u3} 𝕝 (MulZeroClass.toHasZero.{u3} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))))))))))))) -> (forall {S : Set.{u1} E}, Iff (Bornology.IsVonNBounded.{u3, u1} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))) (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))) _inst_6 S) (forall (x : ι -> E), (forall (n : ι), Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) (x n) S) -> (Filter.Tendsto.{u2, u1} ι E (SMul.smul.{max u2 u3, max u2 u1} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u2, u3, u1} ι (fun (ᾰ : ι) => 𝕝) (fun (ᾰ : ι) => E) (fun (i : ι) => SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5))))) ε x) l (nhds.{u1} E _inst_6 (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))))))))))
-but is expected to have type
-  forall {E : Type.{u1}} {ι : Type.{u3}} {𝕝 : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u2, u1} 𝕝 E (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u3} ι} [_inst_8 : Filter.NeBot.{u3} ι l], (Filter.Tendsto.{u3, u2} ι 𝕝 ε l (nhdsWithin.{u2} 𝕝 (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))))) (HasCompl.compl.{u2} (Set.{u2} 𝕝) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} 𝕝) (Set.instBooleanAlgebraSet.{u2} 𝕝)) (Singleton.singleton.{u2, u2} 𝕝 (Set.{u2} 𝕝) (Set.instSingletonSet.{u2} 𝕝) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))))))))) -> (forall {S : Set.{u1} E}, Iff (Bornology.IsVonNBounded.{u2, u1} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))) (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) _inst_6 S) (forall (x : ι -> E), (forall (n : ι), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (x n) S) -> (Filter.Tendsto.{u3, u1} ι E (HSMul.hSMul.{max u3 u2, max u1 u3, max u1 u3} (ι -> 𝕝) (ι -> E) (ι -> E) (instHSMul.{max u3 u2, max u1 u3} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1749 : ι) => 𝕝) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.3297 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))))) ε x) l (nhds.{u1} E _inst_6 (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_3)))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_iff_smul_tendsto_zero Bornology.isVonNBounded_iff_smul_tendsto_zeroₓ'. -/
 /-- Given any sequence `ε` of scalars which tends to `𝓝[≠] 0`, we have that a set `S` is bounded
   if and only if for any sequence `x : ℕ → S`, `ε • x` tends to 0. This actually works for any

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

@@ -134,7 +134,7 @@ variable [SeminormedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 /- warning: bornology.is_vonN_bounded.of_topological_space_le -> Bornology.IsVonNBounded.of_topologicalSpace_le 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)] {t : TopologicalSpace.{u2} E} {t' : TopologicalSpace.{u2} E}, (LE.le.{u2} (TopologicalSpace.{u2} E) (Preorder.toLE.{u2} (TopologicalSpace.{u2} E) (PartialOrder.toPreorder.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.partialOrder.{u2} E))) t t') -> (forall {s : Set.{u2} E}, (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) t s) -> (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) t' s))
+  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)] {t : TopologicalSpace.{u2} E} {t' : TopologicalSpace.{u2} E}, (LE.le.{u2} (TopologicalSpace.{u2} E) (Preorder.toHasLe.{u2} (TopologicalSpace.{u2} E) (PartialOrder.toPreorder.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.partialOrder.{u2} E))) t t') -> (forall {s : Set.{u2} E}, (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) t s) -> (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) t' s))
 but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {t : TopologicalSpace.{u2} E} {t' : TopologicalSpace.{u2} E}, (LE.le.{u2} (TopologicalSpace.{u2} E) (Preorder.toLE.{u2} (TopologicalSpace.{u2} E) (PartialOrder.toPreorder.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.instPartialOrderTopologicalSpace.{u2} E))) t t') -> (forall {s : Set.{u2} E}, (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) t s) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) t' s))
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.of_topological_space_le Bornology.IsVonNBounded.of_topologicalSpace_leₓ'. -/

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

@@ -190,7 +190,7 @@ variable {𝕝 : Type _} [NormedField 𝕜] [NontriviallyNormedField 𝕝] [AddC
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : AddCommGroup.{u2} E] [_inst_4 : 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_3)] [_inst_6 : TopologicalSpace.{u2} E] {S : Set.{u2} E} {ε : ι -> 𝕜} {x : ι -> E} {l : Filter.{u3} ι}, (Bornology.IsVonNBounded.{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_3)))) (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_3)))) (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_3)))) (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_3) _inst_4)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_3))))) _inst_6 S) -> (Filter.Eventually.{u3} ι (fun (n : ι) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (x n) S) l) -> (Filter.Tendsto.{u3, u1} ι 𝕜 ε l (nhds.{u1} 𝕜 (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)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))))))) -> (Filter.Tendsto.{u3, u2} ι E (SMul.smul.{max u3 u1, max u3 u2} (ι -> 𝕜) (ι -> E) (Pi.smul'.{u3, u1, u2} ι (fun (ᾰ : ι) => 𝕜) (fun (ᾰ : ι) => E) (fun (i : ι) => SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_3)))) (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_3)))) (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_3)))) (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_3) _inst_4))))) ε x) l (nhds.{u2} E _inst_6 (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_3))))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {ι : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : AddCommGroup.{u3} E] [_inst_4 : Module.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3)] [_inst_6 : TopologicalSpace.{u3} E] {S : Set.{u3} E} {ε : ι -> 𝕜} {x : ι -> E} {l : Filter.{u2} ι}, (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3) _inst_4)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) _inst_6 S) -> (Filter.Eventually.{u2} ι (fun (n : ι) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (x n) S) l) -> (Filter.Tendsto.{u2, u1} ι 𝕜 ε l (nhds.{u1} 𝕜 (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)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{u2, u3} ι E (HSMul.hSMul.{max u1 u2, max u3 u2, max u3 u2} (ι -> 𝕜) (ι -> E) (ι -> E) (instHSMul.{max u1 u2, max u3 u2} (ι -> 𝕜) (ι -> E) (Pi.smul'.{u2, u1, u3} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1077 : ι) => 𝕜) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1080 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3) _inst_4)))))) ε x) l (nhds.{u3} E _inst_6 (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3)))))))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {ι : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : AddCommGroup.{u3} E] [_inst_4 : Module.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3)] [_inst_6 : TopologicalSpace.{u3} E] {S : Set.{u3} E} {ε : ι -> 𝕜} {x : ι -> E} {l : Filter.{u2} ι}, (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3) _inst_4)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) _inst_6 S) -> (Filter.Eventually.{u2} ι (fun (n : ι) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (x n) S) l) -> (Filter.Tendsto.{u2, u1} ι 𝕜 ε l (nhds.{u1} 𝕜 (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)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{u2, u3} ι E (HSMul.hSMul.{max u1 u2, max u3 u2, max u3 u2} (ι -> 𝕜) (ι -> E) (ι -> E) (instHSMul.{max u1 u2, max u3 u2} (ι -> 𝕜) (ι -> E) (Pi.smul'.{u2, u1, u3} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1071 : ι) => 𝕜) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1074 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3) _inst_4)))))) ε x) l (nhds.{u3} E _inst_6 (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3)))))))))
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zeroₓ'. -/
 theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι → E} {l : Filter ι}
     (hS : IsVonNBounded 𝕜 S) (hxS : ∀ᶠ n in l, x n ∈ S) (hε : Tendsto ε l (𝓝 0)) :
@@ -210,7 +210,7 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
 lean 3 declaration is
   forall {E : Type.{u1}} {ι : Type.{u2}} {𝕝 : Type.{u3}} [_inst_2 : NontriviallyNormedField.{u3} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u3, u1} 𝕝 E (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u3} 𝕝 (PseudoMetricSpace.toUniformSpace.{u3} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u2} ι} [_inst_8 : Filter.NeBot.{u2} ι l], (Filter.Eventually.{u2} ι (fun (n : ι) => Ne.{succ u3} 𝕝 (ε n) (OfNat.ofNat.{u3} 𝕝 0 (OfNat.mk.{u3} 𝕝 0 (Zero.zero.{u3} 𝕝 (MulZeroClass.toHasZero.{u3} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))))))) l) -> (forall {S : Set.{u1} E}, (forall (x : ι -> E), (forall (n : ι), Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) (x n) S) -> (Filter.Tendsto.{u2, u1} ι E (SMul.smul.{max u2 u3, max u2 u1} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u2, u3, u1} ι (fun (ᾰ : ι) => 𝕝) (fun (ᾰ : ι) => E) (fun (i : ι) => SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5))))) ε x) l (nhds.{u1} E _inst_6 (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))))))))) -> (Bornology.IsVonNBounded.{u3, u1} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))) (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))) _inst_6 S))
 but is expected to have type
-  forall {E : Type.{u1}} {ι : Type.{u3}} {𝕝 : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u2, u1} 𝕝 E (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u3} ι} [_inst_8 : Filter.NeBot.{u3} ι l], (Filter.Eventually.{u3} ι (fun (n : ι) => Ne.{succ u2} 𝕝 (ε n) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))))) l) -> (forall {S : Set.{u1} E}, (forall (x : ι -> E), (forall (n : ι), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (x n) S) -> (Filter.Tendsto.{u3, u1} ι E (HSMul.hSMul.{max u3 u2, max u1 u3, max u1 u3} (ι -> 𝕝) (ι -> E) (ι -> E) (instHSMul.{max u3 u2, max u1 u3} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1368 : ι) => 𝕝) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1404 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))))) ε x) l (nhds.{u1} E _inst_6 (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_3)))))))))) -> (Bornology.IsVonNBounded.{u2, u1} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))) (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) _inst_6 S))
+  forall {E : Type.{u1}} {ι : Type.{u3}} {𝕝 : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u2, u1} 𝕝 E (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u3} ι} [_inst_8 : Filter.NeBot.{u3} ι l], (Filter.Eventually.{u3} ι (fun (n : ι) => Ne.{succ u2} 𝕝 (ε n) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))))) l) -> (forall {S : Set.{u1} E}, (forall (x : ι -> E), (forall (n : ι), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (x n) S) -> (Filter.Tendsto.{u3, u1} ι E (HSMul.hSMul.{max u3 u2, max u1 u3, max u1 u3} (ι -> 𝕝) (ι -> E) (ι -> E) (instHSMul.{max u3 u2, max u1 u3} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1362 : ι) => 𝕝) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1398 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))))) ε x) l (nhds.{u1} E _inst_6 (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_3)))))))))) -> (Bornology.IsVonNBounded.{u2, u1} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))) (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) _inst_6 S))
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_of_smul_tendsto_zero Bornology.isVonNBounded_of_smul_tendsto_zeroₓ'. -/
 theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l.ne_bot]
     (hε : ∀ᶠ n in l, ε n ≠ 0) {S : Set E}
@@ -239,7 +239,7 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
 lean 3 declaration is
   forall {E : Type.{u1}} {ι : Type.{u2}} {𝕝 : Type.{u3}} [_inst_2 : NontriviallyNormedField.{u3} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u3, u1} 𝕝 E (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u3} 𝕝 (PseudoMetricSpace.toUniformSpace.{u3} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u2} ι} [_inst_8 : Filter.NeBot.{u2} ι l], (Filter.Tendsto.{u2, u3} ι 𝕝 ε l (nhdsWithin.{u3} 𝕝 (UniformSpace.toTopologicalSpace.{u3} 𝕝 (PseudoMetricSpace.toUniformSpace.{u3} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))) (OfNat.ofNat.{u3} 𝕝 0 (OfNat.mk.{u3} 𝕝 0 (Zero.zero.{u3} 𝕝 (MulZeroClass.toHasZero.{u3} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))))))))) (HasCompl.compl.{u3} (Set.{u3} 𝕝) (BooleanAlgebra.toHasCompl.{u3} (Set.{u3} 𝕝) (Set.booleanAlgebra.{u3} 𝕝)) (Singleton.singleton.{u3, u3} 𝕝 (Set.{u3} 𝕝) (Set.hasSingleton.{u3} 𝕝) (OfNat.ofNat.{u3} 𝕝 0 (OfNat.mk.{u3} 𝕝 0 (Zero.zero.{u3} 𝕝 (MulZeroClass.toHasZero.{u3} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))))))))))))) -> (forall {S : Set.{u1} E}, Iff (Bornology.IsVonNBounded.{u3, u1} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))) (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))) _inst_6 S) (forall (x : ι -> E), (forall (n : ι), Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) (x n) S) -> (Filter.Tendsto.{u2, u1} ι E (SMul.smul.{max u2 u3, max u2 u1} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u2, u3, u1} ι (fun (ᾰ : ι) => 𝕝) (fun (ᾰ : ι) => E) (fun (i : ι) => SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5))))) ε x) l (nhds.{u1} E _inst_6 (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))))))))))
 but is expected to have type
-  forall {E : Type.{u1}} {ι : Type.{u3}} {𝕝 : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u2, u1} 𝕝 E (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u3} ι} [_inst_8 : Filter.NeBot.{u3} ι l], (Filter.Tendsto.{u3, u2} ι 𝕝 ε l (nhdsWithin.{u2} 𝕝 (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))))) (HasCompl.compl.{u2} (Set.{u2} 𝕝) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} 𝕝) (Set.instBooleanAlgebraSet.{u2} 𝕝)) (Singleton.singleton.{u2, u2} 𝕝 (Set.{u2} 𝕝) (Set.instSingletonSet.{u2} 𝕝) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))))))))) -> (forall {S : Set.{u1} E}, Iff (Bornology.IsVonNBounded.{u2, u1} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))) (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) _inst_6 S) (forall (x : ι -> E), (forall (n : ι), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (x n) S) -> (Filter.Tendsto.{u3, u1} ι E (HSMul.hSMul.{max u3 u2, max u1 u3, max u1 u3} (ι -> 𝕝) (ι -> E) (ι -> E) (instHSMul.{max u3 u2, max u1 u3} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1755 : ι) => 𝕝) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.3303 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))))) ε x) l (nhds.{u1} E _inst_6 (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_3)))))))))))
+  forall {E : Type.{u1}} {ι : Type.{u3}} {𝕝 : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u2, u1} 𝕝 E (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u3} ι} [_inst_8 : Filter.NeBot.{u3} ι l], (Filter.Tendsto.{u3, u2} ι 𝕝 ε l (nhdsWithin.{u2} 𝕝 (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))))) (HasCompl.compl.{u2} (Set.{u2} 𝕝) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} 𝕝) (Set.instBooleanAlgebraSet.{u2} 𝕝)) (Singleton.singleton.{u2, u2} 𝕝 (Set.{u2} 𝕝) (Set.instSingletonSet.{u2} 𝕝) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))))))))) -> (forall {S : Set.{u1} E}, Iff (Bornology.IsVonNBounded.{u2, u1} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))) (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) _inst_6 S) (forall (x : ι -> E), (forall (n : ι), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (x n) S) -> (Filter.Tendsto.{u3, u1} ι E (HSMul.hSMul.{max u3 u2, max u1 u3, max u1 u3} (ι -> 𝕝) (ι -> E) (ι -> E) (instHSMul.{max u3 u2, max u1 u3} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1749 : ι) => 𝕝) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.3297 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))))) ε x) l (nhds.{u1} E _inst_6 (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_3)))))))))))
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_iff_smul_tendsto_zero Bornology.isVonNBounded_iff_smul_tendsto_zeroₓ'. -/
 /-- Given any sequence `ε` of scalars which tends to `𝓝[≠] 0`, we have that a set `S` is bounded
   if and only if for any sequence `x : ℕ → S`, `ε • x` tends to 0. This actually works for any

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

@@ -273,14 +273,14 @@ theorem isVonNBounded_singleton (x : E) : IsVonNBounded 𝕜 ({x} : Set E) := fu
 
 /- warning: bornology.is_vonN_bounded_covers -> Bornology.isVonNBounded_covers is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4], Eq.{succ u2} (Set.{u2} E) (Set.unionₛ.{u2} E (setOf.{u2} (Set.{u2} E) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_4))) (Set.univ.{u2} E)
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4], Eq.{succ u2} (Set.{u2} E) (Set.sUnion.{u2} E (setOf.{u2} (Set.{u2} E) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_4))) (Set.univ.{u2} E)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4], Eq.{succ u2} (Set.{u2} E) (Set.unionₛ.{u2} E (setOf.{u2} (Set.{u2} E) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_4))) (Set.univ.{u2} E)
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4], Eq.{succ u2} (Set.{u2} E) (Set.sUnion.{u2} E (setOf.{u2} (Set.{u2} E) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_4))) (Set.univ.{u2} E)
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_covers Bornology.isVonNBounded_coversₓ'. -/
 /-- The union of all bounded set is the whole space. -/
 theorem isVonNBounded_covers : ⋃₀ setOf (IsVonNBounded 𝕜) = (Set.univ : Set E) :=
   Set.eq_univ_iff_forall.mpr fun x =>
-    Set.mem_unionₛ.mpr ⟨{x}, isVonNBounded_singleton _, Set.mem_singleton _⟩
+    Set.mem_sUnion.mpr ⟨{x}, isVonNBounded_singleton _, Set.mem_singleton _⟩
 #align bornology.is_vonN_bounded_covers Bornology.isVonNBounded_covers
 
 variable (𝕜 E)
@@ -332,7 +332,7 @@ Case conversion may be inaccurate. Consider using '#align totally_bounded.is_von
 theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
     Bornology.IsVonNBounded 𝕜 s :=
   by
-  rw [totallyBounded_iff_subset_finite_unionᵢ_nhds_zero] at hs
+  rw [totallyBounded_iff_subset_finite_iUnion_nhds_zero] at hs
   intro U hU
   have h : Filter.Tendsto (fun x : E × E => x.fst + x.snd) (𝓝 (0, 0)) (𝓝 ((0 : E) + (0 : E))) :=
     tendsto_add

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

@@ -156,7 +156,7 @@ variable {𝕜₁ 𝕜₂ : Type _} [NormedDivisionRing 𝕜₁] [NormedDivision
 lean 3 declaration is
   forall {E : Type.{u1}} {F : Type.{u2}} {𝕜₁ : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : NormedDivisionRing.{u3} 𝕜₁] [_inst_2 : NormedDivisionRing.{u4} 𝕜₂] [_inst_3 : AddCommGroup.{u1} E] [_inst_4 : Module.{u3, u1} 𝕜₁ E (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_5 : AddCommGroup.{u2} F] [_inst_6 : Module.{u4, u2} 𝕜₂ F (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)] [_inst_7 : TopologicalSpace.{u1} E] [_inst_8 : TopologicalSpace.{u2} F] {σ : RingHom.{u3, u4} 𝕜₁ 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u3} 𝕜₁ (Ring.toNonAssocRing.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₂ (Ring.toNonAssocRing.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))))} [_inst_9 : RingHomSurjective.{u3, u4} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ] [_inst_10 : RingHomIsometric.{u3, u4} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) (NormedDivisionRing.toHasNorm.{u3} 𝕜₁ _inst_1) (NormedDivisionRing.toHasNorm.{u4} 𝕜₂ _inst_2) σ] {s : Set.{u1} E}, (Bornology.IsVonNBounded.{u3, u1} 𝕜₁ E (NormedRing.toSeminormedRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1)) (SMulZeroClass.toHasSmul.{u3, u1} 𝕜₁ E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕜₁ E (MulZeroClass.toHasZero.{u3} 𝕜₁ (MulZeroOneClass.toMulZeroClass.{u3} 𝕜₁ (MonoidWithZero.toMulZeroOneClass.{u3} 𝕜₁ (Semiring.toMonoidWithZero.{u3} 𝕜₁ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜₁ E (Semiring.toMonoidWithZero.{u3} 𝕜₁ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕜₁ E (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_4)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))) _inst_7 s) -> (forall (f : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6), Bornology.IsVonNBounded.{u4, u2} 𝕜₂ F (NormedRing.toSeminormedRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2)) (SMulZeroClass.toHasSmul.{u4, u2} 𝕜₂ F (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (AddCommMonoid.toAddMonoid.{u2} F (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u4, u2} 𝕜₂ F (MulZeroClass.toHasZero.{u4} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u4} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u4} 𝕜₂ (Semiring.toMonoidWithZero.{u4} 𝕜₂ (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))))))) (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (AddCommMonoid.toAddMonoid.{u2} F (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜₂ F (Semiring.toMonoidWithZero.{u4} 𝕜₂ (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2)))) (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (AddCommMonoid.toAddMonoid.{u2} F (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)))) (Module.toMulActionWithZero.{u4, u2} 𝕜₂ F (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_6)))) (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (AddCommGroup.toAddGroup.{u2} F _inst_5))))) _inst_8 (Set.image.{u1, u2} E F (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6) (fun (_x : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6) => E -> F) (ContinuousLinearMap.toFun.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6) f) s))
 but is expected to have type
-  forall {E : Type.{u2}} {F : Type.{u1}} {𝕜₁ : Type.{u4}} {𝕜₂ : Type.{u3}} [_inst_1 : NormedDivisionRing.{u4} 𝕜₁] [_inst_2 : NormedDivisionRing.{u3} 𝕜₂] [_inst_3 : AddCommGroup.{u2} E] [_inst_4 : Module.{u4, u2} 𝕜₁ E (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_3)] [_inst_5 : AddCommGroup.{u1} F] [_inst_6 : Module.{u3, u1} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F _inst_5)] [_inst_7 : TopologicalSpace.{u2} E] [_inst_8 : TopologicalSpace.{u1} F] {σ : RingHom.{u4, u3} 𝕜₁ 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₁ (Ring.toNonAssocRing.{u4} 𝕜₁ (NormedRing.toRing.{u4} 𝕜₁ (NormedDivisionRing.toNormedRing.{u4} 𝕜₁ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} 𝕜₂ (Ring.toNonAssocRing.{u3} 𝕜₂ (NormedRing.toRing.{u3} 𝕜₂ (NormedDivisionRing.toNormedRing.{u3} 𝕜₂ _inst_2))))} [_inst_9 : RingHomSurjective.{u4, u3} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ] [_inst_10 : RingHomIsometric.{u4, u3} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (NormedDivisionRing.toNorm.{u4} 𝕜₁ _inst_1) (NormedDivisionRing.toNorm.{u3} 𝕜₂ _inst_2) σ] {s : Set.{u2} E}, (Bornology.IsVonNBounded.{u4, u2} 𝕜₁ E (NormedRing.toSeminormedRing.{u4} 𝕜₁ (NormedDivisionRing.toNormedRing.{u4} 𝕜₁ _inst_1)) (SMulZeroClass.toSMul.{u4, u2} 𝕜₁ E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜₁ E (MonoidWithZero.toZero.{u4} 𝕜₁ (Semiring.toMonoidWithZero.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜₁ E (Semiring.toMonoidWithZero.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜₁ E (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) _inst_4)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) _inst_7 s) -> (forall (f : ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6), Bornology.IsVonNBounded.{u3, u1} 𝕜₂ F (NormedRing.toSeminormedRing.{u3} 𝕜₂ (NormedDivisionRing.toNormedRing.{u3} 𝕜₂ _inst_2)) (SMulZeroClass.toSMul.{u3, u1} 𝕜₂ F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜₂ F (MonoidWithZero.toZero.{u3} 𝕜₂ (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜₂ F (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2)))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (Module.toMulActionWithZero.{u3, u1} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_6)))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) _inst_8 (Set.image.{u2, u1} E F (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) E F _inst_7 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6))) f) s))
+  forall {E : Type.{u2}} {F : Type.{u1}} {𝕜₁ : Type.{u4}} {𝕜₂ : Type.{u3}} [_inst_1 : NormedDivisionRing.{u4} 𝕜₁] [_inst_2 : NormedDivisionRing.{u3} 𝕜₂] [_inst_3 : AddCommGroup.{u2} E] [_inst_4 : Module.{u4, u2} 𝕜₁ E (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_3)] [_inst_5 : AddCommGroup.{u1} F] [_inst_6 : Module.{u3, u1} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F _inst_5)] [_inst_7 : TopologicalSpace.{u2} E] [_inst_8 : TopologicalSpace.{u1} F] {σ : RingHom.{u4, u3} 𝕜₁ 𝕜₂ (Semiring.toNonAssocSemiring.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1)))) (Semiring.toNonAssocSemiring.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))))} [_inst_9 : RingHomSurjective.{u4, u3} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ] [_inst_10 : RingHomIsometric.{u4, u3} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (NormedDivisionRing.toNorm.{u4} 𝕜₁ _inst_1) (NormedDivisionRing.toNorm.{u3} 𝕜₂ _inst_2) σ] {s : Set.{u2} E}, (Bornology.IsVonNBounded.{u4, u2} 𝕜₁ E (NormedRing.toSeminormedRing.{u4} 𝕜₁ (NormedDivisionRing.toNormedRing.{u4} 𝕜₁ _inst_1)) (SMulZeroClass.toSMul.{u4, u2} 𝕜₁ E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜₁ E (MonoidWithZero.toZero.{u4} 𝕜₁ (Semiring.toMonoidWithZero.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜₁ E (Semiring.toMonoidWithZero.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜₁ E (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) _inst_4)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) _inst_7 s) -> (forall (f : ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6), Bornology.IsVonNBounded.{u3, u1} 𝕜₂ F (NormedRing.toSeminormedRing.{u3} 𝕜₂ (NormedDivisionRing.toNormedRing.{u3} 𝕜₂ _inst_2)) (SMulZeroClass.toSMul.{u3, u1} 𝕜₂ F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜₂ F (MonoidWithZero.toZero.{u3} 𝕜₂ (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜₂ F (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2)))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (Module.toMulActionWithZero.{u3, u1} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_6)))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) _inst_8 (Set.image.{u2, u1} E F (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) E F _inst_7 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6))) f) s))
 Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.image Bornology.IsVonNBounded.imageₓ'. -/
 /-- A continuous linear image of a bounded set is bounded. -/
 theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ] [RingHomIsometric σ] {s : Set E}

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.locally_convex.bounded
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Topology.UniformSpace.Cauchy
 /-!
 # Von Neumann Boundedness
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines natural or von Neumann bounded sets and proves elementary properties.
 
 ## Main declarations

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

@@ -62,23 +62,39 @@ variable [SeminormedRing 𝕜] [SMul 𝕜 E] [Zero E]
 
 variable [TopologicalSpace E]
 
+#print Bornology.IsVonNBounded /-
 /-- A set `s` is von Neumann bounded if every neighborhood of 0 absorbs `s`. -/
 def IsVonNBounded (s : Set E) : Prop :=
   ∀ ⦃V⦄, V ∈ 𝓝 (0 : E) → Absorbs 𝕜 V s
 #align bornology.is_vonN_bounded Bornology.IsVonNBounded
+-/
 
 variable (E)
 
+/- warning: bornology.is_vonN_bounded_empty -> Bornology.isVonNBounded_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] [_inst_3 : Zero.{u2} E] [_inst_4 : TopologicalSpace.{u2} E], Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 (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] [_inst_3 : Zero.{u1} E] [_inst_4 : TopologicalSpace.{u1} E], Bornology.IsVonNBounded.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))
+Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_empty Bornology.isVonNBounded_emptyₓ'. -/
 @[simp]
 theorem isVonNBounded_empty : IsVonNBounded 𝕜 (∅ : Set E) := fun _ _ => absorbs_empty
 #align bornology.is_vonN_bounded_empty Bornology.isVonNBounded_empty
 
 variable {𝕜 E}
 
+#print Bornology.isVonNBounded_iff /-
 theorem isVonNBounded_iff (s : Set E) : IsVonNBounded 𝕜 s ↔ ∀ V ∈ 𝓝 (0 : E), Absorbs 𝕜 V s :=
   Iff.rfl
 #align bornology.is_vonN_bounded_iff Bornology.isVonNBounded_iff
+-/
 
+/- warning: filter.has_basis.is_vonN_bounded_basis_iff -> Filter.HasBasis.isVonNBounded_basis_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] [_inst_3 : Zero.{u2} E] [_inst_4 : TopologicalSpace.{u2} E] {q : ι -> Prop} {s : ι -> (Set.{u2} E)} {A : Set.{u2} E}, (Filter.HasBasis.{u2, succ u3} E ι (nhds.{u2} E _inst_4 (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E _inst_3)))) q s) -> (Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 A) (forall (i : ι), (q i) -> (Absorbs.{u1, u2} 𝕜 E _inst_1 _inst_2 (s i) A)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {ι : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u3} 𝕜 E] [_inst_3 : Zero.{u3} E] [_inst_4 : TopologicalSpace.{u3} E] {q : ι -> Prop} {s : ι -> (Set.{u3} E)} {A : Set.{u3} E}, (Filter.HasBasis.{u3, succ u2} E ι (nhds.{u3} E _inst_4 (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E _inst_3))) q s) -> (Iff (Bornology.IsVonNBounded.{u1, u3} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 A) (forall (i : ι), (q i) -> (Absorbs.{u1, u3} 𝕜 E _inst_1 _inst_2 (s i) A)))
+Case conversion may be inaccurate. Consider using '#align filter.has_basis.is_vonN_bounded_basis_iff Filter.HasBasis.isVonNBounded_basis_iffₓ'. -/
 theorem Filter.HasBasis.isVonNBounded_basis_iff {q : ι → Prop} {s : ι → Set E} {A : Set E}
     (h : (𝓝 (0 : E)).HasBasis q s) : IsVonNBounded 𝕜 A ↔ ∀ (i) (hi : q i), Absorbs 𝕜 (s i) A :=
   by
@@ -87,11 +103,19 @@ theorem Filter.HasBasis.isVonNBounded_basis_iff {q : ι → Prop} {s : ι → Se
   exact (hA i hi).mono_left hV
 #align filter.has_basis.is_vonN_bounded_basis_iff Filter.HasBasis.isVonNBounded_basis_iff
 
+#print Bornology.IsVonNBounded.subset /-
 /-- Subsets of bounded sets are bounded. -/
 theorem IsVonNBounded.subset {s₁ s₂ : Set E} (h : s₁ ⊆ s₂) (hs₂ : IsVonNBounded 𝕜 s₂) :
     IsVonNBounded 𝕜 s₁ := fun V hV => (hs₂ hV).mono_right h
 #align bornology.is_vonN_bounded.subset Bornology.IsVonNBounded.subset
+-/
 
+/- warning: bornology.is_vonN_bounded.union -> Bornology.IsVonNBounded.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] [_inst_3 : Zero.{u2} E] [_inst_4 : TopologicalSpace.{u2} E] {s₁ : Set.{u2} E} {s₂ : Set.{u2} E}, (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 s₁) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 s₂) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) s₁ s₂))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : SMul.{u1, u2} 𝕜 E] [_inst_3 : Zero.{u2} E] [_inst_4 : TopologicalSpace.{u2} E] {s₁ : Set.{u2} E} {s₂ : Set.{u2} E}, (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 s₁) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 s₂) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 (Union.union.{u2} (Set.{u2} E) (Set.instUnionSet.{u2} E) s₁ s₂))
+Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.union Bornology.IsVonNBounded.unionₓ'. -/
 /-- The union of two bounded sets is bounded. -/
 theorem IsVonNBounded.union {s₁ s₂ : Set E} (hs₁ : IsVonNBounded 𝕜 s₁) (hs₂ : IsVonNBounded 𝕜 s₂) :
     IsVonNBounded 𝕜 (s₁ ∪ s₂) := fun V hV => (hs₁ hV).union (hs₂ hV)
@@ -105,6 +129,12 @@ section MultipleTopologies
 
 variable [SeminormedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
+/- warning: bornology.is_vonN_bounded.of_topological_space_le -> Bornology.IsVonNBounded.of_topologicalSpace_le 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)] {t : TopologicalSpace.{u2} E} {t' : TopologicalSpace.{u2} E}, (LE.le.{u2} (TopologicalSpace.{u2} E) (Preorder.toLE.{u2} (TopologicalSpace.{u2} E) (PartialOrder.toPreorder.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.partialOrder.{u2} E))) t t') -> (forall {s : Set.{u2} E}, (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) t s) -> (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) t' s))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : SeminormedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {t : TopologicalSpace.{u2} E} {t' : TopologicalSpace.{u2} E}, (LE.le.{u2} (TopologicalSpace.{u2} E) (Preorder.toLE.{u2} (TopologicalSpace.{u2} E) (PartialOrder.toPreorder.{u2} (TopologicalSpace.{u2} E) (TopologicalSpace.instPartialOrderTopologicalSpace.{u2} E))) t t') -> (forall {s : Set.{u2} E}, (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) t s) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E _inst_1 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (SeminormedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) t' s))
+Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.of_topological_space_le Bornology.IsVonNBounded.of_topologicalSpace_leₓ'. -/
 /-- If a topology `t'` is coarser than `t`, then any set `s` that is bounded with respect to
 `t` is bounded with respect to `t'`. -/
 theorem IsVonNBounded.of_topologicalSpace_le {t t' : TopologicalSpace E} (h : t ≤ t') {s : Set E}
@@ -119,6 +149,12 @@ section Image
 variable {𝕜₁ 𝕜₂ : Type _} [NormedDivisionRing 𝕜₁] [NormedDivisionRing 𝕜₂] [AddCommGroup E]
   [Module 𝕜₁ E] [AddCommGroup F] [Module 𝕜₂ F] [TopologicalSpace E] [TopologicalSpace F]
 
+/- warning: bornology.is_vonN_bounded.image -> Bornology.IsVonNBounded.image is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} {F : Type.{u2}} {𝕜₁ : Type.{u3}} {𝕜₂ : Type.{u4}} [_inst_1 : NormedDivisionRing.{u3} 𝕜₁] [_inst_2 : NormedDivisionRing.{u4} 𝕜₂] [_inst_3 : AddCommGroup.{u1} E] [_inst_4 : Module.{u3, u1} 𝕜₁ E (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_5 : AddCommGroup.{u2} F] [_inst_6 : Module.{u4, u2} 𝕜₂ F (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)] [_inst_7 : TopologicalSpace.{u1} E] [_inst_8 : TopologicalSpace.{u2} F] {σ : RingHom.{u3, u4} 𝕜₁ 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u3} 𝕜₁ (Ring.toNonAssocRing.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₂ (Ring.toNonAssocRing.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))))} [_inst_9 : RingHomSurjective.{u3, u4} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ] [_inst_10 : RingHomIsometric.{u3, u4} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) (NormedDivisionRing.toHasNorm.{u3} 𝕜₁ _inst_1) (NormedDivisionRing.toHasNorm.{u4} 𝕜₂ _inst_2) σ] {s : Set.{u1} E}, (Bornology.IsVonNBounded.{u3, u1} 𝕜₁ E (NormedRing.toSeminormedRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1)) (SMulZeroClass.toHasSmul.{u3, u1} 𝕜₁ E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕜₁ E (MulZeroClass.toHasZero.{u3} 𝕜₁ (MulZeroOneClass.toMulZeroClass.{u3} 𝕜₁ (MonoidWithZero.toMulZeroOneClass.{u3} 𝕜₁ (Semiring.toMonoidWithZero.{u3} 𝕜₁ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜₁ E (Semiring.toMonoidWithZero.{u3} 𝕜₁ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕜₁ E (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_4)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))) _inst_7 s) -> (forall (f : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6), Bornology.IsVonNBounded.{u4, u2} 𝕜₂ F (NormedRing.toSeminormedRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2)) (SMulZeroClass.toHasSmul.{u4, u2} 𝕜₂ F (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (AddCommMonoid.toAddMonoid.{u2} F (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)))) (SMulWithZero.toSmulZeroClass.{u4, u2} 𝕜₂ F (MulZeroClass.toHasZero.{u4} 𝕜₂ (MulZeroOneClass.toMulZeroClass.{u4} 𝕜₂ (MonoidWithZero.toMulZeroOneClass.{u4} 𝕜₂ (Semiring.toMonoidWithZero.{u4} 𝕜₂ (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))))))) (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (AddCommMonoid.toAddMonoid.{u2} F (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜₂ F (Semiring.toMonoidWithZero.{u4} 𝕜₂ (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2)))) (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (AddCommMonoid.toAddMonoid.{u2} F (AddCommGroup.toAddCommMonoid.{u2} F _inst_5)))) (Module.toMulActionWithZero.{u4, u2} 𝕜₂ F (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_6)))) (AddZeroClass.toHasZero.{u2} F (AddMonoid.toAddZeroClass.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (AddCommGroup.toAddGroup.{u2} F _inst_5))))) _inst_8 (Set.image.{u1, u2} E F (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousLinearMap.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6) (fun (_x : ContinuousLinearMap.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6) => E -> F) (ContinuousLinearMap.toFun.{u3, u4, u1, u2} 𝕜₁ 𝕜₂ (Ring.toSemiring.{u3} 𝕜₁ (NormedRing.toRing.{u3} 𝕜₁ (NormedDivisionRing.toNormedRing.{u3} 𝕜₁ _inst_1))) (Ring.toSemiring.{u4} 𝕜₂ (NormedRing.toRing.{u4} 𝕜₂ (NormedDivisionRing.toNormedRing.{u4} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F _inst_5) _inst_4 _inst_6) f) s))
+but is expected to have type
+  forall {E : Type.{u2}} {F : Type.{u1}} {𝕜₁ : Type.{u4}} {𝕜₂ : Type.{u3}} [_inst_1 : NormedDivisionRing.{u4} 𝕜₁] [_inst_2 : NormedDivisionRing.{u3} 𝕜₂] [_inst_3 : AddCommGroup.{u2} E] [_inst_4 : Module.{u4, u2} 𝕜₁ E (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_3)] [_inst_5 : AddCommGroup.{u1} F] [_inst_6 : Module.{u3, u1} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F _inst_5)] [_inst_7 : TopologicalSpace.{u2} E] [_inst_8 : TopologicalSpace.{u1} F] {σ : RingHom.{u4, u3} 𝕜₁ 𝕜₂ (NonAssocRing.toNonAssocSemiring.{u4} 𝕜₁ (Ring.toNonAssocRing.{u4} 𝕜₁ (NormedRing.toRing.{u4} 𝕜₁ (NormedDivisionRing.toNormedRing.{u4} 𝕜₁ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} 𝕜₂ (Ring.toNonAssocRing.{u3} 𝕜₂ (NormedRing.toRing.{u3} 𝕜₂ (NormedDivisionRing.toNormedRing.{u3} 𝕜₂ _inst_2))))} [_inst_9 : RingHomSurjective.{u4, u3} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ] [_inst_10 : RingHomIsometric.{u4, u3} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (NormedDivisionRing.toNorm.{u4} 𝕜₁ _inst_1) (NormedDivisionRing.toNorm.{u3} 𝕜₂ _inst_2) σ] {s : Set.{u2} E}, (Bornology.IsVonNBounded.{u4, u2} 𝕜₁ E (NormedRing.toSeminormedRing.{u4} 𝕜₁ (NormedDivisionRing.toNormedRing.{u4} 𝕜₁ _inst_1)) (SMulZeroClass.toSMul.{u4, u2} 𝕜₁ E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u4, u2} 𝕜₁ E (MonoidWithZero.toZero.{u4} 𝕜₁ (Semiring.toMonoidWithZero.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u4, u2} 𝕜₁ E (Semiring.toMonoidWithZero.{u4} 𝕜₁ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) (Module.toMulActionWithZero.{u4, u2} 𝕜₁ E (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) _inst_4)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_3))))) _inst_7 s) -> (forall (f : ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6), Bornology.IsVonNBounded.{u3, u1} 𝕜₂ F (NormedRing.toSeminormedRing.{u3} 𝕜₂ (NormedDivisionRing.toNormedRing.{u3} 𝕜₂ _inst_2)) (SMulZeroClass.toSMul.{u3, u1} 𝕜₂ F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜₂ F (MonoidWithZero.toZero.{u3} 𝕜₂ (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜₂ F (Semiring.toMonoidWithZero.{u3} 𝕜₂ (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2)))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) (Module.toMulActionWithZero.{u3, u1} 𝕜₂ F (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_6)))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F _inst_5))))) _inst_8 (Set.image.{u2, u1} E F (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) E F _inst_7 _inst_8 (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u4, u3, u2, u1} (ContinuousLinearMap.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6) 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6 (ContinuousLinearMap.continuousSemilinearMapClass.{u4, u3, u2, u1} 𝕜₁ 𝕜₂ (DivisionSemiring.toSemiring.{u4} 𝕜₁ (DivisionRing.toDivisionSemiring.{u4} 𝕜₁ (NormedDivisionRing.toDivisionRing.{u4} 𝕜₁ _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜₂ (DivisionRing.toDivisionSemiring.{u3} 𝕜₂ (NormedDivisionRing.toDivisionRing.{u3} 𝕜₂ _inst_2))) σ E _inst_7 (AddCommGroup.toAddCommMonoid.{u2} E _inst_3) F _inst_8 (AddCommGroup.toAddCommMonoid.{u1} F _inst_5) _inst_4 _inst_6))) f) s))
+Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.image Bornology.IsVonNBounded.imageₓ'. -/
 /-- A continuous linear image of a bounded set is bounded. -/
 theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ] [RingHomIsometric σ] {s : Set E}
     (hs : IsVonNBounded 𝕜₁ s) (f : E →SL[σ] F) : IsVonNBounded 𝕜₂ (f '' s) :=
@@ -147,6 +183,12 @@ section sequence
 variable {𝕝 : Type _} [NormedField 𝕜] [NontriviallyNormedField 𝕝] [AddCommGroup E] [Module 𝕜 E]
   [Module 𝕝 E] [TopologicalSpace E] [ContinuousSMul 𝕝 E]
 
+/- warning: bornology.is_vonN_bounded.smul_tendsto_zero -> Bornology.IsVonNBounded.smul_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {ι : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : AddCommGroup.{u2} E] [_inst_4 : 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_3)] [_inst_6 : TopologicalSpace.{u2} E] {S : Set.{u2} E} {ε : ι -> 𝕜} {x : ι -> E} {l : Filter.{u3} ι}, (Bornology.IsVonNBounded.{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_3)))) (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_3)))) (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_3)))) (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_3) _inst_4)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_3))))) _inst_6 S) -> (Filter.Eventually.{u3} ι (fun (n : ι) => Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (x n) S) l) -> (Filter.Tendsto.{u3, u1} ι 𝕜 ε l (nhds.{u1} 𝕜 (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)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))))))))) -> (Filter.Tendsto.{u3, u2} ι E (SMul.smul.{max u3 u1, max u3 u2} (ι -> 𝕜) (ι -> E) (Pi.smul'.{u3, u1, u2} ι (fun (ᾰ : ι) => 𝕜) (fun (ᾰ : ι) => E) (fun (i : ι) => SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_3)))) (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_3)))) (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_3)))) (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_3) _inst_4))))) ε x) l (nhds.{u2} E _inst_6 (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_3))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {ι : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : AddCommGroup.{u3} E] [_inst_4 : Module.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3)] [_inst_6 : TopologicalSpace.{u3} E] {S : Set.{u3} E} {ε : ι -> 𝕜} {x : ι -> E} {l : Filter.{u2} ι}, (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3) _inst_4)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) _inst_6 S) -> (Filter.Eventually.{u2} ι (fun (n : ι) => Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) (x n) S) l) -> (Filter.Tendsto.{u2, u1} ι 𝕜 ε l (nhds.{u1} 𝕜 (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)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))))))) -> (Filter.Tendsto.{u2, u3} ι E (HSMul.hSMul.{max u1 u2, max u3 u2, max u3 u2} (ι -> 𝕜) (ι -> E) (ι -> E) (instHSMul.{max u1 u2, max u3 u2} (ι -> 𝕜) (ι -> E) (Pi.smul'.{u2, u1, u3} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1077 : ι) => 𝕜) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1080 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u3} 𝕜 E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} 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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3))))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_3) _inst_4)))))) ε x) l (nhds.{u3} E _inst_6 (OfNat.ofNat.{u3} E 0 (Zero.toOfNat0.{u3} E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_3)))))))))
+Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zeroₓ'. -/
 theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι → E} {l : Filter ι}
     (hS : IsVonNBounded 𝕜 S) (hxS : ∀ᶠ n in l, x n ∈ S) (hε : Tendsto ε l (𝓝 0)) :
     Tendsto (ε • x) l (𝓝 0) := by
@@ -161,6 +203,12 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
     exact hrS _ hnr.le hnS
 #align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zero
 
+/- warning: bornology.is_vonN_bounded_of_smul_tendsto_zero -> Bornology.isVonNBounded_of_smul_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} {ι : Type.{u2}} {𝕝 : Type.{u3}} [_inst_2 : NontriviallyNormedField.{u3} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u3, u1} 𝕝 E (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u3} 𝕝 (PseudoMetricSpace.toUniformSpace.{u3} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u2} ι} [_inst_8 : Filter.NeBot.{u2} ι l], (Filter.Eventually.{u2} ι (fun (n : ι) => Ne.{succ u3} 𝕝 (ε n) (OfNat.ofNat.{u3} 𝕝 0 (OfNat.mk.{u3} 𝕝 0 (Zero.zero.{u3} 𝕝 (MulZeroClass.toHasZero.{u3} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))))))) l) -> (forall {S : Set.{u1} E}, (forall (x : ι -> E), (forall (n : ι), Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) (x n) S) -> (Filter.Tendsto.{u2, u1} ι E (SMul.smul.{max u2 u3, max u2 u1} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u2, u3, u1} ι (fun (ᾰ : ι) => 𝕝) (fun (ᾰ : ι) => E) (fun (i : ι) => SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5))))) ε x) l (nhds.{u1} E _inst_6 (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))))))))) -> (Bornology.IsVonNBounded.{u3, u1} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))) (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))) _inst_6 S))
+but is expected to have type
+  forall {E : Type.{u1}} {ι : Type.{u3}} {𝕝 : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u2, u1} 𝕝 E (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u3} ι} [_inst_8 : Filter.NeBot.{u3} ι l], (Filter.Eventually.{u3} ι (fun (n : ι) => Ne.{succ u2} 𝕝 (ε n) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))))) l) -> (forall {S : Set.{u1} E}, (forall (x : ι -> E), (forall (n : ι), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (x n) S) -> (Filter.Tendsto.{u3, u1} ι E (HSMul.hSMul.{max u3 u2, max u1 u3, max u1 u3} (ι -> 𝕝) (ι -> E) (ι -> E) (instHSMul.{max u3 u2, max u1 u3} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1368 : ι) => 𝕝) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1404 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))))) ε x) l (nhds.{u1} E _inst_6 (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_3)))))))))) -> (Bornology.IsVonNBounded.{u2, u1} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))) (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) _inst_6 S))
+Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_of_smul_tendsto_zero Bornology.isVonNBounded_of_smul_tendsto_zeroₓ'. -/
 theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l.ne_bot]
     (hε : ∀ᶠ n in l, ε n ≠ 0) {S : Set E}
     (H : ∀ x : ι → E, (∀ n, x n ∈ S) → Tendsto (ε • x) l (𝓝 0)) : IsVonNBounded 𝕝 S :=
@@ -184,6 +232,12 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
     (H (coe ∘ x) fun n => (x n).2).Eventually (eventually_mem_set.mpr hV)]using fun n => id
 #align bornology.is_vonN_bounded_of_smul_tendsto_zero Bornology.isVonNBounded_of_smul_tendsto_zero
 
+/- warning: bornology.is_vonN_bounded_iff_smul_tendsto_zero -> Bornology.isVonNBounded_iff_smul_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} {ι : Type.{u2}} {𝕝 : Type.{u3}} [_inst_2 : NontriviallyNormedField.{u3} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u3, u1} 𝕝 E (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u3} 𝕝 (PseudoMetricSpace.toUniformSpace.{u3} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u2} ι} [_inst_8 : Filter.NeBot.{u2} ι l], (Filter.Tendsto.{u2, u3} ι 𝕝 ε l (nhdsWithin.{u3} 𝕝 (UniformSpace.toTopologicalSpace.{u3} 𝕝 (PseudoMetricSpace.toUniformSpace.{u3} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u3} 𝕝 (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))) (OfNat.ofNat.{u3} 𝕝 0 (OfNat.mk.{u3} 𝕝 0 (Zero.zero.{u3} 𝕝 (MulZeroClass.toHasZero.{u3} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))))))))) (HasCompl.compl.{u3} (Set.{u3} 𝕝) (BooleanAlgebra.toHasCompl.{u3} (Set.{u3} 𝕝) (Set.booleanAlgebra.{u3} 𝕝)) (Singleton.singleton.{u3, u3} 𝕝 (Set.{u3} 𝕝) (Set.hasSingleton.{u3} 𝕝) (OfNat.ofNat.{u3} 𝕝 0 (OfNat.mk.{u3} 𝕝 0 (Zero.zero.{u3} 𝕝 (MulZeroClass.toHasZero.{u3} 𝕝 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕝 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕝 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕝 (Ring.toNonAssocRing.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))))))))))))) -> (forall {S : Set.{u1} E}, Iff (Bornology.IsVonNBounded.{u3, u1} 𝕝 E (SeminormedCommRing.toSemiNormedRing.{u3} 𝕝 (NormedCommRing.toSeminormedCommRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))) (SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))) _inst_6 S) (forall (x : ι -> E), (forall (n : ι), Membership.Mem.{u1, u1} E (Set.{u1} E) (Set.hasMem.{u1} E) (x n) S) -> (Filter.Tendsto.{u2, u1} ι E (SMul.smul.{max u2 u3, max u2 u1} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u2, u3, u1} ι (fun (ᾰ : ι) => 𝕝) (fun (ᾰ : ι) => E) (fun (i : ι) => SMulZeroClass.toHasSmul.{u3, u1} 𝕝 E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (SMulWithZero.toSmulZeroClass.{u3, u1} 𝕝 E (MulZeroClass.toHasZero.{u3} 𝕝 (MulZeroOneClass.toMulZeroClass.{u3} 𝕝 (MonoidWithZero.toMulZeroOneClass.{u3} 𝕝 (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕝 E (Semiring.toMonoidWithZero.{u3} 𝕝 (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2)))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)))) (Module.toMulActionWithZero.{u3, u1} 𝕝 E (Ring.toSemiring.{u3} 𝕝 (NormedRing.toRing.{u3} 𝕝 (NormedCommRing.toNormedRing.{u3} 𝕝 (NormedField.toNormedCommRing.{u3} 𝕝 (NontriviallyNormedField.toNormedField.{u3} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5))))) ε x) l (nhds.{u1} E _inst_6 (OfNat.ofNat.{u1} E 0 (OfNat.mk.{u1} E 0 (Zero.zero.{u1} E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_3))))))))))))
+but is expected to have type
+  forall {E : Type.{u1}} {ι : Type.{u3}} {𝕝 : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} 𝕝] [_inst_3 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3)] [_inst_6 : TopologicalSpace.{u1} E] [_inst_7 : ContinuousSMul.{u2, u1} 𝕝 E (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) _inst_6] {ε : ι -> 𝕝} {l : Filter.{u3} ι} [_inst_8 : Filter.NeBot.{u3} ι l], (Filter.Tendsto.{u3, u2} ι 𝕝 ε l (nhdsWithin.{u2} 𝕝 (UniformSpace.toTopologicalSpace.{u2} 𝕝 (PseudoMetricSpace.toUniformSpace.{u2} 𝕝 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕝 (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))))) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))))) (HasCompl.compl.{u2} (Set.{u2} 𝕝) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} 𝕝) (Set.instBooleanAlgebraSet.{u2} 𝕝)) (Singleton.singleton.{u2, u2} 𝕝 (Set.{u2} 𝕝) (Set.instSingletonSet.{u2} 𝕝) (OfNat.ofNat.{u2} 𝕝 0 (Zero.toOfNat0.{u2} 𝕝 (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))))))))) -> (forall {S : Set.{u1} E}, Iff (Bornology.IsVonNBounded.{u2, u1} 𝕝 E (SeminormedCommRing.toSeminormedRing.{u2} 𝕝 (NormedCommRing.toSeminormedCommRing.{u2} 𝕝 (NormedField.toNormedCommRing.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))) (SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) _inst_6 S) (forall (x : ι -> E), (forall (n : ι), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (x n) S) -> (Filter.Tendsto.{u3, u1} ι E (HSMul.hSMul.{max u3 u2, max u1 u3, max u1 u3} (ι -> 𝕝) (ι -> E) (ι -> E) (instHSMul.{max u3 u2, max u1 u3} (ι -> 𝕝) (ι -> E) (Pi.smul'.{u3, u2, u1} ι (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.1755 : ι) => 𝕝) (fun (a._@.Mathlib.Analysis.LocallyConvex.Bounded._hyg.3303 : ι) => E) (fun (i : ι) => SMulZeroClass.toSMul.{u2, u1} 𝕝 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕝 E (CommMonoidWithZero.toZero.{u2} 𝕝 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕝 (Semifield.toCommGroupWithZero.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕝 E (Semiring.toMonoidWithZero.{u2} 𝕝 (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2)))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_3))))) (Module.toMulActionWithZero.{u2, u1} 𝕝 E (DivisionSemiring.toSemiring.{u2} 𝕝 (Semifield.toDivisionSemiring.{u2} 𝕝 (Field.toSemifield.{u2} 𝕝 (NormedField.toField.{u2} 𝕝 (NontriviallyNormedField.toNormedField.{u2} 𝕝 _inst_2))))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_3) _inst_5)))))) ε x) l (nhds.{u1} E _inst_6 (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_3)))))))))))
+Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_iff_smul_tendsto_zero Bornology.isVonNBounded_iff_smul_tendsto_zeroₓ'. -/
 /-- Given any sequence `ε` of scalars which tends to `𝓝[≠] 0`, we have that a set `S` is bounded
   if and only if for any sequence `x : ℕ → S`, `ε • x` tends to 0. This actually works for any
   indexing type `ι`, but in the special case `ι = ℕ` we get the important fact that convergent
@@ -203,11 +257,23 @@ variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
+/- warning: bornology.is_vonN_bounded_singleton -> Bornology.isVonNBounded_singleton is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4] (x : E), Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_4 (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 : NormedField.{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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : TopologicalSpace.{u1} E] [_inst_5 : 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_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 _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 _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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (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_4] (x : E), Bornology.IsVonNBounded.{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_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 _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 _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 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) _inst_4 (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x)
+Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_singleton Bornology.isVonNBounded_singletonₓ'. -/
 /-- Singletons are bounded. -/
 theorem isVonNBounded_singleton (x : E) : IsVonNBounded 𝕜 ({x} : Set E) := fun V hV =>
   (absorbent_nhds_zero hV).Absorbs
 #align bornology.is_vonN_bounded_singleton Bornology.isVonNBounded_singleton
 
+/- warning: bornology.is_vonN_bounded_covers -> Bornology.isVonNBounded_covers is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4], Eq.{succ u2} (Set.{u2} E) (Set.unionₛ.{u2} E (setOf.{u2} (Set.{u2} E) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_4))) (Set.univ.{u2} E)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4], Eq.{succ u2} (Set.{u2} E) (Set.unionₛ.{u2} E (setOf.{u2} (Set.{u2} E) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_4))) (Set.univ.{u2} E)
+Case conversion may be inaccurate. Consider using '#align bornology.is_vonN_bounded_covers Bornology.isVonNBounded_coversₓ'. -/
 /-- The union of all bounded set is the whole space. -/
 theorem isVonNBounded_covers : ⋃₀ setOf (IsVonNBounded 𝕜) = (Set.univ : Set E) :=
   Set.eq_univ_iff_forall.mpr fun x =>
@@ -216,6 +282,7 @@ theorem isVonNBounded_covers : ⋃₀ setOf (IsVonNBounded 𝕜) = (Set.univ : S
 
 variable (𝕜 E)
 
+#print Bornology.vonNBornology /-
 -- See note [reducible non-instances]
 /-- The von Neumann bornology defined by the von Neumann bounded sets.
 
@@ -226,9 +293,16 @@ def vonNBornology : Bornology E :=
   Bornology.ofBounded (setOf (IsVonNBounded 𝕜)) (isVonNBounded_empty 𝕜 E)
     (fun _ hs _ ht => hs.Subset ht) (fun _ hs _ => hs.union) isVonNBounded_singleton
 #align bornology.vonN_bornology Bornology.vonNBornology
+-/
 
 variable {E}
 
+/- warning: bornology.is_bounded_iff_is_vonN_bounded -> Bornology.isBounded_iff_isVonNBounded is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4] {s : Set.{u2} E}, Iff (Bornology.IsBounded.{u2} E (Bornology.vonNBornology.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5) s) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) _inst_4 s)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : TopologicalSpace.{u2} E] [_inst_5 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (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_4] {s : Set.{u2} E}, Iff (Bornology.IsBounded.{u2} E (Bornology.vonNBornology.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 _inst_4 _inst_5) s) (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) _inst_4 s)
+Case conversion may be inaccurate. Consider using '#align bornology.is_bounded_iff_is_vonN_bounded Bornology.isBounded_iff_isVonNBoundedₓ'. -/
 @[simp]
 theorem isBounded_iff_isVonNBounded {s : Set E} :
     @IsBounded _ (vonNBornology 𝕜 E) s ↔ IsVonNBounded 𝕜 s :=
@@ -245,6 +319,12 @@ variable (𝕜) [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 variable [UniformSpace E] [UniformAddGroup E] [ContinuousSMul 𝕜 E]
 
+/- warning: totally_bounded.is_vonN_bounded -> TotallyBounded.isVonNBounded is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : UniformSpace.{u2} E] [_inst_5 : UniformAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_6 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u2} E _inst_4)] {s : Set.{u2} E}, (TotallyBounded.{u2} E _inst_4 s) -> (Bornology.IsVonNBounded.{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)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (UniformSpace.toTopologicalSpace.{u2} E _inst_4) s)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : UniformSpace.{u2} E] [_inst_5 : UniformAddGroup.{u2} E _inst_4 (AddCommGroup.toAddGroup.{u2} E _inst_2)] [_inst_6 : ContinuousSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (UniformSpace.toTopologicalSpace.{u2} E _inst_4)] {s : Set.{u2} E}, (TotallyBounded.{u2} E _inst_4 s) -> (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (UniformSpace.toTopologicalSpace.{u2} E _inst_4) s)
+Case conversion may be inaccurate. Consider using '#align totally_bounded.is_vonN_bounded TotallyBounded.isVonNBoundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
     Bornology.IsVonNBounded 𝕜 s :=
@@ -278,17 +358,35 @@ variable (𝕜 E) [NontriviallyNormedField 𝕜] [SeminormedAddCommGroup E] [Nor
 
 namespace NormedSpace
 
+/- warning: normed_space.is_vonN_bounded_ball -> NormedSpace.isVonNBounded_ball is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] (r : Real), Bornology.IsVonNBounded.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (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 (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2))))))))) r)
+but is expected to have type
+  forall (𝕜 : Type.{u2}) (E : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2] (r : Real), Bornology.IsVonNBounded.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2 _inst_3))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2))) (Metric.ball.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (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 (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) r)
+Case conversion may be inaccurate. Consider using '#align normed_space.is_vonN_bounded_ball NormedSpace.isVonNBounded_ballₓ'. -/
 theorem isVonNBounded_ball (r : ℝ) : Bornology.IsVonNBounded 𝕜 (Metric.ball (0 : E) r) :=
   by
   rw [metric.nhds_basis_ball.is_vonN_bounded_basis_iff, ← ball_normSeminorm 𝕜 E]
   exact fun ε hε => (normSeminorm 𝕜 E).ball_zero_absorbs_ball_zero hε
 #align normed_space.is_vonN_bounded_ball NormedSpace.isVonNBounded_ball
 
+/- warning: normed_space.is_vonN_bounded_closed_ball -> NormedSpace.isVonNBounded_closedBall is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] (r : Real), Bornology.IsVonNBounded.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (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 (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2))))))))) r)
+but is expected to have type
+  forall (𝕜 : Type.{u2}) (E : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2] (r : Real), Bornology.IsVonNBounded.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2 _inst_3))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2))) (Metric.closedBall.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2) (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 (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))))) r)
+Case conversion may be inaccurate. Consider using '#align normed_space.is_vonN_bounded_closed_ball NormedSpace.isVonNBounded_closedBallₓ'. -/
 theorem isVonNBounded_closedBall (r : ℝ) :
     Bornology.IsVonNBounded 𝕜 (Metric.closedBall (0 : E) r) :=
   (isVonNBounded_ball 𝕜 E (r + 1)).Subset (Metric.closedBall_subset_ball <| by linarith)
 #align normed_space.is_vonN_bounded_closed_ball NormedSpace.isVonNBounded_closedBall
 
+/- warning: normed_space.is_vonN_bounded_iff -> NormedSpace.isVonNBounded_iff is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] (s : Set.{u2} E), Iff (Bornology.IsVonNBounded.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) s) (Bornology.IsBounded.{u2} E (PseudoMetricSpace.toBornology.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] (s : Set.{u2} E), Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) s) (Bornology.IsBounded.{u2} E (PseudoMetricSpace.toBornology.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s)
+Case conversion may be inaccurate. Consider using '#align normed_space.is_vonN_bounded_iff NormedSpace.isVonNBounded_iffₓ'. -/
 theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Bornology.IsBounded s :=
   by
   rw [← Metric.bounded_iff_isBounded, Metric.bounded_iff_subset_ball (0 : E)]
@@ -303,16 +401,29 @@ theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Borno
   · exact fun ⟨C, hC⟩ => (is_vonN_bounded_closed_ball 𝕜 E C).Subset hC
 #align normed_space.is_vonN_bounded_iff NormedSpace.isVonNBounded_iff
 
+/- warning: normed_space.is_vonN_bounded_iff' -> NormedSpace.isVonNBounded_iff' is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] (s : Set.{u2} E), Iff (Bornology.IsVonNBounded.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) s) (Exists.{1} Real (fun (r : Real) => forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_2) x) r)))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] (s : Set.{u2} E), Iff (Bornology.IsVonNBounded.{u1, u2} 𝕜 E (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) s) (Exists.{1} Real (fun (r : Real) => forall (x : E), (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} E (SeminormedAddCommGroup.toNorm.{u2} E _inst_2) x) r)))
+Case conversion may be inaccurate. Consider using '#align normed_space.is_vonN_bounded_iff' NormedSpace.isVonNBounded_iff'ₓ'. -/
 theorem isVonNBounded_iff' (s : Set E) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∃ r : ℝ, ∀ (x : E) (hx : x ∈ s), ‖x‖ ≤ r := by
   rw [NormedSpace.isVonNBounded_iff, ← Metric.bounded_iff_isBounded, bounded_iff_forall_norm_le]
 #align normed_space.is_vonN_bounded_iff' NormedSpace.isVonNBounded_iff'
 
+/- warning: normed_space.image_is_vonN_bounded_iff -> NormedSpace.image_isVonNBounded_iff is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) {E' : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] (f : E' -> E) (s : Set.{u3} E'), Iff (Bornology.IsVonNBounded.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2))) (Set.image.{u3, u2} E' E f s)) (Exists.{1} Real (fun (r : Real) => forall (x : E'), (Membership.Mem.{u3, u3} E' (Set.{u3} E') (Set.hasMem.{u3} E') x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u2} E (SeminormedAddCommGroup.toHasNorm.{u2} E _inst_2) (f x)) r)))
+but is expected to have type
+  forall (𝕜 : Type.{u2}) (E : Type.{u1}) {E' : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} E] [_inst_3 : NormedSpace.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2] (f : E' -> E) (s : Set.{u3} E'), Iff (Bornology.IsVonNBounded.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) _inst_2 _inst_3))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E _inst_2))) (Set.image.{u3, u1} E' E f s)) (Exists.{1} Real (fun (r : Real) => forall (x : E'), (Membership.mem.{u3, u3} E' (Set.{u3} E') (Set.instMembershipSet.{u3} E') x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} E (SeminormedAddCommGroup.toNorm.{u1} E _inst_2) (f x)) r)))
+Case conversion may be inaccurate. Consider using '#align normed_space.image_is_vonN_bounded_iff NormedSpace.image_isVonNBounded_iffₓ'. -/
 theorem image_isVonNBounded_iff (f : E' → E) (s : Set E') :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∃ r : ℝ, ∀ (x : E') (hx : x ∈ s), ‖f x‖ ≤ r := by
   simp_rw [is_vonN_bounded_iff', Set.ball_image_iff]
 #align normed_space.image_is_vonN_bounded_iff NormedSpace.image_isVonNBounded_iff
 
+#print NormedSpace.vonNBornology_eq /-
 /-- In a normed space, the von Neumann bornology (`bornology.vonN_bornology`) is equal to the
 metric bornology. -/
 theorem vonNBornology_eq : Bornology.vonNBornology 𝕜 E = PseudoMetricSpace.toBornology :=
@@ -322,9 +433,16 @@ theorem vonNBornology_eq : Bornology.vonNBornology 𝕜 E = PseudoMetricSpace.to
   rw [Bornology.isBounded_iff_isVonNBounded]
   exact is_vonN_bounded_iff 𝕜 E s
 #align normed_space.vonN_bornology_eq NormedSpace.vonNBornology_eq
+-/
 
 variable (𝕜)
 
+/- warning: normed_space.is_bounded_iff_subset_smul_ball -> NormedSpace.isBounded_iff_subset_smul_ball is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] {s : Set.{u2} E}, Iff (Bornology.IsBounded.{u2} E (PseudoMetricSpace.toBornology.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3)))))) a (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (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 (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] {s : Set.{u2} E}, Iff (Bornology.IsBounded.{u2} E (PseudoMetricSpace.toBornology.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) 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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))))) a (Metric.ball.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
+Case conversion may be inaccurate. Consider using '#align normed_space.is_bounded_iff_subset_smul_ball NormedSpace.isBounded_iff_subset_smul_ballₓ'. -/
 theorem isBounded_iff_subset_smul_ball {s : Set E} :
     Bornology.IsBounded s ↔ ∃ a : 𝕜, s ⊆ a • Metric.ball 0 1 :=
   by
@@ -338,6 +456,12 @@ theorem isBounded_iff_subset_smul_ball {s : Set E} :
     exact ((is_vonN_bounded_ball 𝕜 E 1).image (a • 1 : E →L[𝕜] E)).Subset ha
 #align normed_space.is_bounded_iff_subset_smul_ball NormedSpace.isBounded_iff_subset_smul_ball
 
+/- warning: normed_space.is_bounded_iff_subset_smul_closed_ball -> NormedSpace.isBounded_iff_subset_smul_closedBall is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] {s : Set.{u2} E}, Iff (Bornology.IsBounded.{u2} E (PseudoMetricSpace.toBornology.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3)))))) a (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (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 (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E _inst_2))))))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) (E : Type.{u2}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2] {s : Set.{u2} E}, Iff (Bornology.IsBounded.{u2} E (PseudoMetricSpace.toBornology.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2)) s) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) 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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) _inst_2 _inst_3))))))) a (Metric.closedBall.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E _inst_2) (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 (SeminormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
+Case conversion may be inaccurate. Consider using '#align normed_space.is_bounded_iff_subset_smul_closed_ball NormedSpace.isBounded_iff_subset_smul_closedBallₓ'. -/
 theorem isBounded_iff_subset_smul_closedBall {s : Set E} :
     Bornology.IsBounded s ↔ ∃ a : 𝕜, s ⊆ a • Metric.closedBall 0 1 :=
   by

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

@@ -52,13 +52,13 @@ open Topology Pointwise
 
 namespace Bornology
 
-section SemiNormedRing
+section SeminormedRing
 
 section Zero
 
 variable (𝕜)
 
-variable [SemiNormedRing 𝕜] [SMul 𝕜 E] [Zero E]
+variable [SeminormedRing 𝕜] [SMul 𝕜 E] [Zero E]
 
 variable [TopologicalSpace E]
 
@@ -99,11 +99,11 @@ theorem IsVonNBounded.union {s₁ s₂ : Set E} (hs₁ : IsVonNBounded 𝕜 s₁
 
 end Zero
 
-end SemiNormedRing
+end SeminormedRing
 
 section MultipleTopologies
 
-variable [SemiNormedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
+variable [SeminormedRing 𝕜] [AddCommGroup E] [Module 𝕜 E]
 
 /-- If a topology `t'` is coarser than `t`, then any set `s` that is bounded with respect to
 `t` is bounded with respect to `t'`. -/

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

@@ -84,7 +84,7 @@ theorem _root_.Filter.HasBasis.isVonNBounded_iff {q : ι → Prop} {s : ι → S
   exact (hA i hi).mono_left hV
 #align filter.has_basis.is_vonN_bounded_basis_iff Filter.HasBasis.isVonNBounded_iff
 
-@[deprecated] -- since 12 January 2024
+@[deprecated] -- since 2024-01-12
 alias _root_.Filter.HasBasis.isVonNBounded_basis_iff := Filter.HasBasis.isVonNBounded_iff
 
 /-- Subsets of bounded sets are bounded. -/

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -342,7 +342,7 @@ theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
     tendsto_add
   rw [add_zero] at h
   have h' := (nhds_basis_balanced 𝕜 E).prod (nhds_basis_balanced 𝕜 E)
-  simp_rw [← nhds_prod_eq, id.def] at h'
+  simp_rw [← nhds_prod_eq, id] at h'
   rcases h.basis_left h' U hU with ⟨x, hx, h''⟩
   rcases hs x.snd hx.2.1 with ⟨t, ht, hs⟩
   refine Absorbs.mono_right ?_ hs

This is a generalization of Mathlib/Algebra/Module/LinearMap/Pointwise.lean from LinearMapClass to MulActionHomClass.

The preexisting lemmas are generalized.

• image_smul_setₛₗ : under a σ-equivariant map, one has h '' (c • s) = (σ c) • h '' s.

• preimage_smul_setₛₗ' is a general version of the equality h ⁻¹' (σ c • s) = c • h⁻¹' s. It requires that c acts surjectively and σ c acts injectively. It is provided with specific versions:

• preimage_smul_setₛₗ_of_units requires that c and σ c are units

• MonoidHom.preimage_smul_setₛₗ requires that σ is a MonoidHom and c is a unit

• MonoidHomClass.preimage_smul_setₛₗ requires that σ belongs to a MonoidHomClassand that c is a unit

• Group.preimage_smul_setₛₗ requires that the types of c and σ c are groups

• image_smul_set, preimage_smul_set and Group.preimage_smul_set are the variants when σ is the identity.

@@ -3,7 +3,7 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
-import Mathlib.Algebra.Module.LinearMap.Pointwise
+import Mathlib.GroupTheory.GroupAction.Pointwise
 import Mathlib.Analysis.LocallyConvex.Basic
 import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
 import Mathlib.Analysis.Seminorm

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

@@ -310,7 +310,7 @@ variable (𝕜 E)
 /-- The von Neumann bornology defined by the von Neumann bounded sets.
 
 Note that this is not registered as an instance, in order to avoid diamonds with the
-metric bornology.-/
+metric bornology. -/
 @[reducible]
 def vonNBornology : Bornology E :=
   Bornology.ofBounded (setOf (IsVonNBounded 𝕜)) (isVonNBounded_empty 𝕜 E)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -57,9 +57,7 @@ section SeminormedRing
 section Zero
 
 variable (𝕜)
-
 variable [SeminormedRing 𝕜] [SMul 𝕜 E] [Zero E]
-
 variable [TopologicalSpace E]
 
 /-- A set `s` is von Neumann bounded if every neighborhood of 0 absorbs `s`. -/
@@ -232,7 +230,6 @@ end sequence
 section NormedField
 
 variable [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
-
 variable [TopologicalSpace E] [ContinuousSMul 𝕜 E]
 
 /-- Singletons are bounded. -/
@@ -335,7 +332,6 @@ end Bornology
 section UniformAddGroup
 
 variable (𝕜) [NontriviallyNormedField 𝕜] [AddCommGroup E] [Module 𝕜 E]
-
 variable [UniformSpace E] [UniformAddGroup E] [ContinuousSMul 𝕜 E]
 
 theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :

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.

@@ -396,7 +396,7 @@ theorem isVonNBounded_iff' (s : Set E) :
 
 theorem image_isVonNBounded_iff (f : E' → E) (s : Set E') :
     Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∃ r : ℝ, ∀ x ∈ s, ‖f x‖ ≤ r := by
-  simp_rw [isVonNBounded_iff', Set.ball_image_iff]
+  simp_rw [isVonNBounded_iff', Set.forall_mem_image]
 #align normed_space.image_is_vonN_bounded_iff NormedSpace.image_isVonNBounded_iff
 
 /-- In a normed space, the von Neumann bornology (`Bornology.vonNBornology`) is equal to the

• 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

@@ -45,9 +45,8 @@ von Neumann-bounded sets.
 
 variable {𝕜 𝕜' E E' F ι : Type*}
 
-open Set Filter
-
-open Topology Pointwise
+open Set Filter Function
+open scoped Topology Pointwise
 
 set_option linter.uppercaseLean3 false
 
@@ -151,6 +150,22 @@ theorem IsVonNBounded.of_topologicalSpace_le {t t' : TopologicalSpace E} (h : t
 
 end MultipleTopologies
 
+lemma isVonNBounded_iff_tendsto_smallSets_nhds {𝕜 E : Type*} [NormedDivisionRing 𝕜]
+    [AddCommGroup E] [Module 𝕜 E] [TopologicalSpace E] {S : Set E} :
+    IsVonNBounded 𝕜 S ↔ Tendsto (· • S : 𝕜 → Set E) (𝓝 0) (𝓝 0).smallSets := by
+  rw [tendsto_smallSets_iff]
+  refine forall₂_congr fun V hV ↦ ?_
+  simp only [absorbs_iff_eventually_nhds_zero (mem_of_mem_nhds hV), mapsTo', image_smul]
+
+alias ⟨IsVonNBounded.tendsto_smallSets_nhds, _⟩ := isVonNBounded_iff_tendsto_smallSets_nhds
+
+lemma isVonNBounded_pi_iff {𝕜 ι : Type*} {E : ι → Type*} [NormedDivisionRing 𝕜]
+    [∀ i, AddCommGroup (E i)] [∀ i, Module 𝕜 (E i)] [∀ i, TopologicalSpace (E i)]
+    {S : Set (∀ i, E i)} : IsVonNBounded 𝕜 S ↔ ∀ i, IsVonNBounded 𝕜 (eval i '' S) := by
+  simp only [isVonNBounded_iff_tendsto_smallSets_nhds, nhds_pi, Filter.pi, smallSets_iInf,
+    smallSets_comap, tendsto_iInf, tendsto_lift', comp_apply, mem_powerset_iff, ← image_subset_iff,
+    ← image_smul, image_image, tendsto_smallSets_iff]; rfl
+
 section Image
 
 variable {𝕜₁ 𝕜₂ : Type*} [NormedDivisionRing 𝕜₁] [NormedDivisionRing 𝕜₂] [AddCommGroup E]
@@ -159,21 +174,12 @@ variable {𝕜₁ 𝕜₂ : Type*} [NormedDivisionRing 𝕜₁] [NormedDivisionR
 /-- A continuous linear image of a bounded set is bounded. -/
 theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ] [RingHomIsometric σ] {s : Set E}
     (hs : IsVonNBounded 𝕜₁ s) (f : E →SL[σ] F) : IsVonNBounded 𝕜₂ (f '' s) := by
-  let σ' := RingEquiv.ofBijective σ ⟨σ.injective, σ.surjective⟩
   have σ_iso : Isometry σ := AddMonoidHomClass.isometry_of_norm σ fun x => RingHomIsometric.is_iso
-  have σ'_symm_iso : Isometry σ'.symm := σ_iso.right_inv σ'.right_inv
-  have f_tendsto_zero := f.continuous.tendsto 0
-  rw [map_zero] at f_tendsto_zero
-  intro V hV
-  rcases (hs (f_tendsto_zero hV)).exists_pos with ⟨r, hrpos, hr⟩
-  refine' .of_norm ⟨r, fun a ha => _⟩
-  rw [← σ'.apply_symm_apply a]
-  have hanz : a ≠ 0 := norm_pos_iff.mp (hrpos.trans_le ha)
-  have : σ'.symm a ≠ 0 := (map_ne_zero σ'.symm.toRingHom).mpr hanz
-  change _ ⊆ σ _ • _
-  rw [Set.image_subset_iff, preimage_smul_setₛₗ _ _ _ f this.isUnit]
-  refine' hr (σ'.symm a) _
-  rwa [σ'_symm_iso.norm_map_of_map_zero (map_zero _)]
+  have : map σ (𝓝 0) = 𝓝 0 := by
+    rw [σ_iso.embedding.map_nhds_eq, σ.surjective.range_eq, nhdsWithin_univ, map_zero]
+  have hf₀ : Tendsto f (𝓝 0) (𝓝 0) := f.continuous.tendsto' 0 0 (map_zero f)
+  simp only [isVonNBounded_iff_tendsto_smallSets_nhds, ← this, tendsto_map'_iff] at hs ⊢
+  simpa only [comp_def, image_smul_setₛₗ _ _ σ f] using hf₀.image_smallSets.comp hs
 #align bornology.is_vonN_bounded.image Bornology.IsVonNBounded.image
 
 end Image
@@ -185,16 +191,8 @@ variable {𝕝 : Type*} [NormedField 𝕜] [NontriviallyNormedField 𝕝] [AddCo
 
 theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι → E} {l : Filter ι}
     (hS : IsVonNBounded 𝕜 S) (hxS : ∀ᶠ n in l, x n ∈ S) (hε : Tendsto ε l (𝓝 0)) :
-    Tendsto (ε • x) l (𝓝 0) := by
-  rw [tendsto_def] at *
-  intro V hV
-  rcases (hS hV).exists_pos with ⟨r, r_pos, hrS⟩
-  filter_upwards [hxS, hε _ (Metric.ball_mem_nhds 0 <| inv_pos.mpr r_pos)] with n hnS hnr
-  by_cases hε : ε n = 0
-  · simp [hε, mem_of_mem_nhds hV]
-  · rw [mem_preimage, mem_ball_zero_iff, lt_inv (norm_pos_iff.mpr hε) r_pos, ← norm_inv] at hnr
-    rw [mem_preimage, Pi.smul_apply', ← Set.mem_inv_smul_set_iff₀ hε]
-    exact hrS _ hnr.le hnS
+    Tendsto (ε • x) l (𝓝 0) :=
+  (hS.tendsto_smallSets_nhds.comp hε).of_smallSets <| hxS.mono fun _ ↦ smul_mem_smul_set
 #align bornology.is_vonN_bounded.smul_tendsto_zero Bornology.IsVonNBounded.smul_tendsto_zero
 
 theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l.NeBot]

• add IsVonNBounded.add, IsVonNBounded.vadd, and isVonNBounded_vadd;
• generalize some lemmas in Topology/Algebra/Monoid from Monoid to MulOneClass, move them to a new section.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -102,6 +102,40 @@ theorem IsVonNBounded.union {s₁ s₂ : Set E} (hs₁ : IsVonNBounded 𝕜 s₁
 
 end Zero
 
+section ContinuousAdd
+
+variable [SeminormedRing 𝕜] [AddZeroClass E] [TopologicalSpace E] [ContinuousAdd E]
+  [DistribSMul 𝕜 E] {s t : Set E}
+
+protected theorem IsVonNBounded.add (hs : IsVonNBounded 𝕜 s) (ht : IsVonNBounded 𝕜 t) :
+    IsVonNBounded 𝕜 (s + t) := fun U hU ↦ by
+  rcases exists_open_nhds_zero_add_subset hU with ⟨V, hVo, hV, hVU⟩
+  exact ((hs <| hVo.mem_nhds hV).add (ht <| hVo.mem_nhds hV)).mono_left hVU
+
+end ContinuousAdd
+
+section TopologicalAddGroup
+
+variable [SeminormedRing 𝕜] [AddGroup E] [TopologicalSpace E] [TopologicalAddGroup E]
+  [DistribMulAction 𝕜 E] {s t : Set E}
+
+protected theorem IsVonNBounded.neg (hs : IsVonNBounded 𝕜 s) : IsVonNBounded 𝕜 (-s) := fun U hU ↦ by
+  rw [← neg_neg U]
+  exact (hs <| neg_mem_nhds_zero _ hU).neg_neg
+
+@[simp]
+theorem isVonNBounded_neg : IsVonNBounded 𝕜 (-s) ↔ IsVonNBounded 𝕜 s :=
+  ⟨fun h ↦ neg_neg s ▸ h.neg, fun h ↦ h.neg⟩
+
+alias ⟨IsVonNBounded.of_neg, _⟩ := isVonNBounded_neg
+
+protected theorem IsVonNBounded.sub (hs : IsVonNBounded 𝕜 s) (ht : IsVonNBounded 𝕜 t) :
+    IsVonNBounded 𝕜 (s - t) := by
+  rw [sub_eq_add_neg]
+  exact hs.add ht.neg
+
+end TopologicalAddGroup
+
 end SeminormedRing
 
 section MultipleTopologies
@@ -208,6 +242,67 @@ theorem isVonNBounded_singleton (x : E) : IsVonNBounded 𝕜 ({x} : Set E) := fu
   (absorbent_nhds_zero hV).absorbs
 #align bornology.is_vonN_bounded_singleton Bornology.isVonNBounded_singleton
 
+section ContinuousAdd
+
+variable [ContinuousAdd E] {s t : Set E}
+
+protected theorem IsVonNBounded.vadd (hs : IsVonNBounded 𝕜 s) (x : E) :
+    IsVonNBounded 𝕜 (x +ᵥ s) := by
+  rw [← singleton_vadd]
+  -- TODO: dot notation timeouts in the next line
+  exact IsVonNBounded.add (isVonNBounded_singleton x) hs
+
+@[simp]
+theorem isVonNBounded_vadd (x : E) : IsVonNBounded 𝕜 (x +ᵥ s) ↔ IsVonNBounded 𝕜 s :=
+  ⟨fun h ↦ by simpa using h.vadd (-x), fun h ↦ h.vadd x⟩
+
+theorem IsVonNBounded.of_add_right (hst : IsVonNBounded 𝕜 (s + t)) (hs : s.Nonempty) :
+    IsVonNBounded 𝕜 t :=
+  let ⟨x, hx⟩ := hs
+  (isVonNBounded_vadd x).mp <| hst.subset <| image_subset_image2_right hx
+
+theorem IsVonNBounded.of_add_left (hst : IsVonNBounded 𝕜 (s + t)) (ht : t.Nonempty) :
+    IsVonNBounded 𝕜 s :=
+  ((add_comm s t).subst hst).of_add_right ht
+
+theorem isVonNBounded_add_of_nonempty (hs : s.Nonempty) (ht : t.Nonempty) :
+    IsVonNBounded 𝕜 (s + t) ↔ IsVonNBounded 𝕜 s ∧ IsVonNBounded 𝕜 t :=
+  ⟨fun h ↦ ⟨h.of_add_left ht, h.of_add_right hs⟩, and_imp.2 IsVonNBounded.add⟩
+
+theorem isVonNBounded_add :
+    IsVonNBounded 𝕜 (s + t) ↔ s = ∅ ∨ t = ∅ ∨ IsVonNBounded 𝕜 s ∧ IsVonNBounded 𝕜 t := by
+  rcases s.eq_empty_or_nonempty with rfl | hs; · simp
+  rcases t.eq_empty_or_nonempty with rfl | ht; · simp
+  simp [hs.ne_empty, ht.ne_empty, isVonNBounded_add_of_nonempty hs ht]
+
+@[simp]
+theorem isVonNBounded_add_self : IsVonNBounded 𝕜 (s + s) ↔ IsVonNBounded 𝕜 s := by
+  rcases s.eq_empty_or_nonempty with rfl | hs <;> simp [isVonNBounded_add_of_nonempty, *]
+
+theorem IsVonNBounded.of_sub_left (hst : IsVonNBounded 𝕜 (s - t)) (ht : t.Nonempty) :
+    IsVonNBounded 𝕜 s :=
+  ((sub_eq_add_neg s t).subst hst).of_add_left ht.neg
+
+end ContinuousAdd
+
+section TopologicalAddGroup
+
+variable [TopologicalAddGroup E] {s t : Set E}
+
+theorem IsVonNBounded.of_sub_right (hst : IsVonNBounded 𝕜 (s - t)) (hs : s.Nonempty) :
+    IsVonNBounded 𝕜 t :=
+  (((sub_eq_add_neg s t).subst hst).of_add_right hs).of_neg
+
+theorem isVonNBounded_sub_of_nonempty (hs : s.Nonempty) (ht : t.Nonempty) :
+    IsVonNBounded 𝕜 (s - t) ↔ IsVonNBounded 𝕜 s ∧ IsVonNBounded 𝕜 t := by
+  simp [sub_eq_add_neg, isVonNBounded_add_of_nonempty, hs, ht]
+
+theorem isVonNBounded_sub :
+    IsVonNBounded 𝕜 (s - t) ↔ s = ∅ ∨ t = ∅ ∨ IsVonNBounded 𝕜 s ∧ IsVonNBounded 𝕜 t := by
+  simp [sub_eq_add_neg, isVonNBounded_add]
+
+end TopologicalAddGroup
+
 /-- The union of all bounded set is the whole space. -/
 theorem isVonNBounded_covers : ⋃₀ setOf (IsVonNBounded 𝕜) = (Set.univ : Set E) :=
   Set.eq_univ_iff_forall.mpr fun x =>

This way we don't switch between general normed spaces and real normed spaces back and forth throughout the file.

@@ -10,6 +10,7 @@ import Mathlib.Analysis.Seminorm
 import Mathlib.Topology.Bornology.Basic
 import Mathlib.Topology.Algebra.UniformGroup
 import Mathlib.Topology.UniformSpace.Cauchy
+import Mathlib.Topology.Algebra.Module.Basic
 
 #align_import analysis.locally_convex.bounded from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

@@ -3,6 +3,7 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
+import Mathlib.Algebra.Module.LinearMap.Pointwise
 import Mathlib.Analysis.LocallyConvex.Basic
 import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
 import Mathlib.Analysis.Seminorm

Redefine Absorbs and Absorbent in terms of the cobounded filter.

@@ -69,7 +69,7 @@ def IsVonNBounded (s : Set E) : Prop :=
 variable (E)
 
 @[simp]
-theorem isVonNBounded_empty : IsVonNBounded 𝕜 (∅ : Set E) := fun _ _ => absorbs_empty
+theorem isVonNBounded_empty : IsVonNBounded 𝕜 (∅ : Set E) := fun _ _ => Absorbs.empty
 #align bornology.is_vonN_bounded_empty Bornology.isVonNBounded_empty
 
 variable {𝕜 E}
@@ -129,8 +129,8 @@ theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ]
   have f_tendsto_zero := f.continuous.tendsto 0
   rw [map_zero] at f_tendsto_zero
   intro V hV
-  rcases hs (f_tendsto_zero hV) with ⟨r, hrpos, hr⟩
-  refine' ⟨r, hrpos, fun a ha => _⟩
+  rcases (hs (f_tendsto_zero hV)).exists_pos with ⟨r, hrpos, hr⟩
+  refine' .of_norm ⟨r, fun a ha => _⟩
   rw [← σ'.apply_symm_apply a]
   have hanz : a ≠ 0 := norm_pos_iff.mp (hrpos.trans_le ha)
   have : σ'.symm a ≠ 0 := (map_ne_zero σ'.symm.toRingHom).mpr hanz
@@ -152,7 +152,7 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
     Tendsto (ε • x) l (𝓝 0) := by
   rw [tendsto_def] at *
   intro V hV
-  rcases hS hV with ⟨r, r_pos, hrS⟩
+  rcases (hS hV).exists_pos with ⟨r, r_pos, hrS⟩
   filter_upwards [hxS, hε _ (Metric.ball_mem_nhds 0 <| inv_pos.mpr r_pos)] with n hnS hnr
   by_cases hε : ε n = 0
   · simp [hε, mem_of_mem_nhds hV]
@@ -169,9 +169,9 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
   rcases H' with ⟨V, ⟨hV, hVb⟩, hVS⟩
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V := by
     filter_upwards [hε] with n hn
-    rw [Absorbs] at hVS
+    rw [absorbs_iff_norm] at hVS
     push_neg at hVS
-    rcases hVS _ (norm_pos_iff.mpr <| inv_ne_zero hn) with ⟨a, haε, haS⟩
+    rcases hVS ‖(ε n)⁻¹‖ with ⟨a, haε, haS⟩
     rcases Set.not_subset.mp haS with ⟨x, hxS, hx⟩
     refine' ⟨⟨x, hxS⟩, fun hnx => _⟩
     rw [← Set.mem_inv_smul_set_iff₀ hn] at hnx
@@ -254,13 +254,13 @@ theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
   simp_rw [← nhds_prod_eq, id.def] at h'
   rcases h.basis_left h' U hU with ⟨x, hx, h''⟩
   rcases hs x.snd hx.2.1 with ⟨t, ht, hs⟩
-  refine' Absorbs.mono_right _ hs
-  rw [ht.absorbs_iUnion]
+  refine Absorbs.mono_right ?_ hs
+  rw [ht.absorbs_biUnion]
   have hx_fstsnd : x.fst + x.snd ⊆ U := add_subset_iff.mpr fun z1 hz1 z2 hz2 ↦
     h'' <| mk_mem_prod hz1 hz2
-  refine' fun y _ => Absorbs.mono_left _ hx_fstsnd
-  rw [← Set.singleton_vadd, vadd_eq_add]
-  exact (absorbent_nhds_zero hx.1.1).absorbs.add hx.2.2.absorbs_self
+  refine fun y _ => Absorbs.mono_left ?_ hx_fstsnd
+  -- TODO: with dot notation, Lean timeouts on the next line. Why?
+  exact Absorbent.vadd_absorbs (absorbent_nhds_zero hx.1.1) hx.2.2.absorbs_self
 #align totally_bounded.is_vonN_bounded TotallyBounded.isVonNBounded
 
 end UniformAddGroup
@@ -285,7 +285,7 @@ theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Borno
   rw [Metric.isBounded_iff_subset_closedBall (0 : E)]
   constructor
   · intro h
-    rcases h (Metric.ball_mem_nhds 0 zero_lt_one) with ⟨ρ, hρ, hρball⟩
+    rcases (h (Metric.ball_mem_nhds 0 zero_lt_one)).exists_pos with ⟨ρ, hρ, hρball⟩
     rcases NormedField.exists_lt_norm 𝕜 ρ with ⟨a, ha⟩
     specialize hρball a ha.le
     rw [← ball_normSeminorm 𝕜 E, Seminorm.smul_ball_zero (norm_pos_iff.1 <| hρ.trans ha),
@@ -318,7 +318,7 @@ theorem isBounded_iff_subset_smul_ball {s : Set E} :
   rw [← isVonNBounded_iff 𝕜]
   constructor
   · intro h
-    rcases h (Metric.ball_mem_nhds 0 zero_lt_one) with ⟨ρ, _, hρball⟩
+    rcases (h (Metric.ball_mem_nhds 0 zero_lt_one)).exists_pos with ⟨ρ, _, hρball⟩
     rcases NormedField.exists_lt_norm 𝕜 ρ with ⟨a, ha⟩
     exact ⟨a, hρball a ha.le⟩
   · rintro ⟨a, ha⟩

Rename Filter.HasBasis.isVonNBounded_basis_iff to Filter.HasBasis.isVonNBounded_iff. It already has basis in the namespace.

@@ -78,12 +78,15 @@ theorem isVonNBounded_iff (s : Set E) : IsVonNBounded 𝕜 s ↔ ∀ V ∈ 𝓝
   Iff.rfl
 #align bornology.is_vonN_bounded_iff Bornology.isVonNBounded_iff
 
-theorem _root_.Filter.HasBasis.isVonNBounded_basis_iff {q : ι → Prop} {s : ι → Set E} {A : Set E}
+theorem _root_.Filter.HasBasis.isVonNBounded_iff {q : ι → Prop} {s : ι → Set E} {A : Set E}
     (h : (𝓝 (0 : E)).HasBasis q s) : IsVonNBounded 𝕜 A ↔ ∀ i, q i → Absorbs 𝕜 (s i) A := by
   refine' ⟨fun hA i hi => hA (h.mem_of_mem hi), fun hA V hV => _⟩
   rcases h.mem_iff.mp hV with ⟨i, hi, hV⟩
   exact (hA i hi).mono_left hV
-#align filter.has_basis.is_vonN_bounded_basis_iff Filter.HasBasis.isVonNBounded_basis_iff
+#align filter.has_basis.is_vonN_bounded_basis_iff Filter.HasBasis.isVonNBounded_iff
+
+@[deprecated] -- since 12 January 2024
+alias _root_.Filter.HasBasis.isVonNBounded_basis_iff := Filter.HasBasis.isVonNBounded_iff
 
 /-- Subsets of bounded sets are bounded. -/
 theorem IsVonNBounded.subset {s₁ s₂ : Set E} (h : s₁ ⊆ s₂) (hs₂ : IsVonNBounded 𝕜 s₂) :
@@ -161,7 +164,7 @@ theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι 
 theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l.NeBot]
     (hε : ∀ᶠ n in l, ε n ≠ 0) {S : Set E}
     (H : ∀ x : ι → E, (∀ n, x n ∈ S) → Tendsto (ε • x) l (𝓝 0)) : IsVonNBounded 𝕝 S := by
-  rw [(nhds_basis_balanced 𝕝 E).isVonNBounded_basis_iff]
+  rw [(nhds_basis_balanced 𝕝 E).isVonNBounded_iff]
   by_contra! H'
   rcases H' with ⟨V, ⟨hV, hVb⟩, hVS⟩
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V := by
@@ -269,7 +272,7 @@ variable (𝕜 E) [NontriviallyNormedField 𝕜] [SeminormedAddCommGroup E] [Nor
 namespace NormedSpace
 
 theorem isVonNBounded_ball (r : ℝ) : Bornology.IsVonNBounded 𝕜 (Metric.ball (0 : E) r) := by
-  rw [Metric.nhds_basis_ball.isVonNBounded_basis_iff, ← ball_normSeminorm 𝕜 E]
+  rw [Metric.nhds_basis_ball.isVonNBounded_iff, ← ball_normSeminorm 𝕜 E]
   exact fun ε hε => (normSeminorm 𝕜 E).ball_zero_absorbs_ball_zero hε
 #align normed_space.is_vonN_bounded_ball NormedSpace.isVonNBounded_ball
 

Use Set.image2_subset_iff, Set.mul_subset_iff, and Set.add_subset_iff instead of rintros.

Also protect some *.image2 lemmas.

@@ -253,11 +253,8 @@ theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
   rcases hs x.snd hx.2.1 with ⟨t, ht, hs⟩
   refine' Absorbs.mono_right _ hs
   rw [ht.absorbs_iUnion]
-  have hx_fstsnd : x.fst + x.snd ⊆ U := by
-    intro z hz
-    rcases Set.mem_add.mp hz with ⟨z1, z2, hz1, hz2, hz⟩
-    have hz' : (z1, z2) ∈ x.fst ×ˢ x.snd := ⟨hz1, hz2⟩
-    simpa only [hz] using h'' hz'
+  have hx_fstsnd : x.fst + x.snd ⊆ U := add_subset_iff.mpr fun z1 hz1 z2 hz2 ↦
+    h'' <| mk_mem_prod hz1 hz2
   refine' fun y _ => Absorbs.mono_left _ hx_fstsnd
   rw [← Set.singleton_vadd, vadd_eq_add]
   exact (absorbent_nhds_zero hx.1.1).absorbs.add hx.2.2.absorbs_self

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

In some rare cases, golf proofs that needed fixing.

@@ -79,7 +79,7 @@ theorem isVonNBounded_iff (s : Set E) : IsVonNBounded 𝕜 s ↔ ∀ V ∈ 𝓝
 #align bornology.is_vonN_bounded_iff Bornology.isVonNBounded_iff
 
 theorem _root_.Filter.HasBasis.isVonNBounded_basis_iff {q : ι → Prop} {s : ι → Set E} {A : Set E}
-    (h : (𝓝 (0 : E)).HasBasis q s) : IsVonNBounded 𝕜 A ↔ ∀ (i) (_ : q i), Absorbs 𝕜 (s i) A := by
+    (h : (𝓝 (0 : E)).HasBasis q s) : IsVonNBounded 𝕜 A ↔ ∀ i, q i → Absorbs 𝕜 (s i) A := by
   refine' ⟨fun hA i hi => hA (h.mem_of_mem hi), fun hA V hV => _⟩
   rcases h.mem_iff.mp hV with ⟨i, hi, hV⟩
   exact (hA i hi).mono_left hV
@@ -295,12 +295,12 @@ theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Borno
 #align normed_space.is_vonN_bounded_iff NormedSpace.isVonNBounded_iff
 
 theorem isVonNBounded_iff' (s : Set E) :
-    Bornology.IsVonNBounded 𝕜 s ↔ ∃ r : ℝ, ∀ (x : E) (_ : x ∈ s), ‖x‖ ≤ r := by
+    Bornology.IsVonNBounded 𝕜 s ↔ ∃ r : ℝ, ∀ x ∈ s, ‖x‖ ≤ r := by
   rw [NormedSpace.isVonNBounded_iff, isBounded_iff_forall_norm_le]
 #align normed_space.is_vonN_bounded_iff' NormedSpace.isVonNBounded_iff'
 
 theorem image_isVonNBounded_iff (f : E' → E) (s : Set E') :
-    Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∃ r : ℝ, ∀ (x : E') (_ : x ∈ s), ‖f x‖ ≤ r := by
+    Bornology.IsVonNBounded 𝕜 (f '' s) ↔ ∃ r : ℝ, ∀ x ∈ s, ‖f x‖ ≤ r := by
   simp_rw [isVonNBounded_iff', Set.ball_image_iff]
 #align normed_space.image_is_vonN_bounded_iff NormedSpace.image_isVonNBounded_iff
 

To fit with the "please try harder" convention of ! tactics.

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

@@ -162,7 +162,7 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
     (hε : ∀ᶠ n in l, ε n ≠ 0) {S : Set E}
     (H : ∀ x : ι → E, (∀ n, x n ∈ S) → Tendsto (ε • x) l (𝓝 0)) : IsVonNBounded 𝕝 S := by
   rw [(nhds_basis_balanced 𝕝 E).isVonNBounded_basis_iff]
-  by_contra' H'
+  by_contra! H'
   rcases H' with ⟨V, ⟨hV, hVb⟩, hVS⟩
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V := by
     filter_upwards [hε] with n hn

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -165,7 +165,7 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
   by_contra' H'
   rcases H' with ⟨V, ⟨hV, hVb⟩, hVS⟩
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V := by
-    filter_upwards [hε]with n hn
+    filter_upwards [hε] with n hn
     rw [Absorbs] at hVS
     push_neg at hVS
     rcases hVS _ (norm_pos_iff.mpr <| inv_ne_zero hn) with ⟨a, haε, haS⟩

Use Bornology.IsBounded instead.

@@ -282,7 +282,7 @@ theorem isVonNBounded_closedBall (r : ℝ) :
 #align normed_space.is_vonN_bounded_closed_ball NormedSpace.isVonNBounded_closedBall
 
 theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Bornology.IsBounded s := by
-  rw [← Metric.bounded_iff_isBounded, Metric.bounded_iff_subset_ball (0 : E)]
+  rw [Metric.isBounded_iff_subset_closedBall (0 : E)]
   constructor
   · intro h
     rcases h (Metric.ball_mem_nhds 0 zero_lt_one) with ⟨ρ, hρ, hρball⟩
@@ -296,7 +296,7 @@ theorem isVonNBounded_iff (s : Set E) : Bornology.IsVonNBounded 𝕜 s ↔ Borno
 
 theorem isVonNBounded_iff' (s : Set E) :
     Bornology.IsVonNBounded 𝕜 s ↔ ∃ r : ℝ, ∀ (x : E) (_ : x ∈ s), ‖x‖ ≤ r := by
-  rw [NormedSpace.isVonNBounded_iff, ← Metric.bounded_iff_isBounded, bounded_iff_forall_norm_le]
+  rw [NormedSpace.isVonNBounded_iff, isBounded_iff_forall_norm_le]
 #align normed_space.is_vonN_bounded_iff' NormedSpace.isVonNBounded_iff'
 
 theorem image_isVonNBounded_iff (f : E' → E) (s : Set E') :

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

This has nice performance benefits.

@@ -41,7 +41,7 @@ von Neumann-bounded sets.
 -/
 
 
-variable {𝕜 𝕜' E E' F ι : Type _}
+variable {𝕜 𝕜' E E' F ι : Type*}
 
 open Set Filter
 
@@ -114,7 +114,7 @@ end MultipleTopologies
 
 section Image
 
-variable {𝕜₁ 𝕜₂ : Type _} [NormedDivisionRing 𝕜₁] [NormedDivisionRing 𝕜₂] [AddCommGroup E]
+variable {𝕜₁ 𝕜₂ : Type*} [NormedDivisionRing 𝕜₁] [NormedDivisionRing 𝕜₂] [AddCommGroup E]
   [Module 𝕜₁ E] [AddCommGroup F] [Module 𝕜₂ F] [TopologicalSpace E] [TopologicalSpace F]
 
 /-- A continuous linear image of a bounded set is bounded. -/
@@ -141,7 +141,7 @@ end Image
 
 section sequence
 
-variable {𝕝 : Type _} [NormedField 𝕜] [NontriviallyNormedField 𝕝] [AddCommGroup E] [Module 𝕜 E]
+variable {𝕝 : Type*} [NormedField 𝕜] [NontriviallyNormedField 𝕝] [AddCommGroup E] [Module 𝕜 E]
   [Module 𝕝 E] [TopologicalSpace E] [ContinuousSMul 𝕝 E]
 
 theorem IsVonNBounded.smul_tendsto_zero {S : Set E} {ε : ι → 𝕜} {x : ι → E} {l : Filter ι}

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module analysis.locally_convex.bounded
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.LocallyConvex.Basic
 import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
@@ -15,6 +10,8 @@ import Mathlib.Topology.Bornology.Basic
 import Mathlib.Topology.Algebra.UniformGroup
 import Mathlib.Topology.UniformSpace.Cauchy
 
+#align_import analysis.locally_convex.bounded from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Von Neumann Boundedness
 

Changes are of the form

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

@@ -170,7 +170,7 @@ theorem isVonNBounded_of_smul_tendsto_zero {ε : ι → 𝕝} {l : Filter ι} [l
   have : ∀ᶠ n in l, ∃ x : S, ε n • (x : E) ∉ V := by
     filter_upwards [hε]with n hn
     rw [Absorbs] at hVS
-    push_neg  at hVS
+    push_neg at hVS
     rcases hVS _ (norm_pos_iff.mpr <| inv_ne_zero hn) with ⟨a, haε, haS⟩
     rcases Set.not_subset.mp haS with ⟨x, hxS, hx⟩
     refine' ⟨⟨x, hxS⟩, fun hnx => _⟩

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

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

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

@@ -120,7 +120,6 @@ section Image
 variable {𝕜₁ 𝕜₂ : Type _} [NormedDivisionRing 𝕜₁] [NormedDivisionRing 𝕜₂] [AddCommGroup E]
   [Module 𝕜₁ E] [AddCommGroup F] [Module 𝕜₂ F] [TopologicalSpace E] [TopologicalSpace F]
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- A continuous linear image of a bounded set is bounded. -/
 theorem IsVonNBounded.image {σ : 𝕜₁ →+* 𝕜₂} [RingHomSurjective σ] [RingHomIsometric σ] {s : Set E}
     (hs : IsVonNBounded 𝕜₁ s) (f : E →SL[σ] F) : IsVonNBounded 𝕜₂ (f '' s) := by
@@ -317,7 +316,6 @@ theorem vonNBornology_eq : Bornology.vonNBornology 𝕜 E = PseudoMetricSpace.to
   exact isVonNBounded_iff 𝕜 E s
 #align normed_space.vonN_bornology_eq NormedSpace.vonNBornology_eq
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem isBounded_iff_subset_smul_ball {s : Set E} :
     Bornology.IsBounded s ↔ ∃ a : 𝕜, s ⊆ a • Metric.ball (0 : E) 1 := by
   rw [← isVonNBounded_iff 𝕜]
@@ -330,7 +328,6 @@ theorem isBounded_iff_subset_smul_ball {s : Set E} :
     exact ((isVonNBounded_ball 𝕜 E 1).image (a • (1 : E →L[𝕜] E))).subset ha
 #align normed_space.is_bounded_iff_subset_smul_ball NormedSpace.isBounded_iff_subset_smul_ball
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem isBounded_iff_subset_smul_closedBall {s : Set E} :
     Bornology.IsBounded s ↔ ∃ a : 𝕜, s ⊆ a • Metric.closedBall (0 : E) 1 := by
   constructor

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>

@@ -210,7 +210,7 @@ theorem isVonNBounded_singleton (x : E) : IsVonNBounded 𝕜 ({x} : Set E) := fu
 /-- The union of all bounded set is the whole space. -/
 theorem isVonNBounded_covers : ⋃₀ setOf (IsVonNBounded 𝕜) = (Set.univ : Set E) :=
   Set.eq_univ_iff_forall.mpr fun x =>
-    Set.mem_unionₛ.mpr ⟨{x}, isVonNBounded_singleton _, Set.mem_singleton _⟩
+    Set.mem_sUnion.mpr ⟨{x}, isVonNBounded_singleton _, Set.mem_singleton _⟩
 #align bornology.is_vonN_bounded_covers Bornology.isVonNBounded_covers
 
 variable (𝕜 E)
@@ -246,7 +246,7 @@ variable [UniformSpace E] [UniformAddGroup E] [ContinuousSMul 𝕜 E]
 
 theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
     Bornology.IsVonNBounded 𝕜 s := by
-  rw [totallyBounded_iff_subset_finite_unionᵢ_nhds_zero] at hs
+  rw [totallyBounded_iff_subset_finite_iUnion_nhds_zero] at hs
   intro U hU
   have h : Filter.Tendsto (fun x : E × E => x.fst + x.snd) (𝓝 (0, 0)) (𝓝 ((0 : E) + (0 : E))) :=
     tendsto_add
@@ -256,7 +256,7 @@ theorem TotallyBounded.isVonNBounded {s : Set E} (hs : TotallyBounded s) :
   rcases h.basis_left h' U hU with ⟨x, hx, h''⟩
   rcases hs x.snd hx.2.1 with ⟨t, ht, hs⟩
   refine' Absorbs.mono_right _ hs
-  rw [ht.absorbs_unionᵢ]
+  rw [ht.absorbs_iUnion]
   have hx_fstsnd : x.fst + x.snd ⊆ U := by
     intro z hz
     rcases Set.mem_add.mp hz with ⟨z1, z2, hz1, hz2, hz⟩

@@ -28,9 +28,9 @@ absorbs `s`.
 
 ## Main results
 
-* `Bornology.isVonNBounded.of_topological_space_le`: A coarser topology admits more
+* `Bornology.IsVonNBounded.of_topologicalSpace_le`: A coarser topology admits more
 von Neumann-bounded sets.
-* `Bornology.isVonNBounded.image`: A continuous linear image of a bounded set is bounded.
+* `Bornology.IsVonNBounded.image`: A continuous linear image of a bounded set is bounded.
 * `Bornology.isVonNBounded_iff_smul_tendsto_zero`: Given any sequence `ε` of scalars which tends
   to `𝓝[≠] 0`, we have that a set `S` is bounded if and only if for any sequence `x : ℕ → S`,
   `ε • x` tends to 0. This shows that bounded sets are completely determined by sequences, which is