topology.algebra.uniform_convergence | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

f2ce6086

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

f2b757fc

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -227,13 +227,13 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
     refine' ⟨U, hU, ⟨S, W⟩, ⟨hS, hW⟩, _⟩
     rw [Set.smul_subset_iff]
     intro a ha u hu x hx
-    rw [SMulHomClass.map_smul]
+    rw [MulActionSemiHomClass.map_smul]
     exact hUW (⟨ha, hu x hx⟩ : (a, φ u x) ∈ U ×ˢ W)
   · rintro a ⟨S, V⟩ ⟨hS, hV⟩
     have : tendsto (fun x : E => a • x) (𝓝 0) (𝓝 <| a • 0) := tendsto_id.const_smul a
     rw [smul_zero] at this
     refine' ⟨⟨S, (· • ·) a ⁻¹' V⟩, ⟨hS, this hV⟩, fun f hf x hx => _⟩
-    rw [SMulHomClass.map_smul]
+    rw [MulActionSemiHomClass.map_smul]
     exact hf x hx
   · rintro u ⟨S, V⟩ ⟨hS, hV⟩
     rcases h u S hS hV with ⟨r, hrpos, hr⟩
@@ -243,7 +243,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
     · rw [ha0]
       simp [mem_of_mem_nhds hV]
     · rw [mem_ball_zero_iff] at ha
-      rw [SMulHomClass.map_smul, Pi.smul_apply]
+      rw [MulActionSemiHomClass.map_smul, Pi.smul_apply]
       have : φ u x ∈ a⁻¹ • V :=
         by
         have ha0 : 0 < ‖a‖ := norm_pos_iff.mpr ha0

f2b757fc

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -126,7 +126,7 @@ protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : 
     (𝓝 1 : Filter (α →ᵤ G)).HasBasis p fun i => {f : α →ᵤ G | ∀ x, f x ∈ b i} :=
   by
   have := h.comap fun p : G × G => p.2 / p.1
-  rw [← uniformity_eq_comap_nhds_one] at this 
+  rw [← uniformity_eq_comap_nhds_one] at this
   convert UniformFun.hasBasis_nhds_of_basis α _ 1 this
   ext i f
   simp [UniformFun.gen]
@@ -167,7 +167,7 @@ protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α)
       {f : α →ᵤ[𝔖] G | ∀ x ∈ Si.1, f x ∈ b Si.2} :=
   by
   have := h.comap fun p : G × G => p.1 / p.2
-  rw [← uniformity_eq_comap_nhds_one_swapped] at this 
+  rw [← uniformity_eq_comap_nhds_one_swapped] at this
   convert UniformOnFun.hasBasis_nhds_of_basis α _ 𝔖 1 h𝔖₁ h𝔖₂ this
   ext i f
   simp [UniformOnFun.gen]
@@ -220,9 +220,9 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
   · rintro ⟨S, V⟩ ⟨hS, hV⟩
     have : tendsto (fun kx : 𝕜 × E => kx.1 • kx.2) (𝓝 (0, 0)) (𝓝 <| (0 : 𝕜) • 0) :=
       continuous_smul.tendsto (0 : 𝕜 × E)
-    rw [zero_smul, nhds_prod_eq] at this 
+    rw [zero_smul, nhds_prod_eq] at this
     have := this hV
-    rw [mem_map, mem_prod_iff] at this 
+    rw [mem_map, mem_prod_iff] at this
     rcases this with ⟨U, hU, W, hW, hUW⟩
     refine' ⟨U, hU, ⟨S, W⟩, ⟨hS, hW⟩, _⟩
     rw [Set.smul_subset_iff]
@@ -231,7 +231,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
     exact hUW (⟨ha, hu x hx⟩ : (a, φ u x) ∈ U ×ˢ W)
   · rintro a ⟨S, V⟩ ⟨hS, hV⟩
     have : tendsto (fun x : E => a • x) (𝓝 0) (𝓝 <| a • 0) := tendsto_id.const_smul a
-    rw [smul_zero] at this 
+    rw [smul_zero] at this
     refine' ⟨⟨S, (· • ·) a ⁻¹' V⟩, ⟨hS, this hV⟩, fun f hf x hx => _⟩
     rw [SMulHomClass.map_smul]
     exact hf x hx
@@ -242,7 +242,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
     by_cases ha0 : a = 0
     · rw [ha0]
       simp [mem_of_mem_nhds hV]
-    · rw [mem_ball_zero_iff] at ha 
+    · rw [mem_ball_zero_iff] at ha
       rw [SMulHomClass.map_smul, Pi.smul_apply]
       have : φ u x ∈ a⁻¹ • V :=
         by
@@ -250,7 +250,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
         refine' (hr a⁻¹ _) (Set.mem_image_of_mem (φ u) hx)
         rw [norm_inv, le_inv hrpos ha0]
         exact ha.le
-      rwa [Set.mem_inv_smul_set_iff₀ ha0] at this 
+      rwa [Set.mem_inv_smul_set_iff₀ ha0] at this
 #align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_bounded
 -/

f2b757fc

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 -/
-import Mathbin.Topology.UniformSpace.UniformConvergenceTopology
-import Mathbin.Analysis.LocallyConvex.Bounded
-import Mathbin.Topology.Algebra.FilterBasis
+import Topology.UniformSpace.UniformConvergenceTopology
+import Analysis.LocallyConvex.Bounded
+import Topology.Algebra.FilterBasis
 
 #align_import topology.algebra.uniform_convergence from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"

f2b757fc

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module topology.algebra.uniform_convergence
-! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.UniformSpace.UniformConvergenceTopology
 import Mathbin.Analysis.LocallyConvex.Bounded
 import Mathbin.Topology.Algebra.FilterBasis
 
+#align_import topology.algebra.uniform_convergence from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
+
 /-!
 # Algebraic facts about the topology of uniform convergence

f2b757fc

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -131,7 +131,7 @@ protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : 
   have := h.comap fun p : G × G => p.2 / p.1
   rw [← uniformity_eq_comap_nhds_one] at this 
   convert UniformFun.hasBasis_nhds_of_basis α _ 1 this
-  ext (i f)
+  ext i f
   simp [UniformFun.gen]
 #align uniform_fun.has_basis_nhds_one_of_basis UniformFun.hasBasis_nhds_one_of_basis
 #align uniform_fun.has_basis_nhds_zero_of_basis UniformFun.hasBasis_nhds_zero_of_basis
@@ -172,7 +172,7 @@ protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α)
   have := h.comap fun p : G × G => p.1 / p.2
   rw [← uniformity_eq_comap_nhds_one_swapped] at this 
   convert UniformOnFun.hasBasis_nhds_of_basis α _ 𝔖 1 h𝔖₁ h𝔖₂ this
-  ext (i f)
+  ext i f
   simp [UniformOnFun.gen]
 #align uniform_on_fun.has_basis_nhds_one_of_basis UniformOnFun.hasBasis_nhds_one_of_basis
 #align uniform_on_fun.has_basis_nhds_zero_of_basis UniformOnFun.hasBasis_nhds_zero_of_basis

f2b757fc

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -122,6 +122,7 @@ instance : UniformGroup (α →ᵤ G) :=
           uniformContinuous_div).comp
       UniformFun.uniformEquivProdArrow.symm.UniformContinuous⟩
 
+#print UniformFun.hasBasis_nhds_one_of_basis /-
 @[to_additive]
 protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : ι → Set G}
     (h : (𝓝 1 : Filter G).HasBasis p b) :
@@ -134,7 +135,9 @@ protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : 
   simp [UniformFun.gen]
 #align uniform_fun.has_basis_nhds_one_of_basis UniformFun.hasBasis_nhds_one_of_basis
 #align uniform_fun.has_basis_nhds_zero_of_basis UniformFun.hasBasis_nhds_zero_of_basis
+-/
 
+#print UniformFun.hasBasis_nhds_one /-
 @[to_additive]
 protected theorem UniformFun.hasBasis_nhds_one :
     (𝓝 1 : Filter (α →ᵤ G)).HasBasis (fun V : Set G => V ∈ (𝓝 1 : Filter G)) fun V =>
@@ -142,6 +145,7 @@ protected theorem UniformFun.hasBasis_nhds_one :
   UniformFun.hasBasis_nhds_one_of_basis (basis_sets _)
 #align uniform_fun.has_basis_nhds_one UniformFun.hasBasis_nhds_one
 #align uniform_fun.has_basis_nhds_zero UniformFun.hasBasis_nhds_zero
+-/
 
 /-- Let `𝔖 : set (set α)`. If `G` is a uniform group, then `α →ᵤ[𝔖] G` is a uniform group as
 well. -/
@@ -157,6 +161,7 @@ instance : UniformGroup (α →ᵤ[𝔖] G) :=
           uniformContinuous_div).comp
       UniformOnFun.uniformEquivProdArrow.symm.UniformContinuous⟩
 
+#print UniformOnFun.hasBasis_nhds_one_of_basis /-
 @[to_additive]
 protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α) (h𝔖₁ : 𝔖.Nonempty)
     (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) {p : ι → Prop} {b : ι → Set G}
@@ -171,7 +176,9 @@ protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α)
   simp [UniformOnFun.gen]
 #align uniform_on_fun.has_basis_nhds_one_of_basis UniformOnFun.hasBasis_nhds_one_of_basis
 #align uniform_on_fun.has_basis_nhds_zero_of_basis UniformOnFun.hasBasis_nhds_zero_of_basis
+-/
 
+#print UniformOnFun.hasBasis_nhds_one /-
 @[to_additive]
 protected theorem UniformOnFun.hasBasis_nhds_one (𝔖 : Set <| Set α) (h𝔖₁ : 𝔖.Nonempty)
     (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) :
@@ -181,6 +188,7 @@ protected theorem UniformOnFun.hasBasis_nhds_one (𝔖 : Set <| Set α) (h𝔖
   UniformOnFun.hasBasis_nhds_one_of_basis 𝔖 h𝔖₁ h𝔖₂ (basis_sets _)
 #align uniform_on_fun.has_basis_nhds_one UniformOnFun.hasBasis_nhds_one
 #align uniform_on_fun.has_basis_nhds_zero UniformOnFun.hasBasis_nhds_zero
+-/
 
 end Group
 
@@ -191,6 +199,7 @@ variable (𝕜 α E H : Type _) {hom : Type _} [NormedField 𝕜] [AddCommGroup
   [ContinuousSMul 𝕜 E] {𝔖 : Set <| Set α} [LinearMapClass hom 𝕜 H (α →ᵤ[𝔖] E)]
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UniformOnFun.continuousSMul_induced_of_image_bounded /-
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `bornology.is_vonN_bounded`), then `H`,
 equipped with the topology of `𝔖`-convergence, is a TVS.
@@ -246,7 +255,9 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
         exact ha.le
       rwa [Set.mem_inv_smul_set_iff₀ ha0] at this 
 #align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_bounded
+-/
 
+#print UniformOnFun.continuousSMul_submodule_of_image_bounded /-
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `bornology.is_vonN_bounded`), then `H`,
 equipped with the topology of `𝔖`-convergence, is a TVS.
@@ -261,6 +272,7 @@ theorem UniformOnFun.continuousSMul_submodule_of_image_bounded (h𝔖₁ : 𝔖.
   UniformOnFun.continuousSMul_induced_of_image_bounded 𝕜 α E H h𝔖₁ h𝔖₂
     (linear_map.id.dom_restrict H : H →ₗ[𝕜] α → E) inducing_subtype_val fun ⟨u, hu⟩ => h u hu
 #align uniform_on_fun.has_continuous_smul_submodule_of_image_bounded UniformOnFun.continuousSMul_submodule_of_image_bounded
+-/
 
 end Module

f2b757fc

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -125,7 +125,7 @@ instance : UniformGroup (α →ᵤ G) :=
 @[to_additive]
 protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : ι → Set G}
     (h : (𝓝 1 : Filter G).HasBasis p b) :
-    (𝓝 1 : Filter (α →ᵤ G)).HasBasis p fun i => { f : α →ᵤ G | ∀ x, f x ∈ b i } :=
+    (𝓝 1 : Filter (α →ᵤ G)).HasBasis p fun i => {f : α →ᵤ G | ∀ x, f x ∈ b i} :=
   by
   have := h.comap fun p : G × G => p.2 / p.1
   rw [← uniformity_eq_comap_nhds_one] at this 
@@ -138,7 +138,7 @@ protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : 
 @[to_additive]
 protected theorem UniformFun.hasBasis_nhds_one :
     (𝓝 1 : Filter (α →ᵤ G)).HasBasis (fun V : Set G => V ∈ (𝓝 1 : Filter G)) fun V =>
-      { f : α → G | ∀ x, f x ∈ V } :=
+      {f : α → G | ∀ x, f x ∈ V} :=
   UniformFun.hasBasis_nhds_one_of_basis (basis_sets _)
 #align uniform_fun.has_basis_nhds_one UniformFun.hasBasis_nhds_one
 #align uniform_fun.has_basis_nhds_zero UniformFun.hasBasis_nhds_zero
@@ -162,7 +162,7 @@ protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α)
     (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) {p : ι → Prop} {b : ι → Set G}
     (h : (𝓝 1 : Filter G).HasBasis p b) :
     (𝓝 1 : Filter (α →ᵤ[𝔖] G)).HasBasis (fun Si : Set α × ι => Si.1 ∈ 𝔖 ∧ p Si.2) fun Si =>
-      { f : α →ᵤ[𝔖] G | ∀ x ∈ Si.1, f x ∈ b Si.2 } :=
+      {f : α →ᵤ[𝔖] G | ∀ x ∈ Si.1, f x ∈ b Si.2} :=
   by
   have := h.comap fun p : G × G => p.1 / p.2
   rw [← uniformity_eq_comap_nhds_one_swapped] at this 
@@ -177,7 +177,7 @@ protected theorem UniformOnFun.hasBasis_nhds_one (𝔖 : Set <| Set α) (h𝔖
     (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) :
     (𝓝 1 : Filter (α →ᵤ[𝔖] G)).HasBasis
       (fun SV : Set α × Set G => SV.1 ∈ 𝔖 ∧ SV.2 ∈ (𝓝 1 : Filter G)) fun SV =>
-      { f : α →ᵤ[𝔖] G | ∀ x ∈ SV.1, f x ∈ SV.2 } :=
+      {f : α →ᵤ[𝔖] G | ∀ x ∈ SV.1, f x ∈ SV.2} :=
   UniformOnFun.hasBasis_nhds_one_of_basis 𝔖 h𝔖₁ h𝔖₂ (basis_sets _)
 #align uniform_on_fun.has_basis_nhds_one UniformOnFun.hasBasis_nhds_one
 #align uniform_on_fun.has_basis_nhds_zero UniformOnFun.hasBasis_nhds_zero

f2b757fc

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -128,7 +128,7 @@ protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : 
     (𝓝 1 : Filter (α →ᵤ G)).HasBasis p fun i => { f : α →ᵤ G | ∀ x, f x ∈ b i } :=
   by
   have := h.comap fun p : G × G => p.2 / p.1
-  rw [← uniformity_eq_comap_nhds_one] at this
+  rw [← uniformity_eq_comap_nhds_one] at this 
   convert UniformFun.hasBasis_nhds_of_basis α _ 1 this
   ext (i f)
   simp [UniformFun.gen]
@@ -165,7 +165,7 @@ protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α)
       { f : α →ᵤ[𝔖] G | ∀ x ∈ Si.1, f x ∈ b Si.2 } :=
   by
   have := h.comap fun p : G × G => p.1 / p.2
-  rw [← uniformity_eq_comap_nhds_one_swapped] at this
+  rw [← uniformity_eq_comap_nhds_one_swapped] at this 
   convert UniformOnFun.hasBasis_nhds_of_basis α _ 𝔖 1 h𝔖₁ h𝔖₂ this
   ext (i f)
   simp [UniformOnFun.gen]
@@ -214,9 +214,9 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
   · rintro ⟨S, V⟩ ⟨hS, hV⟩
     have : tendsto (fun kx : 𝕜 × E => kx.1 • kx.2) (𝓝 (0, 0)) (𝓝 <| (0 : 𝕜) • 0) :=
       continuous_smul.tendsto (0 : 𝕜 × E)
-    rw [zero_smul, nhds_prod_eq] at this
+    rw [zero_smul, nhds_prod_eq] at this 
     have := this hV
-    rw [mem_map, mem_prod_iff] at this
+    rw [mem_map, mem_prod_iff] at this 
     rcases this with ⟨U, hU, W, hW, hUW⟩
     refine' ⟨U, hU, ⟨S, W⟩, ⟨hS, hW⟩, _⟩
     rw [Set.smul_subset_iff]
@@ -225,7 +225,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
     exact hUW (⟨ha, hu x hx⟩ : (a, φ u x) ∈ U ×ˢ W)
   · rintro a ⟨S, V⟩ ⟨hS, hV⟩
     have : tendsto (fun x : E => a • x) (𝓝 0) (𝓝 <| a • 0) := tendsto_id.const_smul a
-    rw [smul_zero] at this
+    rw [smul_zero] at this 
     refine' ⟨⟨S, (· • ·) a ⁻¹' V⟩, ⟨hS, this hV⟩, fun f hf x hx => _⟩
     rw [SMulHomClass.map_smul]
     exact hf x hx
@@ -236,7 +236,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
     by_cases ha0 : a = 0
     · rw [ha0]
       simp [mem_of_mem_nhds hV]
-    · rw [mem_ball_zero_iff] at ha
+    · rw [mem_ball_zero_iff] at ha 
       rw [SMulHomClass.map_smul, Pi.smul_apply]
       have : φ u x ∈ a⁻¹ • V :=
         by
@@ -244,7 +244,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
         refine' (hr a⁻¹ _) (Set.mem_image_of_mem (φ u) hx)
         rw [norm_inv, le_inv hrpos ha0]
         exact ha.le
-      rwa [Set.mem_inv_smul_set_iff₀ ha0] at this
+      rwa [Set.mem_inv_smul_set_iff₀ ha0] at this 
 #align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_bounded
 
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any

f2b757fc

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -59,7 +59,7 @@ uniform convergence, strong dual
 
 open Filter
 
-open Topology Pointwise UniformConvergence
+open scoped Topology Pointwise UniformConvergence
 
 section AlgebraicInstances

f2b757fc

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -122,12 +122,6 @@ instance : UniformGroup (α →ᵤ G) :=
           uniformContinuous_div).comp
       UniformFun.uniformEquivProdArrow.symm.UniformContinuous⟩
 
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 @[to_additive]
 protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : ι → Set G}
     (h : (𝓝 1 : Filter G).HasBasis p b) :
@@ -141,12 +135,6 @@ protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : 
 #align uniform_fun.has_basis_nhds_one_of_basis UniformFun.hasBasis_nhds_one_of_basis
 #align uniform_fun.has_basis_nhds_zero_of_basis UniformFun.hasBasis_nhds_zero_of_basis
 
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 @[to_additive]
 protected theorem UniformFun.hasBasis_nhds_one :
     (𝓝 1 : Filter (α →ᵤ G)).HasBasis (fun V : Set G => V ∈ (𝓝 1 : Filter G)) fun V =>
@@ -169,12 +157,6 @@ instance : UniformGroup (α →ᵤ[𝔖] G) :=
           uniformContinuous_div).comp
       UniformOnFun.uniformEquivProdArrow.symm.UniformContinuous⟩
 
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 @[to_additive]
 protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α) (h𝔖₁ : 𝔖.Nonempty)
     (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) {p : ι → Prop} {b : ι → Set G}
@@ -190,12 +172,6 @@ protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α)
 #align uniform_on_fun.has_basis_nhds_one_of_basis UniformOnFun.hasBasis_nhds_one_of_basis
 #align uniform_on_fun.has_basis_nhds_zero_of_basis UniformOnFun.hasBasis_nhds_zero_of_basis
 
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-Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_basis_nhds_one UniformOnFun.hasBasis_nhds_oneₓ'. -/
 @[to_additive]
 protected theorem UniformOnFun.hasBasis_nhds_one (𝔖 : Set <| Set α) (h𝔖₁ : 𝔖.Nonempty)
     (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) :
@@ -214,9 +190,6 @@ variable (𝕜 α E H : Type _) {hom : Type _} [NormedField 𝕜] [AddCommGroup
   [AddCommGroup E] [Module 𝕜 E] [TopologicalSpace H] [UniformSpace E] [UniformAddGroup E]
   [ContinuousSMul 𝕜 E] {𝔖 : Set <| Set α} [LinearMapClass hom 𝕜 H (α →ᵤ[𝔖] E)]
 
-/- warning: uniform_on_fun.has_continuous_smul_induced_of_image_bounded -> UniformOnFun.continuousSMul_induced_of_image_bounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_boundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `bornology.is_vonN_bounded`), then `H`,
@@ -274,9 +247,6 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
       rwa [Set.mem_inv_smul_set_iff₀ ha0] at this
 #align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_bounded
 
-/- warning: uniform_on_fun.has_continuous_smul_submodule_of_image_bounded -> UniformOnFun.continuousSMul_submodule_of_image_bounded is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_continuous_smul_submodule_of_image_bounded UniformOnFun.continuousSMul_submodule_of_image_boundedₓ'. -/
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `bornology.is_vonN_bounded`), then `H`,
 equipped with the topology of `𝔖`-convergence, is a TVS.

f2b757fc

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -215,10 +215,7 @@ variable (𝕜 α E H : Type _) {hom : Type _} [NormedField 𝕜] [AddCommGroup
   [ContinuousSMul 𝕜 E] {𝔖 : Set <| Set α} [LinearMapClass hom 𝕜 H (α →ᵤ[𝔖] E)]
 
 /- warning: uniform_on_fun.has_continuous_smul_induced_of_image_bounded -> UniformOnFun.continuousSMul_induced_of_image_bounded is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) (α : Type.{u2}) (E : Type.{u3}) (H : Type.{u4}) {hom : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u4} H] [_inst_3 : Module.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)] [_inst_6 : TopologicalSpace.{u4} H] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (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)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u2} (Set.{u2} α)} [_inst_10 : LinearMapClass.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)], (Set.Nonempty.{u2} (Set.{u2} α) 𝔖) -> (DirectedOn.{u2} (Set.{u2} α) (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α)) 𝔖) -> (forall (φ : hom), (Inducing.{u4, max u2 u3} H (UniformOnFun.{u2, u3} α E 𝔖) _inst_6 (UniformOnFun.topologicalSpace.{u2, u3} α E _inst_7 𝔖) (coeFn.{succ u5, max (succ u4) (succ (max u2 u3))} hom (fun (_x : hom) => H -> (UniformOnFun.{u2, u3} α E 𝔖)) (FunLike.hasCoeToFun.{succ u5, succ u4, succ (max u2 u3)} hom H (fun (_x : H) => UniformOnFun.{u2, u3} α E 𝔖) (SMulHomClass.toFunLike.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (SMulZeroClass.toHasSmul.{u1, u4} 𝕜 H (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H 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(UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSmulHomClass.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 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𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10)))) φ)) -> (forall (u : H) (s : Set.{u2} α), (Membership.Mem.{u2, u2} (Set.{u2} α) (Set.{u2} (Set.{u2} α)) (Set.hasMem.{u2} (Set.{u2} α)) s 𝔖) -> (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E 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𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u2 u3, u5} 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) hom (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10)))) φ u) s))) -> (ContinuousSMul.{u1, u4} 𝕜 H (SMulZeroClass.toHasSmul.{u1, u4} 𝕜 H (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u4} 𝕜 H (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.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u4} 𝕜 H (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (Module.toMulActionWithZero.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _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_6))
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-  forall (𝕜 : Type.{u1}) (α : Type.{u5}) (E : Type.{u3}) (H : Type.{u4}) {hom : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u4} H] [_inst_3 : Module.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : 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_4)] [_inst_6 : TopologicalSpace.{u4} H] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u5} (Set.{u5} α)} [_inst_10 : LinearMapClass.{u2, u1, u4, max u3 u5} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)], (Set.Nonempty.{u5} (Set.{u5} α) 𝔖) -> (DirectedOn.{u5} (Set.{u5} α) (fun (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1900 : Set.{u5} α) (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1902 : Set.{u5} α) => HasSubset.Subset.{u5} (Set.{u5} α) (Set.instHasSubsetSet.{u5} α) x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1900 x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1902) 𝔖) -> (forall (φ : hom), (Inducing.{u4, max u5 u3} H (UniformOnFun.{u5, u3} α E 𝔖) _inst_6 (UniformOnFun.topologicalSpace.{u5, u3} α E _inst_7 𝔖) (FunLike.coe.{succ u2, succ u4, max (succ u5) (succ u3)} hom H (fun (_x : H) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : H) => UniformOnFun.{u5, u3} α E 𝔖) _x) (SMulHomClass.toFunLike.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (AddMonoid.toZero.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toZero.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribSMul.toSMulZeroClass.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u5 u3, u2} 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) hom (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10))) φ)) -> (forall (u : H) (s : Set.{u5} α), (Membership.mem.{u5, u5} (Set.{u5} α) (Set.{u5} (Set.{u5} α)) (Set.instMembershipSet.{u5} (Set.{u5} α)) s 𝔖) -> (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7) (Set.image.{u5, u3} α E (FunLike.coe.{succ u2, succ u4, max (succ u5) (succ u3)} hom H (fun (_x : H) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : H) => UniformOnFun.{u5, u3} α E 𝔖) _x) (SMulHomClass.toFunLike.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (AddMonoid.toZero.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toZero.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribSMul.toSMulZeroClass.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u5 u3, u2} 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) hom (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10))) φ u) s))) -> (ContinuousSMul.{u1, u4} 𝕜 H (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u4} 𝕜 H (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 𝕜 H (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (Module.toMulActionWithZero.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _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_6))
+<too large>
 Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_boundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
@@ -278,10 +275,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
 #align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_bounded
 
 /- warning: uniform_on_fun.has_continuous_smul_submodule_of_image_bounded -> UniformOnFun.continuousSMul_submodule_of_image_bounded is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) (α : Type.{u2}) (E : Type.{u3}) [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (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)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u2} (Set.{u2} α)}, (Set.Nonempty.{u2} (Set.{u2} α) 𝔖) -> (DirectedOn.{u2} (Set.{u2} α) (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α)) 𝔖) -> (forall (H : Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)), (forall (u : α -> E), (Membership.Mem.{max u2 u3, max u2 u3} (α -> E) (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SetLike.hasMem.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) u H) -> (forall (s : Set.{u2} α), (Membership.Mem.{u2, u2} (Set.{u2} α) (Set.{u2} (Set.{u2} α)) (Set.hasMem.{u2} (Set.{u2} α)) s 𝔖) -> (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7) (Set.image.{u2, u3} α E u s)))) -> (ContinuousSMul.{u1, max u2 u3} 𝕜 (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (Submodule.smul.{u1, u1, max u2 u3} 𝕜 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) H (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (MulAction.toHasSmul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (MulActionWithZero.toMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (IsScalarTower.left.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (MulActionWithZero.toMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (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)))))) (TopologicalSpace.induced.{max u2 u3, max u2 u3} (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (UniformOnFun.{u2, u3} α E 𝔖) ((fun (a : Type.{max u2 u3}) (b : Sort.{max (succ u2) (succ u3)}) [self : HasLiftT.{succ (max u2 u3), max (succ u2) (succ u3)} a b] => self.0) (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 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(Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) u H) -> (forall (s : Set.{u3} α), (Membership.mem.{u3, u3} (Set.{u3} α) (Set.{u3} (Set.{u3} α)) (Set.instMembershipSet.{u3} (Set.{u3} α)) s 𝔖) -> (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u1} E _inst_7) (Set.image.{u3, u1} α E u s)))) -> (ContinuousSMul.{u2, max u3 u1} 𝕜 (Subtype.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} 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(Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) x H)) (Submodule.smul.{u2, u2, max u3 u1} 𝕜 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5) H (Algebra.toSMul.{u2, u2} 𝕜 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u2, u2} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (NormedAlgebra.id.{u2} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (Module.toMulActionWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) (IsScalarTower.left.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (Module.toMulActionWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (TopologicalSpace.induced.{max u3 u1, max u3 u1} (Subtype.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) x H)) (UniformOnFun.{u3, u1} α E 𝔖) (Subtype.val.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Set.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖)) (Set.instMembershipSet.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖)) x (SetLike.coe.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) H))) (UniformOnFun.topologicalSpace.{u3, u1} α E _inst_7 𝔖))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_continuous_smul_submodule_of_image_bounded UniformOnFun.continuousSMul_submodule_of_image_boundedₓ'. -/
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `bornology.is_vonN_bounded`), then `H`,

f2b757fc

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -218,7 +218,7 @@ variable (𝕜 α E H : Type _) {hom : Type _} [NormedField 𝕜] [AddCommGroup
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) (α : Type.{u2}) (E : Type.{u3}) (H : Type.{u4}) {hom : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u4} H] [_inst_3 : Module.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)] [_inst_6 : TopologicalSpace.{u4} H] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (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)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u2} (Set.{u2} α)} [_inst_10 : LinearMapClass.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)], (Set.Nonempty.{u2} (Set.{u2} α) 𝔖) -> (DirectedOn.{u2} (Set.{u2} α) (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α)) 𝔖) -> (forall (φ : hom), (Inducing.{u4, max u2 u3} H (UniformOnFun.{u2, u3} α E 𝔖) _inst_6 (UniformOnFun.topologicalSpace.{u2, u3} α E _inst_7 𝔖) (coeFn.{succ u5, max (succ u4) (succ (max u2 u3))} hom (fun (_x : hom) => H -> (UniformOnFun.{u2, u3} α E 𝔖)) (FunLike.hasCoeToFun.{succ u5, succ u4, succ (max u2 u3)} hom H (fun (_x : H) => UniformOnFun.{u2, u3} α E 𝔖) (SMulHomClass.toFunLike.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (SMulZeroClass.toHasSmul.{u1, u4} 𝕜 H (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (AddZeroClass.toHasZero.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))))) (DistribSMul.toSmulZeroClass.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSmulHomClass.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u2 u3, u5} 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) hom (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10)))) φ)) -> (forall (u : H) (s : Set.{u2} α), (Membership.Mem.{u2, u2} (Set.{u2} α) (Set.{u2} (Set.{u2} α)) (Set.hasMem.{u2} (Set.{u2} α)) s 𝔖) -> (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7) (Set.image.{u2, u3} α E (coeFn.{succ u5, max (succ u4) (succ (max u2 u3))} hom (fun (_x : hom) => H -> (UniformOnFun.{u2, u3} α E 𝔖)) (FunLike.hasCoeToFun.{succ u5, succ u4, succ (max u2 u3)} hom H (fun (_x : H) => UniformOnFun.{u2, u3} α E 𝔖) (SMulHomClass.toFunLike.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (SMulZeroClass.toHasSmul.{u1, u4} 𝕜 H (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (AddZeroClass.toHasZero.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))))) (DistribSMul.toSmulZeroClass.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSmulHomClass.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u2 u3, u5} 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) hom (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10)))) φ u) s))) -> (ContinuousSMul.{u1, u4} 𝕜 H (SMulZeroClass.toHasSmul.{u1, u4} 𝕜 H (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u4} 𝕜 H (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.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u4} 𝕜 H (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (Module.toMulActionWithZero.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _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_6))
 but is expected to have type
-  forall (𝕜 : Type.{u1}) (α : Type.{u5}) (E : Type.{u3}) (H : Type.{u4}) {hom : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u4} H] [_inst_3 : Module.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : 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_4)] [_inst_6 : TopologicalSpace.{u4} H] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u5} (Set.{u5} α)} [_inst_10 : LinearMapClass.{u2, u1, u4, max u3 u5} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)], (Set.Nonempty.{u5} (Set.{u5} α) 𝔖) -> (DirectedOn.{u5} (Set.{u5} α) (fun (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1900 : Set.{u5} α) (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1902 : Set.{u5} α) => HasSubset.Subset.{u5} (Set.{u5} α) (Set.instHasSubsetSet.{u5} α) x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1900 x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1902) 𝔖) -> (forall (φ : hom), (Inducing.{u4, max u5 u3} H (UniformOnFun.{u5, u3} α E 𝔖) _inst_6 (UniformOnFun.topologicalSpace.{u5, u3} α E _inst_7 𝔖) (FunLike.coe.{succ u2, succ u4, max (succ u5) (succ u3)} hom H (fun (_x : H) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : H) => UniformOnFun.{u5, u3} α E 𝔖) _x) (SMulHomClass.toFunLike.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (AddMonoid.toZero.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toZero.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribSMul.toSMulZeroClass.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u5 u3, u2} 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) hom (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10))) φ)) -> (forall (u : H) (s : Set.{u5} α), (Membership.mem.{u5, u5} (Set.{u5} α) (Set.{u5} (Set.{u5} α)) (Set.instMembershipSet.{u5} (Set.{u5} α)) s 𝔖) -> (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7) (Set.image.{u5, u3} α E (FunLike.coe.{succ u2, succ u4, max (succ u5) (succ u3)} hom H (fun (_x : H) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : H) => UniformOnFun.{u5, u3} α E 𝔖) _x) (SMulHomClass.toFunLike.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (AddMonoid.toZero.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toZero.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribSMul.toSMulZeroClass.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u5 u3, u2} 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) hom (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10))) φ u) s))) -> (ContinuousSMul.{u1, u4} 𝕜 H (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u4} 𝕜 H (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 𝕜 H (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (Module.toMulActionWithZero.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _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_6))
+  forall (𝕜 : Type.{u1}) (α : Type.{u5}) (E : Type.{u3}) (H : Type.{u4}) {hom : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u4} H] [_inst_3 : Module.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : 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_4)] [_inst_6 : TopologicalSpace.{u4} H] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u5} (Set.{u5} α)} [_inst_10 : LinearMapClass.{u2, u1, u4, max u3 u5} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)], (Set.Nonempty.{u5} (Set.{u5} α) 𝔖) -> (DirectedOn.{u5} (Set.{u5} α) (fun (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1900 : Set.{u5} α) (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1902 : Set.{u5} α) => HasSubset.Subset.{u5} (Set.{u5} α) (Set.instHasSubsetSet.{u5} α) x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1900 x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1902) 𝔖) -> (forall (φ : hom), (Inducing.{u4, max u5 u3} H (UniformOnFun.{u5, u3} α E 𝔖) _inst_6 (UniformOnFun.topologicalSpace.{u5, u3} α E _inst_7 𝔖) (FunLike.coe.{succ u2, succ u4, max (succ u5) (succ u3)} hom H (fun (_x : H) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : H) => UniformOnFun.{u5, u3} α E 𝔖) _x) (SMulHomClass.toFunLike.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (AddMonoid.toZero.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toZero.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribSMul.toSMulZeroClass.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u5 u3, u2} 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) hom (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10))) φ)) -> (forall (u : H) (s : Set.{u5} α), (Membership.mem.{u5, u5} (Set.{u5} α) (Set.{u5} (Set.{u5} α)) (Set.instMembershipSet.{u5} (Set.{u5} α)) s 𝔖) -> (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7) (Set.image.{u5, u3} α E (FunLike.coe.{succ u2, succ u4, max (succ u5) (succ u3)} hom H (fun (_x : H) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : H) => UniformOnFun.{u5, u3} α E 𝔖) _x) (SMulHomClass.toFunLike.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (AddMonoid.toZero.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toZero.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribSMul.toSMulZeroClass.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u5 u3, u2} 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) hom (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10))) φ u) s))) -> (ContinuousSMul.{u1, u4} 𝕜 H (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u4} 𝕜 H (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 𝕜 H (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (Module.toMulActionWithZero.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _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_6))
 Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_boundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any

f2b757fc

bump to nightly-2023-05-16-14

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

b356e20f

Diff

@@ -281,7 +281,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) (α : Type.{u2}) (E : Type.{u3}) [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (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)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u2} (Set.{u2} α)}, (Set.Nonempty.{u2} (Set.{u2} α) 𝔖) -> (DirectedOn.{u2} (Set.{u2} α) (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α)) 𝔖) -> (forall (H : Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)), (forall (u : α -> E), (Membership.Mem.{max u2 u3, max u2 u3} (α -> E) (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SetLike.hasMem.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) u H) -> (forall (s : Set.{u2} α), (Membership.Mem.{u2, u2} (Set.{u2} α) (Set.{u2} (Set.{u2} α)) (Set.hasMem.{u2} (Set.{u2} α)) s 𝔖) -> (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7) (Set.image.{u2, u3} α E u s)))) -> (ContinuousSMul.{u1, max u2 u3} 𝕜 (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (Submodule.smul.{u1, u1, max u2 u3} 𝕜 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) H (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (MulAction.toHasSmul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (MulActionWithZero.toMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (IsScalarTower.left.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (MulActionWithZero.toMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (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)))))) (TopologicalSpace.induced.{max u2 u3, max u2 u3} (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (UniformOnFun.{u2, u3} α E 𝔖) ((fun (a : Type.{max u2 u3}) (b : Sort.{max (succ u2) (succ u3)}) [self : HasLiftT.{succ (max u2 u3), max (succ u2) (succ u3)} a b] => self.0) (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (UniformOnFun.{u2, u3} α E 𝔖) (HasLiftT.mk.{succ (max u2 u3), max (succ u2) (succ u3)} (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (UniformOnFun.{u2, u3} α E 𝔖) (CoeTCₓ.coe.{succ (max u2 u3), max (succ u2) (succ u3)} (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (UniformOnFun.{u2, u3} α E 𝔖) (coeBase.{succ (max u2 u3), max (succ u2) (succ u3)} (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (UniformOnFun.{u2, u3} α E 𝔖) (coeSubtype.{max (succ u2) (succ u3)} (UniformOnFun.{u2, u3} α E 𝔖) (fun (x : UniformOnFun.{u2, u3} α E 𝔖) => Membership.Mem.{max u2 u3, max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SetLike.hasMem.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) x H)))))) (UniformOnFun.topologicalSpace.{u2, u3} α E _inst_7 𝔖))))
 but is expected to have type
-  forall (𝕜 : Type.{u2}) (α : Type.{u3}) (E : Type.{u1}) [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] [_inst_7 : UniformSpace.{u1} E] [_inst_8 : UniformAddGroup.{u1} E _inst_7 (AddCommGroup.toAddGroup.{u1} E _inst_4)] [_inst_9 : ContinuousSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} E _inst_7)] {𝔖 : Set.{u3} (Set.{u3} α)}, (Set.Nonempty.{u3} (Set.{u3} α) 𝔖) -> (DirectedOn.{u3} (Set.{u3} α) (fun (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2968 : Set.{u3} α) (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2970 : Set.{u3} α) => HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2968 x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2970) 𝔖) -> (forall (H : Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)), (forall (u : UniformOnFun.{u3, u1} α E 𝔖), (Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} 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(Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) u H) -> (forall (s : Set.{u3} α), (Membership.mem.{u3, u3} (Set.{u3} α) (Set.{u3} (Set.{u3} α)) (Set.instMembershipSet.{u3} (Set.{u3} α)) s 𝔖) -> (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u1} E _inst_7) (Set.image.{u3, u1} α E u s)))) -> (ContinuousSMul.{u2, max u3 u1} 𝕜 (Subtype.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} 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(Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) x H)) (Submodule.smul.{u2, u2, max u3 u1} 𝕜 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5) H (Algebra.toSMul.{u2, u2} 𝕜 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u2, u2} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (NormedAlgebra.id.{u2} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (Module.toMulActionWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) (IsScalarTower.left.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (Module.toMulActionWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (TopologicalSpace.induced.{max u3 u1, max u3 u1} (Subtype.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) x H)) (UniformOnFun.{u3, u1} α E 𝔖) (Subtype.val.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Set.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖)) (Set.instMembershipSet.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖)) x (SetLike.coe.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) H))) (UniformOnFun.topologicalSpace.{u3, u1} α E _inst_7 𝔖))))
+  forall (𝕜 : Type.{u2}) (α : Type.{u3}) (E : Type.{u1}) [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] [_inst_7 : UniformSpace.{u1} E] [_inst_8 : UniformAddGroup.{u1} E _inst_7 (AddCommGroup.toAddGroup.{u1} E _inst_4)] [_inst_9 : ContinuousSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} E _inst_7)] {𝔖 : Set.{u3} (Set.{u3} α)}, (Set.Nonempty.{u3} (Set.{u3} α) 𝔖) -> (DirectedOn.{u3} (Set.{u3} α) (fun (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2965 : Set.{u3} α) (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2967 : Set.{u3} α) => HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2965 x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2967) 𝔖) -> (forall (H : Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)), (forall (u : UniformOnFun.{u3, u1} α E 𝔖), (Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) u H) -> (forall (s : Set.{u3} α), (Membership.mem.{u3, u3} (Set.{u3} α) (Set.{u3} (Set.{u3} α)) (Set.instMembershipSet.{u3} (Set.{u3} α)) s 𝔖) -> (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u1} E _inst_7) (Set.image.{u3, u1} α E u s)))) -> (ContinuousSMul.{u2, max u3 u1} 𝕜 (Subtype.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) x H)) (Submodule.smul.{u2, u2, max u3 u1} 𝕜 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5) H (Algebra.toSMul.{u2, u2} 𝕜 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u2, u2} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (NormedAlgebra.id.{u2} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (Module.toMulActionWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) (IsScalarTower.left.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (Module.toMulActionWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (TopologicalSpace.induced.{max u3 u1, max u3 u1} (Subtype.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) x H)) (UniformOnFun.{u3, u1} α E 𝔖) (Subtype.val.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Set.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖)) (Set.instMembershipSet.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖)) x (SetLike.coe.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) H))) (UniformOnFun.topologicalSpace.{u3, u1} α E _inst_7 𝔖))))
 Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_continuous_smul_submodule_of_image_bounded UniformOnFun.continuousSMul_submodule_of_image_boundedₓ'. -/
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `bornology.is_vonN_bounded`), then `H`,

f2b757fc

bump to nightly-2023-04-30-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/86d04064ca33ee3d3405fbfc497d494fd2dd4796

648ff713

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
 
 ! This file was ported from Lean 3 source module topology.algebra.uniform_convergence
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Algebra.FilterBasis
 /-!
 # Algebraic facts about the topology of uniform convergence
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains algebraic compatibility results about the uniform structure of uniform
 convergence / `𝔖`-convergence. They will mostly be useful for defining strong topologies on the
 space of continuous linear maps between two topological vector spaces.

f2ce6086

bump to nightly-2023-04-27-16

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

c8f7a684

Diff

@@ -119,6 +119,12 @@ instance : UniformGroup (α →ᵤ G) :=
           uniformContinuous_div).comp
       UniformFun.uniformEquivProdArrow.symm.UniformContinuous⟩
 
+/- warning: uniform_fun.has_basis_nhds_one_of_basis -> UniformFun.hasBasis_nhds_one_of_basis is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {G : Type.{u2}} {ι : Type.{u3}} [_inst_1 : Group.{u2} G] [_inst_2 : UniformSpace.{u2} G] [_inst_3 : UniformGroup.{u2} G _inst_2 _inst_1] {p : ι -> Prop} {b : ι -> (Set.{u2} G)}, (Filter.HasBasis.{u2, succ u3} G ι (nhds.{u2} G (UniformSpace.toTopologicalSpace.{u2} G _inst_2) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))))) p b) -> (Filter.HasBasis.{max u1 u2, succ u3} (UniformFun.{u1, u2} α G) ι (nhds.{max u1 u2} (UniformFun.{u1, u2} α G) (UniformFun.topologicalSpace.{u1, u2} α G _inst_2) (OfNat.ofNat.{max u1 u2} (UniformFun.{u1, u2} α G) 1 (OfNat.mk.{max u1 u2} (UniformFun.{u1, u2} α G) 1 (One.one.{max u1 u2} (UniformFun.{u1, u2} α G) (MulOneClass.toHasOne.{max u1 u2} (UniformFun.{u1, u2} α G) (Monoid.toMulOneClass.{max u1 u2} (UniformFun.{u1, u2} α G) (UniformFun.monoid.{u1, u2} α G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))))))) p (fun (i : ι) => setOf.{max u1 u2} (UniformFun.{u1, u2} α G) (fun (f : UniformFun.{u1, u2} α G) => forall (x : α), Membership.Mem.{u2, u2} G (Set.{u2} G) (Set.hasMem.{u2} G) (f x) (b i))))
+but is expected to have type
+  forall {α : Type.{u1}} {G : Type.{u3}} {ι : Type.{u2}} [_inst_1 : Group.{u3} G] [_inst_2 : UniformSpace.{u3} G] [_inst_3 : UniformGroup.{u3} G _inst_2 _inst_1] {p : ι -> Prop} {b : ι -> (Set.{u3} G)}, (Filter.HasBasis.{u3, succ u2} G ι (nhds.{u3} G (UniformSpace.toTopologicalSpace.{u3} G _inst_2) (OfNat.ofNat.{u3} G 1 (One.toOfNat1.{u3} G (InvOneClass.toOne.{u3} G (DivInvOneMonoid.toInvOneClass.{u3} G (DivisionMonoid.toDivInvOneMonoid.{u3} G (Group.toDivisionMonoid.{u3} G _inst_1))))))) p b) -> (Filter.HasBasis.{max u1 u3, succ u2} (UniformFun.{u1, u3} α G) ι (nhds.{max u1 u3} (UniformFun.{u1, u3} α G) (UniformFun.topologicalSpace.{u1, u3} α G _inst_2) (OfNat.ofNat.{max u1 u3} (UniformFun.{u1, u3} α G) 1 (One.toOfNat1.{max u1 u3} (UniformFun.{u1, u3} α G) (InvOneClass.toOne.{max u1 u3} (UniformFun.{u1, u3} α G) (DivInvOneMonoid.toInvOneClass.{max u1 u3} (UniformFun.{u1, u3} α G) (DivisionMonoid.toDivInvOneMonoid.{max u1 u3} (UniformFun.{u1, u3} α G) (Group.toDivisionMonoid.{max u1 u3} (UniformFun.{u1, u3} α G) (instGroupUniformFun.{u1, u3} α G _inst_1)))))))) p (fun (i : ι) => setOf.{max u1 u3} (UniformFun.{u1, u3} α G) (fun (f : UniformFun.{u1, u3} α G) => forall (x : α), Membership.mem.{u3, u3} G (Set.{u3} G) (Set.instMembershipSet.{u3} G) (f x) (b i))))
+Case conversion may be inaccurate. Consider using '#align uniform_fun.has_basis_nhds_one_of_basis UniformFun.hasBasis_nhds_one_of_basisₓ'. -/
 @[to_additive]
 protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : ι → Set G}
     (h : (𝓝 1 : Filter G).HasBasis p b) :
@@ -132,6 +138,12 @@ protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : 
 #align uniform_fun.has_basis_nhds_one_of_basis UniformFun.hasBasis_nhds_one_of_basis
 #align uniform_fun.has_basis_nhds_zero_of_basis UniformFun.hasBasis_nhds_zero_of_basis
 
+/- warning: uniform_fun.has_basis_nhds_one -> UniformFun.hasBasis_nhds_one is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_2 : UniformSpace.{u2} G] [_inst_3 : UniformGroup.{u2} G _inst_2 _inst_1], Filter.HasBasis.{max u1 u2, succ u2} (UniformFun.{u1, u2} α G) (Set.{u2} G) (nhds.{max u1 u2} (UniformFun.{u1, u2} α G) (UniformFun.topologicalSpace.{u1, u2} α G _inst_2) (OfNat.ofNat.{max u1 u2} (UniformFun.{u1, u2} α G) 1 (OfNat.mk.{max u1 u2} (UniformFun.{u1, u2} α G) 1 (One.one.{max u1 u2} (UniformFun.{u1, u2} α G) (MulOneClass.toHasOne.{max u1 u2} (UniformFun.{u1, u2} α G) (Monoid.toMulOneClass.{max u1 u2} (UniformFun.{u1, u2} α G) (UniformFun.monoid.{u1, u2} α G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))))))) (fun (V : Set.{u2} G) => Membership.Mem.{u2, u2} (Set.{u2} G) (Filter.{u2} G) (Filter.hasMem.{u2} G) V (nhds.{u2} G (UniformSpace.toTopologicalSpace.{u2} G _inst_2) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))))))) (fun (V : Set.{u2} G) => setOf.{max u1 u2} (UniformFun.{u1, u2} α G) (fun (f : α -> G) => forall (x : α), Membership.Mem.{u2, u2} G (Set.{u2} G) (Set.hasMem.{u2} G) (f x) V))
+but is expected to have type
+  forall {α : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u1} G] [_inst_2 : UniformSpace.{u1} G] [_inst_3 : UniformGroup.{u1} G _inst_2 _inst_1], Filter.HasBasis.{max u2 u1, succ u1} (UniformFun.{u2, u1} α G) (Set.{u1} G) (nhds.{max u2 u1} (UniformFun.{u2, u1} α G) (UniformFun.topologicalSpace.{u2, u1} α G _inst_2) (OfNat.ofNat.{max u2 u1} (UniformFun.{u2, u1} α G) 1 (One.toOfNat1.{max u2 u1} (UniformFun.{u2, u1} α G) (InvOneClass.toOne.{max u2 u1} (UniformFun.{u2, u1} α G) (DivInvOneMonoid.toInvOneClass.{max u2 u1} (UniformFun.{u2, u1} α G) (DivisionMonoid.toDivInvOneMonoid.{max u2 u1} (UniformFun.{u2, u1} α G) (Group.toDivisionMonoid.{max u2 u1} (UniformFun.{u2, u1} α G) (instGroupUniformFun.{u2, u1} α G _inst_1)))))))) (fun (V : Set.{u1} G) => Membership.mem.{u1, u1} (Set.{u1} G) (Filter.{u1} G) (instMembershipSetFilter.{u1} G) V (nhds.{u1} G (UniformSpace.toTopologicalSpace.{u1} G _inst_2) (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))))))) (fun (V : Set.{u1} G) => setOf.{max u2 u1} (UniformFun.{u2, u1} α G) (fun (f : α -> G) => forall (x : α), Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) (f x) V))
+Case conversion may be inaccurate. Consider using '#align uniform_fun.has_basis_nhds_one UniformFun.hasBasis_nhds_oneₓ'. -/
 @[to_additive]
 protected theorem UniformFun.hasBasis_nhds_one :
     (𝓝 1 : Filter (α →ᵤ G)).HasBasis (fun V : Set G => V ∈ (𝓝 1 : Filter G)) fun V =>
@@ -154,6 +166,12 @@ instance : UniformGroup (α →ᵤ[𝔖] G) :=
           uniformContinuous_div).comp
       UniformOnFun.uniformEquivProdArrow.symm.UniformContinuous⟩
 
+/- warning: uniform_on_fun.has_basis_nhds_one_of_basis -> UniformOnFun.hasBasis_nhds_one_of_basis is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {G : Type.{u2}} {ι : Type.{u3}} [_inst_1 : Group.{u2} G] [_inst_2 : UniformSpace.{u2} G] [_inst_3 : UniformGroup.{u2} G _inst_2 _inst_1] (𝔖 : Set.{u1} (Set.{u1} α)), (Set.Nonempty.{u1} (Set.{u1} α) 𝔖) -> (DirectedOn.{u1} (Set.{u1} α) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α)) 𝔖) -> (forall {p : ι -> Prop} {b : ι -> (Set.{u2} G)}, (Filter.HasBasis.{u2, succ u3} G ι (nhds.{u2} G (UniformSpace.toTopologicalSpace.{u2} G _inst_2) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))))) p b) -> (Filter.HasBasis.{max u1 u2, max (succ u1) (succ u3)} (UniformOnFun.{u1, u2} α G 𝔖) (Prod.{u1, u3} (Set.{u1} α) ι) (nhds.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (UniformOnFun.topologicalSpace.{u1, u2} α G _inst_2 𝔖) (OfNat.ofNat.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) 1 (OfNat.mk.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) 1 (One.one.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (MulOneClass.toHasOne.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (Monoid.toMulOneClass.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (UniformOnFun.monoid.{u1, u2} α G 𝔖 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))))))) (fun (Si : Prod.{u1, u3} (Set.{u1} α) ι) => And (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) (Prod.fst.{u1, u3} (Set.{u1} α) ι Si) 𝔖) (p (Prod.snd.{u1, u3} (Set.{u1} α) ι Si))) (fun (Si : Prod.{u1, u3} (Set.{u1} α) ι) => setOf.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (fun (f : UniformOnFun.{u1, u2} α G 𝔖) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Prod.fst.{u1, u3} (Set.{u1} α) ι Si)) -> (Membership.Mem.{u2, u2} G (Set.{u2} G) (Set.hasMem.{u2} G) (f x) (b (Prod.snd.{u1, u3} (Set.{u1} α) ι Si)))))))
+but is expected to have type
+  forall {α : Type.{u3}} {G : Type.{u2}} {ι : Type.{u1}} [_inst_1 : Group.{u2} G] [_inst_2 : UniformSpace.{u2} G] [_inst_3 : UniformGroup.{u2} G _inst_2 _inst_1] (𝔖 : Set.{u3} (Set.{u3} α)), (Set.Nonempty.{u3} (Set.{u3} α) 𝔖) -> (DirectedOn.{u3} (Set.{u3} α) (fun (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1382 : Set.{u3} α) (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1384 : Set.{u3} α) => HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1382 x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1384) 𝔖) -> (forall {p : ι -> Prop} {b : ι -> (Set.{u2} G)}, (Filter.HasBasis.{u2, succ u1} G ι (nhds.{u2} G (UniformSpace.toTopologicalSpace.{u2} G _inst_2) (OfNat.ofNat.{u2} G 1 (One.toOfNat1.{u2} G (InvOneClass.toOne.{u2} G (DivInvOneMonoid.toInvOneClass.{u2} G (DivisionMonoid.toDivInvOneMonoid.{u2} G (Group.toDivisionMonoid.{u2} G _inst_1))))))) p b) -> (Filter.HasBasis.{max u3 u2, max (succ u3) (succ u1)} (UniformOnFun.{u3, u2} α G 𝔖) (Prod.{u3, u1} (Set.{u3} α) ι) (nhds.{max u3 u2} (UniformOnFun.{u3, u2} α G 𝔖) (UniformOnFun.topologicalSpace.{u3, u2} α G _inst_2 𝔖) (OfNat.ofNat.{max u3 u2} (UniformOnFun.{u3, u2} α G 𝔖) 1 (One.toOfNat1.{max u3 u2} (UniformOnFun.{u3, u2} α G 𝔖) (InvOneClass.toOne.{max u3 u2} (UniformOnFun.{u3, u2} α G 𝔖) (DivInvOneMonoid.toInvOneClass.{max u3 u2} (UniformOnFun.{u3, u2} α G 𝔖) (DivisionMonoid.toDivInvOneMonoid.{max u3 u2} (UniformOnFun.{u3, u2} α G 𝔖) (Group.toDivisionMonoid.{max u3 u2} (UniformOnFun.{u3, u2} α G 𝔖) (instGroupUniformOnFun.{u3, u2} α G 𝔖 _inst_1)))))))) (fun (Si : Prod.{u3, u1} (Set.{u3} α) ι) => And (Membership.mem.{u3, u3} (Set.{u3} α) (Set.{u3} (Set.{u3} α)) (Set.instMembershipSet.{u3} (Set.{u3} α)) (Prod.fst.{u3, u1} (Set.{u3} α) ι Si) 𝔖) (p (Prod.snd.{u3, u1} (Set.{u3} α) ι Si))) (fun (Si : Prod.{u3, u1} (Set.{u3} α) ι) => setOf.{max u3 u2} (UniformOnFun.{u3, u2} α G 𝔖) (fun (f : UniformOnFun.{u3, u2} α G 𝔖) => forall (x : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x (Prod.fst.{u3, u1} (Set.{u3} α) ι Si)) -> (Membership.mem.{u2, u2} G (Set.{u2} G) (Set.instMembershipSet.{u2} G) (f x) (b (Prod.snd.{u3, u1} (Set.{u3} α) ι Si)))))))
+Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_basis_nhds_one_of_basis UniformOnFun.hasBasis_nhds_one_of_basisₓ'. -/
 @[to_additive]
 protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α) (h𝔖₁ : 𝔖.Nonempty)
     (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) {p : ι → Prop} {b : ι → Set G}
@@ -169,6 +187,12 @@ protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α)
 #align uniform_on_fun.has_basis_nhds_one_of_basis UniformOnFun.hasBasis_nhds_one_of_basis
 #align uniform_on_fun.has_basis_nhds_zero_of_basis UniformOnFun.hasBasis_nhds_zero_of_basis
 
+/- warning: uniform_on_fun.has_basis_nhds_one -> UniformOnFun.hasBasis_nhds_one is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u2} G] [_inst_2 : UniformSpace.{u2} G] [_inst_3 : UniformGroup.{u2} G _inst_2 _inst_1] (𝔖 : Set.{u1} (Set.{u1} α)), (Set.Nonempty.{u1} (Set.{u1} α) 𝔖) -> (DirectedOn.{u1} (Set.{u1} α) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α)) 𝔖) -> (Filter.HasBasis.{max u1 u2, max (succ u1) (succ u2)} (UniformOnFun.{u1, u2} α G 𝔖) (Prod.{u1, u2} (Set.{u1} α) (Set.{u2} G)) (nhds.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (UniformOnFun.topologicalSpace.{u1, u2} α G _inst_2 𝔖) (OfNat.ofNat.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) 1 (OfNat.mk.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) 1 (One.one.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (MulOneClass.toHasOne.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (Monoid.toMulOneClass.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (UniformOnFun.monoid.{u1, u2} α G 𝔖 (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))))))))) (fun (SV : Prod.{u1, u2} (Set.{u1} α) (Set.{u2} G)) => And (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) (Prod.fst.{u1, u2} (Set.{u1} α) (Set.{u2} G) SV) 𝔖) (Membership.Mem.{u2, u2} (Set.{u2} G) (Filter.{u2} G) (Filter.hasMem.{u2} G) (Prod.snd.{u1, u2} (Set.{u1} α) (Set.{u2} G) SV) (nhds.{u2} G (UniformSpace.toTopologicalSpace.{u2} G _inst_2) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))))))) (fun (SV : Prod.{u1, u2} (Set.{u1} α) (Set.{u2} G)) => setOf.{max u1 u2} (UniformOnFun.{u1, u2} α G 𝔖) (fun (f : UniformOnFun.{u1, u2} α G 𝔖) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Prod.fst.{u1, u2} (Set.{u1} α) (Set.{u2} G) SV)) -> (Membership.Mem.{u2, u2} G (Set.{u2} G) (Set.hasMem.{u2} G) (f x) (Prod.snd.{u1, u2} (Set.{u1} α) (Set.{u2} G) SV)))))
+but is expected to have type
+  forall {α : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u1} G] [_inst_2 : UniformSpace.{u1} G] [_inst_3 : UniformGroup.{u1} G _inst_2 _inst_1] (𝔖 : Set.{u2} (Set.{u2} α)), (Set.Nonempty.{u2} (Set.{u2} α) 𝔖) -> (DirectedOn.{u2} (Set.{u2} α) (fun (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1656 : Set.{u2} α) (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1658 : Set.{u2} α) => HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1656 x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1658) 𝔖) -> (Filter.HasBasis.{max u2 u1, max (succ u2) (succ u1)} (UniformOnFun.{u2, u1} α G 𝔖) (Prod.{u2, u1} (Set.{u2} α) (Set.{u1} G)) (nhds.{max u2 u1} (UniformOnFun.{u2, u1} α G 𝔖) (UniformOnFun.topologicalSpace.{u2, u1} α G _inst_2 𝔖) (OfNat.ofNat.{max u2 u1} (UniformOnFun.{u2, u1} α G 𝔖) 1 (One.toOfNat1.{max u2 u1} (UniformOnFun.{u2, u1} α G 𝔖) (InvOneClass.toOne.{max u2 u1} (UniformOnFun.{u2, u1} α G 𝔖) (DivInvOneMonoid.toInvOneClass.{max u2 u1} (UniformOnFun.{u2, u1} α G 𝔖) (DivisionMonoid.toDivInvOneMonoid.{max u2 u1} (UniformOnFun.{u2, u1} α G 𝔖) (Group.toDivisionMonoid.{max u2 u1} (UniformOnFun.{u2, u1} α G 𝔖) (instGroupUniformOnFun.{u2, u1} α G 𝔖 _inst_1)))))))) (fun (SV : Prod.{u2, u1} (Set.{u2} α) (Set.{u1} G)) => And (Membership.mem.{u2, u2} (Set.{u2} α) (Set.{u2} (Set.{u2} α)) (Set.instMembershipSet.{u2} (Set.{u2} α)) (Prod.fst.{u2, u1} (Set.{u2} α) (Set.{u1} G) SV) 𝔖) (Membership.mem.{u1, u1} (Set.{u1} G) (Filter.{u1} G) (instMembershipSetFilter.{u1} G) (Prod.snd.{u2, u1} (Set.{u2} α) (Set.{u1} G) SV) (nhds.{u1} G (UniformSpace.toTopologicalSpace.{u1} G _inst_2) (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1))))))))) (fun (SV : Prod.{u2, u1} (Set.{u2} α) (Set.{u1} G)) => setOf.{max u2 u1} (UniformOnFun.{u2, u1} α G 𝔖) (fun (f : UniformOnFun.{u2, u1} α G 𝔖) => forall (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (Prod.fst.{u2, u1} (Set.{u2} α) (Set.{u1} G) SV)) -> (Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) (f x) (Prod.snd.{u2, u1} (Set.{u2} α) (Set.{u1} G) SV)))))
+Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_basis_nhds_one UniformOnFun.hasBasis_nhds_oneₓ'. -/
 @[to_additive]
 protected theorem UniformOnFun.hasBasis_nhds_one (𝔖 : Set <| Set α) (h𝔖₁ : 𝔖.Nonempty)
     (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) :
@@ -187,6 +211,12 @@ variable (𝕜 α E H : Type _) {hom : Type _} [NormedField 𝕜] [AddCommGroup
   [AddCommGroup E] [Module 𝕜 E] [TopologicalSpace H] [UniformSpace E] [UniformAddGroup E]
   [ContinuousSMul 𝕜 E] {𝔖 : Set <| Set α} [LinearMapClass hom 𝕜 H (α →ᵤ[𝔖] E)]
 
+/- warning: uniform_on_fun.has_continuous_smul_induced_of_image_bounded -> UniformOnFun.continuousSMul_induced_of_image_bounded is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (α : Type.{u2}) (E : Type.{u3}) (H : Type.{u4}) {hom : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u4} H] [_inst_3 : Module.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)] [_inst_6 : TopologicalSpace.{u4} H] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (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)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u2} (Set.{u2} α)} [_inst_10 : LinearMapClass.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)], (Set.Nonempty.{u2} (Set.{u2} α) 𝔖) -> (DirectedOn.{u2} (Set.{u2} α) (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α)) 𝔖) -> (forall (φ : hom), (Inducing.{u4, max u2 u3} H (UniformOnFun.{u2, u3} α E 𝔖) _inst_6 (UniformOnFun.topologicalSpace.{u2, u3} α E _inst_7 𝔖) (coeFn.{succ u5, max (succ u4) (succ (max u2 u3))} hom (fun (_x : hom) => H -> (UniformOnFun.{u2, u3} α E 𝔖)) (FunLike.hasCoeToFun.{succ u5, succ u4, succ (max u2 u3)} hom H (fun (_x : H) => UniformOnFun.{u2, u3} α E 𝔖) (SMulHomClass.toFunLike.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (SMulZeroClass.toHasSmul.{u1, u4} 𝕜 H (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (AddZeroClass.toHasZero.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))))) (DistribSMul.toSmulZeroClass.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSmulHomClass.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u2 u3, u5} 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) hom (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10)))) φ)) -> (forall (u : H) (s : Set.{u2} α), (Membership.Mem.{u2, u2} (Set.{u2} α) (Set.{u2} (Set.{u2} α)) (Set.hasMem.{u2} (Set.{u2} α)) s 𝔖) -> (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7) (Set.image.{u2, u3} α E (coeFn.{succ u5, max (succ u4) (succ (max u2 u3))} hom (fun (_x : hom) => H -> (UniformOnFun.{u2, u3} α E 𝔖)) (FunLike.hasCoeToFun.{succ u5, succ u4, succ (max u2 u3)} hom H (fun (_x : H) => UniformOnFun.{u2, u3} α E 𝔖) (SMulHomClass.toFunLike.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (SMulZeroClass.toHasSmul.{u1, u4} 𝕜 H (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (DistribSMul.toSmulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toHasSmul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (AddZeroClass.toHasZero.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))))) (DistribSMul.toSmulZeroClass.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSmulHomClass.{u5, u1, u4, max u2 u3} hom 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u2 u3, u5} 𝕜 H (UniformOnFun.{u2, u3} α E 𝔖) hom (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10)))) φ u) s))) -> (ContinuousSMul.{u1, u4} 𝕜 H (SMulZeroClass.toHasSmul.{u1, u4} 𝕜 H (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u4} 𝕜 H (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.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u4} 𝕜 H (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u4} H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)))) (Module.toMulActionWithZero.{u1, u4} 𝕜 H (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _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_6))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) (α : Type.{u5}) (E : Type.{u3}) (H : Type.{u4}) {hom : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u4} H] [_inst_3 : Module.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : 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_4)] [_inst_6 : TopologicalSpace.{u4} H] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u5} (Set.{u5} α)} [_inst_10 : LinearMapClass.{u2, u1, u4, max u3 u5} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)], (Set.Nonempty.{u5} (Set.{u5} α) 𝔖) -> (DirectedOn.{u5} (Set.{u5} α) (fun (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1900 : Set.{u5} α) (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1902 : Set.{u5} α) => HasSubset.Subset.{u5} (Set.{u5} α) (Set.instHasSubsetSet.{u5} α) x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1900 x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.1902) 𝔖) -> (forall (φ : hom), (Inducing.{u4, max u5 u3} H (UniformOnFun.{u5, u3} α E 𝔖) _inst_6 (UniformOnFun.topologicalSpace.{u5, u3} α E _inst_7 𝔖) (FunLike.coe.{succ u2, succ u4, max (succ u5) (succ u3)} hom H (fun (_x : H) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : H) => UniformOnFun.{u5, u3} α E 𝔖) _x) (SMulHomClass.toFunLike.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (AddMonoid.toZero.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toZero.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribSMul.toSMulZeroClass.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u5 u3, u2} 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) hom (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10))) φ)) -> (forall (u : H) (s : Set.{u5} α), (Membership.mem.{u5, u5} (Set.{u5} α) (Set.{u5} (Set.{u5} α)) (Set.instMembershipSet.{u5} (Set.{u5} α)) s 𝔖) -> (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_4))))) (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_4))))) (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_4))))) (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_4) _inst_5)))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7) (Set.image.{u5, u3} α E (FunLike.coe.{succ u2, succ u4, max (succ u5) (succ u3)} hom H (fun (_x : H) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : H) => UniformOnFun.{u5, u3} α E 𝔖) _x) (SMulHomClass.toFunLike.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (AddMonoid.toZero.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u4} 𝕜 H (AddMonoid.toAddZeroClass.{u4} H (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2))) (DistribMulAction.toDistribSMul.{u1, u4} 𝕜 H (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toZero.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribSMul.toSMulZeroClass.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (DistribMulAction.toDistribSMul.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u4, max u5 u3} hom 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) (MonoidWithZero.toMonoid.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u4} H (AddCommGroup.toAddCommMonoid.{u4} H _inst_2)) (AddCommMonoid.toAddMonoid.{max u5 u3} (UniformOnFun.{u5, u3} α E 𝔖) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))) (Module.toDistribMulAction.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u5 u3} 𝕜 (UniformOnFun.{u5, u3} α E 𝔖) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SemilinearMapClass.distribMulActionHomClass.{u1, u4, max u5 u3, u2} 𝕜 H (UniformOnFun.{u5, u3} α E 𝔖) hom (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _inst_2) (instAddCommMonoidUniformOnFun.{u5, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) _inst_3 (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u5, u3, u1} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) _inst_10))) φ u) s))) -> (ContinuousSMul.{u1, u4} 𝕜 H (SMulZeroClass.toSMul.{u1, u4} 𝕜 H (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u4} 𝕜 H (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 𝕜 H (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} H (SubNegZeroMonoid.toNegZeroClass.{u4} H (SubtractionMonoid.toSubNegZeroMonoid.{u4} H (SubtractionCommMonoid.toSubtractionMonoid.{u4} H (AddCommGroup.toDivisionAddCommMonoid.{u4} H _inst_2))))) (Module.toMulActionWithZero.{u1, u4} 𝕜 H (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} H _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_6))
+Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_boundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `bornology.is_vonN_bounded`), then `H`,
@@ -244,6 +274,12 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
       rwa [Set.mem_inv_smul_set_iff₀ ha0] at this
 #align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_bounded
 
+/- warning: uniform_on_fun.has_continuous_smul_submodule_of_image_bounded -> UniformOnFun.continuousSMul_submodule_of_image_bounded is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) (α : Type.{u2}) (E : Type.{u3}) [_inst_1 : NormedField.{u1} 𝕜] [_inst_4 : AddCommGroup.{u3} E] [_inst_5 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)] [_inst_7 : UniformSpace.{u3} E] [_inst_8 : UniformAddGroup.{u3} E _inst_7 (AddCommGroup.toAddGroup.{u3} E _inst_4)] [_inst_9 : ContinuousSMul.{u1, u3} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (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)))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7)] {𝔖 : Set.{u2} (Set.{u2} α)}, (Set.Nonempty.{u2} (Set.{u2} α) 𝔖) -> (DirectedOn.{u2} (Set.{u2} α) (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α)) 𝔖) -> (forall (H : Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)), (forall (u : α -> E), (Membership.Mem.{max u2 u3, max u2 u3} (α -> E) (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (SetLike.hasMem.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) u H) -> (forall (s : Set.{u2} α), (Membership.Mem.{u2, u2} (Set.{u2} α) (Set.{u2} (Set.{u2} α)) (Set.hasMem.{u2} (Set.{u2} α)) s 𝔖) -> (Bornology.IsVonNBounded.{u1, u3} 𝕜 E (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (SubNegMonoid.toAddMonoid.{u3} E (AddGroup.toSubNegMonoid.{u3} E (AddCommGroup.toAddGroup.{u3} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u3} E _inst_7) (Set.image.{u2, u3} α E u s)))) -> (ContinuousSMul.{u1, max u2 u3} 𝕜 (coeSort.{succ (max u2 u3), succ (succ (max u2 u3))} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) Type.{max u2 u3} (SetLike.hasCoeToSort.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (Submodule.smul.{u1, u1, max u2 u3} 𝕜 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5) H (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (MulAction.toHasSmul.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (MulActionWithZero.toMulAction.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddMonoid.toAddZeroClass.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (AddCommMonoid.toAddMonoid.{max u2 u3} (UniformOnFun.{u2, u3} α E 𝔖) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 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(UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) H) (UniformOnFun.{u2, u3} α E 𝔖) (coeSubtype.{max (succ u2) (succ u3)} (UniformOnFun.{u2, u3} α E 𝔖) (fun (x : 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(Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5)) (UniformOnFun.{u2, u3} α E 𝔖) (Submodule.setLike.{u1, max u2 u3} 𝕜 (UniformOnFun.{u2, u3} α E 𝔖) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (UniformOnFun.addCommMonoid.{u2, u3} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u3} E _inst_4)) (UniformOnFun.module.{u2, u3, u1} α E 𝕜 𝔖 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} E _inst_4) _inst_5))) x H)))))) (UniformOnFun.topologicalSpace.{u2, u3} α E _inst_7 𝔖))))
+but is expected to have type
+  forall (𝕜 : Type.{u2}) (α : Type.{u3}) (E : Type.{u1}) [_inst_1 : NormedField.{u2} 𝕜] [_inst_4 : AddCommGroup.{u1} E] [_inst_5 : Module.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)] [_inst_7 : UniformSpace.{u1} E] [_inst_8 : UniformAddGroup.{u1} E _inst_7 (AddCommGroup.toAddGroup.{u1} E _inst_4)] [_inst_9 : ContinuousSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} E _inst_7)] {𝔖 : Set.{u3} (Set.{u3} α)}, (Set.Nonempty.{u3} (Set.{u3} α) 𝔖) -> (DirectedOn.{u3} (Set.{u3} α) (fun (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2968 : Set.{u3} α) (x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2970 : Set.{u3} α) => HasSubset.Subset.{u3} (Set.{u3} α) (Set.instHasSubsetSet.{u3} α) x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2968 x._@.Mathlib.Topology.Algebra.UniformConvergence._hyg.2970) 𝔖) -> (forall (H : Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)), (forall (u : UniformOnFun.{u3, u1} α E 𝔖), (Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) u H) -> (forall (s : Set.{u3} α), (Membership.mem.{u3, u3} (Set.{u3} α) (Set.{u3} (Set.{u3} α)) (Set.instMembershipSet.{u3} (Set.{u3} α)) s 𝔖) -> (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_4))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_4))))) (UniformSpace.toTopologicalSpace.{u1} E _inst_7) (Set.image.{u3, u1} α E u s)))) -> (ContinuousSMul.{u2, max u3 u1} 𝕜 (Subtype.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) x H)) (Submodule.smul.{u2, u2, max u3 u1} 𝕜 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5) H (Algebra.toSMul.{u2, u2} 𝕜 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u2, u2} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1))) (NormedAlgebra.id.{u2} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (Module.toMulActionWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) (IsScalarTower.left.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubNegZeroMonoid.toNegZeroClass.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionMonoid.toSubNegZeroMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (SubtractionCommMonoid.toSubtractionMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (instAddCommGroupUniformOnFun.{u3, u1} α E 𝔖 _inst_4)))))) (Module.toMulActionWithZero.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))))) (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 _inst_1)))))) (TopologicalSpace.induced.{max u3 u1, max u3 u1} (Subtype.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (SetLike.instMembership.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5))) x H)) (UniformOnFun.{u3, u1} α E 𝔖) (Subtype.val.{succ (max u3 u1)} (UniformOnFun.{u3, u1} α E 𝔖) (fun (x : UniformOnFun.{u3, u1} α E 𝔖) => Membership.mem.{max u3 u1, max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖) (Set.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖)) (Set.instMembershipSet.{max u3 u1} (UniformOnFun.{u3, u1} α E 𝔖)) x (SetLike.coe.{max u3 u1, max u3 u1} (Submodule.{u2, max u1 u3} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) (UniformOnFun.{u3, u1} α E 𝔖) (Submodule.setLike.{u2, max u3 u1} 𝕜 (UniformOnFun.{u3, u1} α E 𝔖) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (instAddCommMonoidUniformOnFun.{u3, u1} α E 𝔖 (AddCommGroup.toAddCommMonoid.{u1} E _inst_4)) (instModuleUniformOnFunInstAddCommMonoidUniformOnFun.{u3, u1, u2} α E 𝕜 𝔖 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_4) _inst_5)) H))) (UniformOnFun.topologicalSpace.{u3, u1} α E _inst_7 𝔖))))
+Case conversion may be inaccurate. Consider using '#align uniform_on_fun.has_continuous_smul_submodule_of_image_bounded UniformOnFun.continuousSMul_submodule_of_image_boundedₓ'. -/
 /-- Let `E` be a TVS, `𝔖 : set (set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `bornology.is_vonN_bounded`), then `H`,
 equipped with the topology of `𝔖`-convergence, is a TVS.

f2ce6086

bump to nightly-2023-02-21-22

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

d36dd541

Diff

@@ -202,7 +202,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
   by
   have : TopologicalAddGroup H := by
     rw [hφ.induced]
-    exact topological_add_group_induced φ
+    exact topologicalAddGroup_induced φ
   have : (𝓝 0 : Filter H).HasBasis _ _ :=
     by
     rw [hφ.induced, nhds_induced, map_zero]
@@ -254,7 +254,7 @@ theorem UniformOnFun.continuousSMul_submodule_of_image_bounded (h𝔖₁ : 𝔖.
     (h : ∀ u ∈ H, ∀ s ∈ 𝔖, Bornology.IsVonNBounded 𝕜 (u '' s)) :
     @ContinuousSMul 𝕜 H _ _ ((UniformOnFun.topologicalSpace α E 𝔖).induced (coe : H → α →ᵤ[𝔖] E)) :=
   haveI : TopologicalAddGroup H :=
-    topological_add_group_induced (linear_map.id.dom_restrict H : H →ₗ[𝕜] α → E)
+    topologicalAddGroup_induced (linear_map.id.dom_restrict H : H →ₗ[𝕜] α → E)
   UniformOnFun.continuousSMul_induced_of_image_bounded 𝕜 α E H h𝔖₁ h𝔖₂
     (linear_map.id.dom_restrict H : H →ₗ[𝕜] α → E) inducing_subtype_val fun ⟨u, hu⟩ => h u hu
 #align uniform_on_fun.has_continuous_smul_submodule_of_image_bounded UniformOnFun.continuousSMul_submodule_of_image_bounded

f2ce6086

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f2ce6086

feat(Algebra/UniformConvergence): drop unneeded assumptions (#10321)

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

faecefeb

Diff

@@ -32,13 +32,6 @@ Like in `Topology/UniformSpace/UniformConvergenceTopology`, we use the type alia
 `UniformFun` (denoted `α →ᵤ β`) and `UniformOnFun` (denoted `α →ᵤ[𝔖] β`) for functions from `α`
 to `β` endowed with the structures of uniform convergence and `𝔖`-convergence.
 
-## TODO
-
-* `UniformOnFun.continuousSMul_induced_of_image_bounded` unnecessarily asks for `𝔖` to be
-  nonempty and directed. This will be easy to solve once we know that replacing `𝔖` by its
-  ***noncovering*** bornology (i.e ***not*** what `Bornology` currently refers to in mathlib)
-  doesn't change the topology.
-
 ## References
 
 * [N. Bourbaki, *General Topology, Chapter X*][bourbaki1966]
@@ -51,7 +44,8 @@ uniform convergence, strong dual
 -/
 
 open Filter
-open scoped Topology Pointwise UniformConvergence
+
+open scoped Topology Pointwise UniformConvergence Uniformity
 
 section AlgebraicInstances
 
@@ -313,7 +307,41 @@ section Module
 variable (𝕜 α E H : Type*) {hom : Type*} [NormedField 𝕜] [AddCommGroup H] [Module 𝕜 H]
   [AddCommGroup E] [Module 𝕜 E] [TopologicalSpace H] [UniformSpace E] [UniformAddGroup E]
   [ContinuousSMul 𝕜 E] {𝔖 : Set <| Set α}
-  [FunLike hom H (α →ᵤ[𝔖] E)] [LinearMapClass hom 𝕜 H (α →ᵤ[𝔖] E)]
+  [FunLike hom H (α → E)] [LinearMapClass hom 𝕜 H (α → E)]
+
+/-- Let `E` be a topological vector space over a normed field `𝕜`, let `α` be any type.
+Let `H` be a submodule of `α →ᵤ E` such that the range of each `f ∈ H` is von Neumann bounded.
+Then `H` is a topological vector space over `𝕜`,
+i.e., the pointwise scalar multiplication is continuous in both variables.
+
+For convenience we require that `H` is a vector space over `𝕜`
+with a topology induced by `UniformFun.ofFun ∘ φ`, where `φ : H →ₗ[𝕜] (α → E)`. -/
+lemma UniformFun.continuousSMul_induced_of_range_bounded (φ : hom)
+    (hφ : Inducing (ofFun ∘ φ)) (h : ∀ u : H, Bornology.IsVonNBounded 𝕜 (Set.range (φ u))) :
+    ContinuousSMul 𝕜 H := by
+  have : TopologicalAddGroup H :=
+    let ofFun' : (α → E) →+ (α →ᵤ E) := AddMonoidHom.id _
+    Inducing.topologicalAddGroup (ofFun'.comp (φ : H →+ (α → E))) hφ
+  have hb : (𝓝 (0 : H)).HasBasis (· ∈ 𝓝 (0 : E)) fun V ↦ {u | ∀ x, φ u x ∈ V} := by
+    simp only [hφ.nhds_eq_comap, Function.comp_apply, map_zero]
+    exact UniformFun.hasBasis_nhds_zero.comap _
+  apply ContinuousSMul.of_basis_zero hb
+  · intro U hU
+    have : Tendsto (fun x : 𝕜 × E ↦ x.1 • x.2) (𝓝 0) (𝓝 0) :=
+      continuous_smul.tendsto' _ _ (zero_smul _ _)
+    rcases ((Filter.basis_sets _).prod_nhds (Filter.basis_sets _)).tendsto_left_iff.1 this U hU
+      with ⟨⟨V, W⟩, ⟨hV, hW⟩, hVW⟩
+    refine ⟨V, hV, W, hW, Set.smul_subset_iff.2 fun a ha u hu x ↦ ?_⟩
+    rw [map_smul]
+    exact hVW (Set.mk_mem_prod ha (hu x))
+  · intro c U hU
+    have : Tendsto (c • · : E → E) (𝓝 0) (𝓝 0) :=
+      (continuous_const_smul c).tendsto' _ _ (smul_zero _)
+    refine ⟨_, this hU, fun u hu x ↦ ?_⟩
+    simpa only [map_smul] using hu x
+  · intro u U hU
+    simp only [Set.mem_setOf_eq, map_smul, Pi.smul_apply]
+    simpa only [Set.mapsTo_range_iff] using (h u hU).eventually_nhds_zero (mem_of_mem_nhds hU)
 
 /-- Let `E` be a TVS, `𝔖 : Set (Set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `Bornology.IsVonNBounded`), then `H`,
@@ -323,50 +351,20 @@ For convenience, we don't literally ask for `H : Submodule (α →ᵤ[𝔖] E)`.
 result for any vector space `H` equipped with a linear inducing to `α →ᵤ[𝔖] E`, which is often
 easier to use. We also state the `Submodule` version as
 `UniformOnFun.continuousSMul_submodule_of_image_bounded`. -/
-theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.Nonempty)
-    (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) (φ : hom) (hφ : Inducing φ)
+theorem UniformOnFun.continuousSMul_induced_of_image_bounded (φ : hom) (hφ : Inducing (ofFun 𝔖 ∘ φ))
     (h : ∀ u : H, ∀ s ∈ 𝔖, Bornology.IsVonNBounded 𝕜 ((φ u : α → E) '' s)) :
     ContinuousSMul 𝕜 H := by
-  have : TopologicalAddGroup H := by
-    rw [hφ.induced]
-    exact topologicalAddGroup_induced φ
-  have : (𝓝 0 : Filter H).HasBasis _ _ := by
-    rw [hφ.induced, nhds_induced, map_zero]
-    exact (UniformOnFun.hasBasis_nhds_zero 𝔖 h𝔖₁ h𝔖₂).comap φ
-  refine' ContinuousSMul.of_basis_zero this _ _ _
-  · rintro ⟨S, V⟩ ⟨hS, hV⟩
-    have : Tendsto (fun kx : 𝕜 × E => kx.1 • kx.2) (𝓝 (0, 0)) (𝓝 <| (0 : 𝕜) • (0 : E)) :=
-      continuous_smul.tendsto (0 : 𝕜 × E)
-    rw [zero_smul, nhds_prod_eq] at this
-    have := this hV
-    rw [mem_map, mem_prod_iff] at this
-    rcases this with ⟨U, hU, W, hW, hUW⟩
-    refine' ⟨U, hU, ⟨S, W⟩, ⟨hS, hW⟩, _⟩
-    rw [Set.smul_subset_iff]
-    intro a ha u hu x hx
-    rw [map_smul]
-    exact hUW (⟨ha, hu x hx⟩ : (a, φ u x) ∈ U ×ˢ W)
-  · rintro a ⟨S, V⟩ ⟨hS, hV⟩
-    have : Tendsto (fun x : E => a • x) (𝓝 0) (𝓝 <| a • (0 : E)) := tendsto_id.const_smul a
-    rw [smul_zero] at this
-    refine' ⟨⟨S, (a • ·) ⁻¹' V⟩, ⟨hS, this hV⟩, fun f hf x hx => _⟩
-    rw [map_smul]
-    exact hf x hx
-  · rintro u ⟨S, V⟩ ⟨hS, hV⟩
-    rcases (h u S hS hV).exists_pos with ⟨r, hrpos, hr⟩
-    rw [Metric.eventually_nhds_iff_ball]
-    refine' ⟨r⁻¹, inv_pos.mpr hrpos, fun a ha x hx => _⟩
-    by_cases ha0 : a = 0
-    · rw [ha0]
-      simpa using mem_of_mem_nhds hV
-    · rw [mem_ball_zero_iff] at ha
-      rw [map_smul, Pi.smul_apply]
-      have : φ u x ∈ a⁻¹ • V := by
-        have ha0 : 0 < ‖a‖ := norm_pos_iff.mpr ha0
-        refine' (hr a⁻¹ _) (Set.mem_image_of_mem (φ u) hx)
-        rw [norm_inv, le_inv hrpos ha0]
-        exact ha.le
-      rwa [Set.mem_inv_smul_set_iff₀ ha0] at this
+  obtain rfl := hφ.induced; clear hφ
+  simp only [induced_iInf, UniformOnFun.topologicalSpace_eq, induced_compose]
+  refine continuousSMul_iInf fun s ↦ continuousSMul_iInf fun hs ↦ ?_
+  letI : TopologicalSpace H :=
+    .induced (UniformFun.ofFun ∘ s.restrict ∘ φ) (UniformFun.topologicalSpace s E)
+  set φ' : H →ₗ[𝕜] (s → E) :=
+    { toFun := s.restrict ∘ φ,
+      map_smul' := fun c x ↦ by exact congr_arg s.restrict (map_smul φ c x),
+      map_add' := fun x y ↦ by exact congr_arg s.restrict (map_add φ x y) }
+  refine UniformFun.continuousSMul_induced_of_range_bounded 𝕜 s E H φ' ⟨rfl⟩ fun u ↦ ?_
+  simpa only [Set.image_eq_range] using h u s hs
 #align uniform_on_fun.has_continuous_smul_induced_of_image_bounded UniformOnFun.continuousSMul_induced_of_image_bounded
 
 /-- Let `E` be a TVS, `𝔖 : Set (Set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
@@ -374,13 +372,10 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
 equipped with the topology of `𝔖`-convergence, is a TVS.
 
 If you have a hard time using this lemma, try the one above instead. -/
-theorem UniformOnFun.continuousSMul_submodule_of_image_bounded (h𝔖₁ : 𝔖.Nonempty)
-    (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) (H : Submodule 𝕜 (α →ᵤ[𝔖] E))
+theorem UniformOnFun.continuousSMul_submodule_of_image_bounded (H : Submodule 𝕜 (α →ᵤ[𝔖] E))
     (h : ∀ u ∈ H, ∀ s ∈ 𝔖, Bornology.IsVonNBounded 𝕜 (u '' s)) :
     @ContinuousSMul 𝕜 H _ _ ((UniformOnFun.topologicalSpace α E 𝔖).induced ((↑) : H → α →ᵤ[𝔖] E)) :=
-  haveI : TopologicalAddGroup H :=
-    topologicalAddGroup_induced (LinearMap.id.domRestrict H : H →ₗ[𝕜] α → E)
-  UniformOnFun.continuousSMul_induced_of_image_bounded 𝕜 α E H h𝔖₁ h𝔖₂
+  UniformOnFun.continuousSMul_induced_of_image_bounded 𝕜 α E H
     (LinearMap.id.domRestrict H : H →ₗ[𝕜] α → E) inducing_subtype_val fun ⟨u, hu⟩ => h u hu
 #align uniform_on_fun.has_continuous_smul_submodule_of_image_bounded UniformOnFun.continuousSMul_submodule_of_image_bounded

f2ce6086

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -312,7 +312,8 @@ section Module
 
 variable (𝕜 α E H : Type*) {hom : Type*} [NormedField 𝕜] [AddCommGroup H] [Module 𝕜 H]
   [AddCommGroup E] [Module 𝕜 E] [TopologicalSpace H] [UniformSpace E] [UniformAddGroup E]
-  [ContinuousSMul 𝕜 E] {𝔖 : Set <| Set α} [LinearMapClass hom 𝕜 H (α →ᵤ[𝔖] E)]
+  [ContinuousSMul 𝕜 E] {𝔖 : Set <| Set α}
+  [FunLike hom H (α →ᵤ[𝔖] E)] [LinearMapClass hom 𝕜 H (α →ᵤ[𝔖] E)]
 
 /-- Let `E` be a TVS, `𝔖 : Set (Set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `Bornology.IsVonNBounded`), then `H`,

f2ce6086

refactor: redefine Absorbs (#9676)

Redefine Absorbs and Absorbent in terms of the cobounded filter.

8bb0d697

Diff

@@ -352,7 +352,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
     rw [map_smul]
     exact hf x hx
   · rintro u ⟨S, V⟩ ⟨hS, hV⟩
-    rcases h u S hS hV with ⟨r, hrpos, hr⟩
+    rcases (h u S hS hV).exists_pos with ⟨r, hrpos, hr⟩
     rw [Metric.eventually_nhds_iff_ball]
     refine' ⟨r⁻¹, inv_pos.mpr hrpos, fun a ha x hx => _⟩
     by_cases ha0 : a = 0

f2ce6086

feat: action on UniformOnFun is uniformly continuous (#9714)

add UniformInducing.uniformContinuousConstSMul and its additive version;
use it to prove that the pointwise actions on α →ᵤ X and α →ᵤ[𝔖] X are uniformly continuous;
use the latter facts to prove that the pointwise action on E →SL[σ] F is uniformly continuous;
make M explicit in ContinuousLinearMap.strongTopology.continuousConstSMul, drop unneeded arguments.

6dd549bf

Diff

@@ -292,6 +292,22 @@ protected theorem UniformOnFun.hasBasis_nhds_one (𝔖 : Set <| Set α) (h𝔖
 
 end Group
 
+section ConstSMul
+
+variable (M α X : Type*) [SMul M X] [UniformSpace X] [UniformContinuousConstSMul M X]
+
+instance UniformFun.uniformContinuousConstSMul :
+    UniformContinuousConstSMul M (α →ᵤ X) where
+  uniformContinuous_const_smul c := UniformFun.postcomp_uniformContinuous <|
+    uniformContinuous_const_smul c
+
+instance UniformFunOn.uniformContinuousConstSMul {𝔖 : Set (Set α)} :
+    UniformContinuousConstSMul M (α →ᵤ[𝔖] X) where
+  uniformContinuous_const_smul c := UniformOnFun.postcomp_uniformContinuous <|
+    uniformContinuous_const_smul c
+
+end ConstSMul
+
 section Module
 
 variable (𝕜 α E H : Type*) {hom : Type*} [NormedField 𝕜] [AddCommGroup H] [Module 𝕜 H]

f2ce6086

chore(UniformConvergenceTopology): use variable, fix types (#9132)

Use variable.
Add toFun/ofFun to abuse the definitional equality less often.
Review instances in Topology.Algebra.UniformConvergence.
Replace *_apply lemmas with toFun_*/ofFun_* lemmas.

56ce93a6

Diff

@@ -50,16 +50,80 @@ uniform convergence, strong dual
 
 -/
 
-set_option autoImplicit true
+open Filter
+open scoped Topology Pointwise UniformConvergence
 
+section AlgebraicInstances
 
-open Filter
+variable {α β ι R : Type*} {𝔖 : Set <| Set α} {x : α}
 
-open Topology Pointwise UniformConvergence
+@[to_additive] instance [One β] : One (α →ᵤ β) := Pi.instOne
 
-section AlgebraicInstances
+@[to_additive (attr := simp)]
+lemma UniformFun.toFun_one [One β] : toFun (1 : α →ᵤ β) = 1 := rfl
+
+@[to_additive (attr := simp)]
+lemma UniformFun.ofFun_one [One β] : ofFun (1 : α → β) = 1 := rfl
+
+@[to_additive] instance [One β] : One (α →ᵤ[𝔖] β) := Pi.instOne
+
+@[to_additive (attr := simp)]
+lemma UniformOnFun.toFun_one [One β] : toFun 𝔖 (1 : α →ᵤ[𝔖] β) = 1 := rfl
+
+@[to_additive (attr := simp)]
+lemma UniformOnFun.one_apply [One β] : ofFun 𝔖 (1 : α → β) = 1 := rfl
+
+@[to_additive] instance [Mul β] : Mul (α →ᵤ β) := Pi.instMul
+
+@[to_additive (attr := simp)]
+lemma UniformFun.toFun_mul [Mul β] (f g : α →ᵤ β) : toFun (f * g) = toFun f * toFun g := rfl
+
+@[to_additive (attr := simp)]
+lemma UniformFun.ofFun_mul [Mul β] (f g : α → β) : ofFun (f * g) = ofFun f * ofFun g := rfl
+
+@[to_additive] instance [Mul β] : Mul (α →ᵤ[𝔖] β) := Pi.instMul
+
+@[to_additive (attr := simp)]
+lemma UniformOnFun.toFun_mul [Mul β] (f g : α →ᵤ[𝔖] β) :
+    toFun 𝔖 (f * g) = toFun 𝔖 f * toFun 𝔖 g :=
+  rfl
+
+@[to_additive (attr := simp)]
+lemma UniformOnFun.ofFun_mul [Mul β] (f g : α → β) : ofFun 𝔖 (f * g) = ofFun 𝔖 f * ofFun 𝔖 g := rfl
+
+@[to_additive] instance [Inv β] : Inv (α →ᵤ β) := Pi.instInv
+
+@[to_additive (attr := simp)]
+lemma UniformFun.toFun_inv [Inv β] (f : α →ᵤ β) : toFun (f⁻¹) = (toFun f)⁻¹ := rfl
+
+@[to_additive (attr := simp)]
+lemma UniformFun.ofFun_inv [Inv β] (f : α → β) : ofFun (f⁻¹) = (ofFun f)⁻¹ := rfl
+
+@[to_additive] instance [Inv β] : Inv (α →ᵤ[𝔖] β) := Pi.instInv
+
+@[to_additive (attr := simp)]
+lemma UniformOnFun.toFun_inv [Inv β] (f : α →ᵤ[𝔖] β) : toFun 𝔖 (f⁻¹) = (toFun 𝔖 f)⁻¹ := rfl
+
+@[to_additive (attr := simp)]
+lemma UniformOnFun.ofFun_inv [Inv β] (f : α → β) : ofFun 𝔖 (f⁻¹) = (ofFun 𝔖 f)⁻¹ := rfl
 
-variable {α β ι R : Type*} {𝔖 : Set <| Set α}
+@[to_additive] instance [Div β] : Div (α →ᵤ β) := Pi.instDiv
+
+@[to_additive (attr := simp)]
+lemma UniformFun.toFun_div [Div β] (f g : α →ᵤ β) : toFun (f / g) = toFun f / toFun g := rfl
+
+@[to_additive (attr := simp)]
+lemma UniformFun.ofFun_div [Div β] (f g : α → β) : ofFun (f / g) = ofFun f / ofFun g := rfl
+
+@[to_additive] instance [Div β] : Div (α →ᵤ[𝔖] β) := Pi.instDiv
+
+@[to_additive (attr := simp)]
+lemma UniformOnFun.toFun_div [Div β] (f g : α →ᵤ[𝔖] β) :
+    toFun 𝔖 (f / g) = toFun 𝔖 f / toFun 𝔖 g :=
+  rfl
+
+@[to_additive (attr := simp)]
+lemma UniformOnFun.ofFun_div [Div β] (f g : α → β) : ofFun 𝔖 (f / g) = ofFun 𝔖 f / ofFun 𝔖 g := rfl
 
 @[to_additive]
 instance [Monoid β] : Monoid (α →ᵤ β) :=
@@ -93,37 +157,63 @@ instance [CommGroup β] : CommGroup (α →ᵤ β) :=
 instance [CommGroup β] : CommGroup (α →ᵤ[𝔖] β) :=
   Pi.commGroup
 
-instance [Semiring R] [AddCommMonoid β] [Module R β] : Module R (α →ᵤ β) :=
-  Pi.module _ _ _
+instance {M : Type*} [SMul M β] : SMul M (α →ᵤ β) := Pi.instSMul
 
-instance [Semiring R] [AddCommMonoid β] [Module R β] : Module R (α →ᵤ[𝔖] β) :=
-  Pi.module _ _ _
+@[simp]
+lemma UniformFun.toFun_smul {M : Type*} [SMul M β] (c : M) (f : α →ᵤ β) :
+    toFun (c • f) = c • toFun f :=
+  rfl
 
--- Porting note: unfortunately `simp` will no longer use `Pi.one_apply` etc.
--- on `α →ᵤ β` or `α →ᵤ[𝔖] β`, so we restate some of these here. More may be needed later.
-@[to_additive (attr := simp)]
-lemma UniformFun.one_apply [Monoid β] : (1 : α →ᵤ β) x = 1 := Pi.one_apply x
+@[simp]
+lemma UniformFun.ofFun_smul {M : Type*} [SMul M β] (c : M) (f : α → β) :
+    ofFun (c • f) = c • ofFun f :=
+  rfl
 
-@[to_additive (attr := simp)]
-lemma UniformOnFun.one_apply [Monoid β] : (1 : α →ᵤ[𝔖] β) x = 1 := Pi.one_apply x
+instance {M : Type*} [SMul M β] : SMul M (α →ᵤ[𝔖] β) := Pi.instSMul
 
-@[to_additive (attr := simp)]
-lemma UniformFun.mul_apply [Monoid β] : (f * g : α →ᵤ β) x = f x * g x := Pi.mul_apply f g x
+@[simp]
+lemma UniformOnFun.toFun_smul {M : Type*} [SMul M β] (c : M) (f : α →ᵤ[𝔖] β) :
+    toFun 𝔖 (c • f) = c • toFun 𝔖 f :=
+  rfl
 
-@[to_additive (attr := simp)]
-lemma UniformOnFun.mul_apply [Monoid β] : (f * g : α →ᵤ[𝔖] β) x = f x * g x := Pi.mul_apply f g x
+@[simp]
+lemma UniformOnFun.ofFun_smul {M : Type*} [SMul M β] (c : M) (f : α → β) :
+    ofFun 𝔖 (c • f) = c • ofFun 𝔖 f :=
+  rfl
 
-@[to_additive (attr := simp)]
-lemma UniformFun.inv_apply [Group β] : (f : α →ᵤ β)⁻¹ x = (f x)⁻¹ := Pi.inv_apply f x
+instance {M N : Type*} [SMul M N] [SMul M β] [SMul N β] [IsScalarTower M N β] :
+    IsScalarTower M N (α →ᵤ β) :=
+  Pi.isScalarTower
 
-@[to_additive (attr := simp)]
-lemma UniformOnFun.inv_apply [Group β] : (f : α →ᵤ[𝔖] β)⁻¹ x = (f x)⁻¹ := Pi.inv_apply f x
+instance {M N : Type*} [SMul M N] [SMul M β] [SMul N β] [IsScalarTower M N β] :
+    IsScalarTower M N (α →ᵤ[𝔖] β) :=
+  Pi.isScalarTower
 
-@[to_additive (attr := simp)]
-lemma UniformFun.div_apply [Group β] : (f / g : α →ᵤ β) x = f x / g x := Pi.div_apply f g x
+instance {M N : Type*} [SMul M β] [SMul N β] [SMulCommClass M N β] :
+    SMulCommClass M N (α →ᵤ β) :=
+  Pi.smulCommClass
 
-@[to_additive (attr := simp)]
-lemma UniformOnFun.div_apply [Group β] : (f / g : α →ᵤ[𝔖] β) x = f x / g x := Pi.div_apply f g x
+instance {M N : Type*} [SMul M β] [SMul N β] [SMulCommClass M N β] :
+    SMulCommClass M N (α →ᵤ[𝔖] β) :=
+  Pi.smulCommClass
+
+instance {M : Type*} [Monoid M] [MulAction M β] : MulAction M (α →ᵤ β) := Pi.mulAction _
+
+instance {M : Type*} [Monoid M] [MulAction M β] : MulAction M (α →ᵤ[𝔖] β) := Pi.mulAction _
+
+instance {M : Type*} [Monoid M] [AddMonoid β] [DistribMulAction M β] :
+    DistribMulAction M (α →ᵤ β) :=
+  Pi.distribMulAction _
+
+instance {M : Type*} [Monoid M] [AddMonoid β] [DistribMulAction M β] :
+    DistribMulAction M (α →ᵤ[𝔖] β) :=
+  Pi.distribMulAction _
+
+instance [Semiring R] [AddCommMonoid β] [Module R β] : Module R (α →ᵤ β) :=
+  Pi.module _ _ _
+
+instance [Semiring R] [AddCommMonoid β] [Module R β] : Module R (α →ᵤ[𝔖] β) :=
+  Pi.module _ _ _
 
 end AlgebraicInstances
 
@@ -146,12 +236,12 @@ instance : UniformGroup (α →ᵤ G) :=
 @[to_additive]
 protected theorem UniformFun.hasBasis_nhds_one_of_basis {p : ι → Prop} {b : ι → Set G}
     (h : (𝓝 1 : Filter G).HasBasis p b) :
-    (𝓝 1 : Filter (α →ᵤ G)).HasBasis p fun i => { f : α →ᵤ G | ∀ x, f x ∈ b i } := by
+    (𝓝 1 : Filter (α →ᵤ G)).HasBasis p fun i => { f : α →ᵤ G | ∀ x, toFun f x ∈ b i } := by
   have := h.comap fun p : G × G => p.2 / p.1
   rw [← uniformity_eq_comap_nhds_one] at this
   convert UniformFun.hasBasis_nhds_of_basis α _ (1 : α →ᵤ G) this
   -- Porting note: removed `ext i f` here, as it has already been done by `convert`.
-  simp [UniformFun.gen]
+  simp
 #align uniform_fun.has_basis_nhds_one_of_basis UniformFun.hasBasis_nhds_one_of_basis
 #align uniform_fun.has_basis_nhds_zero_of_basis UniformFun.hasBasis_nhds_zero_of_basis
 
@@ -181,7 +271,7 @@ protected theorem UniformOnFun.hasBasis_nhds_one_of_basis (𝔖 : Set <| Set α)
     (h𝔖₂ : DirectedOn (· ⊆ ·) 𝔖) {p : ι → Prop} {b : ι → Set G}
     (h : (𝓝 1 : Filter G).HasBasis p b) :
     (𝓝 1 : Filter (α →ᵤ[𝔖] G)).HasBasis (fun Si : Set α × ι => Si.1 ∈ 𝔖 ∧ p Si.2) fun Si =>
-      { f : α →ᵤ[𝔖] G | ∀ x ∈ Si.1, f x ∈ b Si.2 } := by
+      { f : α →ᵤ[𝔖] G | ∀ x ∈ Si.1, toFun 𝔖 f x ∈ b Si.2 } := by
   have := h.comap fun p : G × G => p.1 / p.2
   rw [← uniformity_eq_comap_nhds_one_swapped] at this
   convert UniformOnFun.hasBasis_nhds_of_basis α _ 𝔖 (1 : α →ᵤ[𝔖] G) h𝔖₁ h𝔖₂ this

f2ce6086

chore(Order/Filter): protect Filter.map_smul (#8935)

We use SMulHomClass.map_smul much more often, even when the Filter namespace is opened.

06295115

Diff

@@ -237,13 +237,13 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
     refine' ⟨U, hU, ⟨S, W⟩, ⟨hS, hW⟩, _⟩
     rw [Set.smul_subset_iff]
     intro a ha u hu x hx
-    rw [SMulHomClass.map_smul]
+    rw [map_smul]
     exact hUW (⟨ha, hu x hx⟩ : (a, φ u x) ∈ U ×ˢ W)
   · rintro a ⟨S, V⟩ ⟨hS, hV⟩
     have : Tendsto (fun x : E => a • x) (𝓝 0) (𝓝 <| a • (0 : E)) := tendsto_id.const_smul a
     rw [smul_zero] at this
     refine' ⟨⟨S, (a • ·) ⁻¹' V⟩, ⟨hS, this hV⟩, fun f hf x hx => _⟩
-    rw [SMulHomClass.map_smul]
+    rw [map_smul]
     exact hf x hx
   · rintro u ⟨S, V⟩ ⟨hS, hV⟩
     rcases h u S hS hV with ⟨r, hrpos, hr⟩
@@ -253,7 +253,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
     · rw [ha0]
       simpa using mem_of_mem_nhds hV
     · rw [mem_ball_zero_iff] at ha
-      rw [SMulHomClass.map_smul, Pi.smul_apply]
+      rw [map_smul, Pi.smul_apply]
       have : φ u x ∈ a⁻¹ • V := by
         have ha0 : 0 < ‖a‖ := norm_pos_iff.mpr ha0
         refine' (hr a⁻¹ _) (Set.mem_image_of_mem (φ u) hx)

f2ce6086

fix: disable autoImplicit globally (#6528)

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

Assuming variables are in scope, but pasting the lemma in the wrong section
Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

0c24f831

Diff

@@ -50,6 +50,8 @@ uniform convergence, strong dual
 
 -/
 
+set_option autoImplicit true
+
 
 open Filter

f2ce6086

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -57,7 +57,7 @@ open Topology Pointwise UniformConvergence
 
 section AlgebraicInstances
 
-variable {α β ι R : Type _} {𝔖 : Set <| Set α}
+variable {α β ι R : Type*} {𝔖 : Set <| Set α}
 
 @[to_additive]
 instance [Monoid β] : Monoid (α →ᵤ β) :=
@@ -127,7 +127,7 @@ end AlgebraicInstances
 
 section Group
 
-variable {α G ι : Type _} [Group G] {𝔖 : Set <| Set α} [UniformSpace G] [UniformGroup G]
+variable {α G ι : Type*} [Group G] {𝔖 : Set <| Set α} [UniformSpace G] [UniformGroup G]
 
 /-- If `G` is a uniform group, then `α →ᵤ G` is a uniform group as well. -/
 @[to_additive "If `G` is a uniform additive group,
@@ -202,7 +202,7 @@ end Group
 
 section Module
 
-variable (𝕜 α E H : Type _) {hom : Type _} [NormedField 𝕜] [AddCommGroup H] [Module 𝕜 H]
+variable (𝕜 α E H : Type*) {hom : Type*} [NormedField 𝕜] [AddCommGroup H] [Module 𝕜 H]
   [AddCommGroup E] [Module 𝕜 E] [TopologicalSpace H] [UniformSpace E] [UniformAddGroup E]
   [ContinuousSMul 𝕜 E] {𝔖 : Set <| Set α} [LinearMapClass hom 𝕜 H (α →ᵤ[𝔖] E)]

f2ce6086

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anatole Dedecker
-
-! This file was ported from Lean 3 source module topology.algebra.uniform_convergence
-! 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.Topology.UniformSpace.UniformConvergenceTopology
 import Mathlib.Analysis.LocallyConvex.Bounded
 import Mathlib.Topology.Algebra.FilterBasis
 
+#align_import topology.algebra.uniform_convergence from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Algebraic facts about the topology of uniform convergence

f2ce6086

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

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>

a6e1045f

Diff

@@ -209,10 +209,6 @@ variable (𝕜 α E H : Type _) {hom : Type _} [NormedField 𝕜] [AddCommGroup
   [AddCommGroup E] [Module 𝕜 E] [TopologicalSpace H] [UniformSpace E] [UniformAddGroup E]
   [ContinuousSMul 𝕜 E] {𝔖 : Set <| Set α} [LinearMapClass hom 𝕜 H (α →ᵤ[𝔖] E)]
 
--- Porting note:
--- This is another alarming location where we need to use
--- `eta_experiment%` to elaborate a particular subterm, but having `synthInstance.etaExperiment`
--- on for the whole declaration breaks other typeclass search.
 /-- Let `E` be a TVS, `𝔖 : Set (Set α)` and `H` a submodule of `α →ᵤ[𝔖] E`. If the image of any
 `S ∈ 𝔖` by any `u ∈ H` is bounded (in the sense of `Bornology.IsVonNBounded`), then `H`,
 equipped with the topology of `𝔖`-convergence, is a TVS.
@@ -231,7 +227,7 @@ theorem UniformOnFun.continuousSMul_induced_of_image_bounded (h𝔖₁ : 𝔖.No
   have : (𝓝 0 : Filter H).HasBasis _ _ := by
     rw [hφ.induced, nhds_induced, map_zero]
     exact (UniformOnFun.hasBasis_nhds_zero 𝔖 h𝔖₁ h𝔖₂).comap φ
-  refine' eta_experiment% ContinuousSMul.of_basis_zero this _ _ _
+  refine' ContinuousSMul.of_basis_zero this _ _ _
   · rintro ⟨S, V⟩ ⟨hS, hV⟩
     have : Tendsto (fun kx : 𝕜 × E => kx.1 • kx.2) (𝓝 (0, 0)) (𝓝 <| (0 : 𝕜) • (0 : E)) :=
       continuous_smul.tendsto (0 : 𝕜 × E)

f2ce6086

feat: port Topology.Algebra.UniformConvergence (#3664)

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

4f8d8faf

`topology.algebra.uniform_convergence` ⟷ `Mathlib.Topology.Algebra.UniformConvergence`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 629

topology.algebra.uniform_convergence ⟷ Mathlib.Topology.Algebra.UniformConvergence

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 629

`topology.algebra.uniform_convergence` ⟷ `Mathlib.Topology.Algebra.UniformConvergence`

`simp` not firing sometimes